| Type: | Package |
| Title: | Statistics for Matrix Distributions |
| Version: | 1.1.9 |
| Date: | 2023-08-01 |
| Maintainer: | Martin Bladt <martinbladt@gmail.com> |
| URL: | https://github.com/martinbladt/matrixdist_1.0 |
| BugReports: | https://github.com/martinbladt/matrixdist_1.0/issues |
| Description: | Tools for phase-type distributions including the following variants: continuous, discrete, multivariate, in-homogeneous, right-censored, and regression. Methods for functional evaluation, simulation and estimation using the expectation-maximization (EM) algorithm are provided for all models. The methods of this package are based on the following references. Asmussen, S., Nerman, O., & Olsson, M. (1996). Fitting phase-type distributions via the EM algorithm, Olsson, M. (1996). Estimation of phase-type distributions from censored data, Albrecher, H., & Bladt, M. (2019) <doi:10.1017/jpr.2019.60>, Albrecher, H., Bladt, M., & Yslas, J. (2022) <doi:10.1111/sjos.12505>, Albrecher, H., Bladt, M., Bladt, M., & Yslas, J. (2022) <doi:10.1016/j.insmatheco.2022.08.001>, Bladt, M., & Yslas, J. (2022) <doi:10.1080/03461238.2022.2097019>, Bladt, M. (2022) <doi:10.1017/asb.2021.40>, Bladt, M. (2023) <doi:10.1080/10920277.2023.2167833>, Albrecher, H., Bladt, M., & Mueller, A. (2023) <doi:10.1515/demo-2022-0153>, Bladt, M. & Yslas, J. (2023) <doi:10.1016/j.insmatheco.2023.02.008>. |
| Depends: | R (≥ 4.2.0) |
| License: | GPL-3 |
| Imports: | Rcpp, methods, nnet, reshape2 |
| LinkingTo: | Rcpp, RcppArmadillo |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | yes |
| Packaged: | 2023-08-01 12:54:23 UTC; martinbladt |
| Author: | Martin Bladt [aut, cre], Jorge Yslas [aut], Alaric Müller [ctb] |
| Repository: | CRAN |
| Date/Publication: | 2023-08-08 11:00:02 UTC |
Statistics for Matrix Distributions
Description
This package implements tools which are useful for the statistical analysis of discrete, continuous, multivariate, right-censored or regression variants of phase-type distributions. These distributions are absorption times of Markov jump processes, and thus the maximization of their likelihood for statistical estimation is best dealt with using the EM algorithm.
Author(s)
Martin Bladt and Jorge Yslas.
Maintainer: Martin Bladt <martinbladt@gmail.com>
References
Asmussen, S., Nerman, O., & Olsson, M. (1996). Fitting phase-type distributions via the EM algorithm. Scandinavian Journal of Statistics, 23(4),419-441.
Olsson, M. (1996). Estimation of phase-type distributions from censored data. Scandinavian journal of statistics, 24(4), 443-460.
Albrecher, H., & Bladt, M. (2019). Inhomogeneous phase-type distributions and heavy tails. Journal of Applied Probability, 56(4), 1044-1064.
Albrecher, H., Bladt, M., & Yslas, J. (2022). Fitting inhomogeneous Phase-Type distributions to data: The univariate and the multivariate case. Scandinavian Journal of Statistics, 49(1), 44-77
Albrecher, H., Bladt, M., Bladt, M., & Yslas, J. (2020). Mortality modeling and regression with matrix distributions. Insurance: Mathematics and Economics, 107, 68-87.
Bladt, M., & Yslas, J. (2022). Phase-type mixture-of-experts regression for loss severities. ScandinavianActuarialJournal, 1-27.
Bladt, M. (2022). Phase-type distributions for claim severity regression modeling. ASTIN Bulletin: The journal of the IAA, 52(2), 417-448.
Bladt, M. (2023). A tractable class of Multivariate Phase-type distributions for loss modeling. North American Actuarial Journal, to appear.
Albrecher, H., Bladt, M., & Mueller, A. (2023). Joint lifetime modelling with matrix distributions. Dependence Modeling, 11(1), 1-22.
Bladt, M. & Yslas, J. (2023). Robust claim frequency modeling through phase-type mixture-of-experts regression.Insurance: Mathematics and Economics, 111, 1-22.
Sum method for discrete phase-type distributions
Description
Sum method for discrete phase-type distributions
Usage
## S4 method for signature 'dph,dph'
e1 + e2
Arguments
e1 |
An object of class dph. |
e2 |
An object of class dph. |
Value
An object of class dph.
Examples
dph1 <- dph(structure = "general", dimension = 3)
dph2 <- dph(structure = "general", dimension = 5)
dph_sum <- dph1 + dph2
dph_sum
Sum method for phase-type distributions
Description
Sum method for phase-type distributions
Usage
## S4 method for signature 'ph,ph'
e1 + e2
Arguments
e1 |
An object of class ph. |
e2 |
An object of class ph. |
Value
An object of class ph.
Examples
ph1 <- ph(structure = "general", dimension = 3)
ph2 <- ph(structure = "gcoxian", dimension = 5)
ph_sum <- ph1 + ph2
ph_sum
EM step for the mPH class with right-censoring, for different marginal sub-intensity matrices
Description
EM step for the mPH class with right-censoring, for different marginal sub-intensity matrices
Usage
EM_step_mPH_rc(alpha, S_list, y, delta, h)
Arguments
alpha |
Common initial distribution vector. |
S_list |
List of marginal sub-intensity matrices. |
y |
Matrix of marginal observations. |
delta |
Matrix with right-censoring indications (1 uncensored, 0 right-censored). |
h |
Tolerance of uniformization. |
EM for PH-MoE
Description
No recycling of information
Usage
EMstep_MoE_PADE(alpha, S, obs, weight, rcens, rcweight)
Arguments
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
The weights for the observations. |
rcens |
Censored observations. |
rcweight |
The weights for the censored observations. |
EM for phase-type distributions using Pade approximation for matrix exponential
Description
EM for phase-type distributions using Pade approximation for matrix exponential
Usage
EMstep_PADE(h, alpha, S, obs, weight, rcens, rcweight)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
The weights for the observations. |
rcens |
Censored observations. |
rcweight |
The weights for the censored observations. |
EM step for phase-type using Runge-Kutta
Description
Computes one step of the EM algorithm by using a Runge-Kutta method of fourth order.
Usage
EMstep_RK(h, alpha, S, obs, weight, rcens, rcweight)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
The weights for the observations. |
rcens |
Censored observations. |
rcweight |
The weights for the censored observations. |
EM for phase-type using uniformization for matrix exponential
Description
EM for phase-type using uniformization for matrix exponential
Usage
EMstep_UNI(h, alpha, S, obs, weight, rcens, rcweight)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
The weights for the observations. |
rcens |
Censored observations. |
rcweight |
The weights for the censored observations. |
EM for discrete bivariate phase-type
Description
EM for discrete bivariate phase-type
Usage
EMstep_bivdph(alpha, S11, S12, S22, obs, weight)
Arguments
alpha |
Initial probabilities. |
S11 |
Sub-transition matrix. |
S12 |
Matrix. |
S22 |
Sub-transition matrix. |
obs |
The observations. |
weight |
The weights for the observations. |
EM for discrete bivariate phase-type MoE
Description
EM for discrete bivariate phase-type MoE
Usage
EMstep_bivdph_MoE(alpha, S11, S12, S22, obs, weight)
Arguments
alpha |
Initial probabilities. |
S11 |
Sub-transition matrix. |
S12 |
Matrix. |
S22 |
Sub-transition matrix. |
obs |
The observations. |
weight |
The weights for the observations. |
EM for bivariate phase-type distributions using Pade for matrix exponential
Description
EM for bivariate phase-type distributions using Pade for matrix exponential
Usage
EMstep_bivph(alpha, S11, S12, S22, obs, weight)
Arguments
alpha |
Initial probabilities. |
S11 |
Sub-intensity. |
S12 |
A matrix. |
S22 |
Sub-intensity. |
obs |
The observations. |
weight |
The weights for the observations. |
Value
Fitted alpha, S11, S12 and S22 after one iteration.
EM for discrete phase-type
Description
EM for discrete phase-type
Usage
EMstep_dph(alpha, S, obs, weight)
Arguments
alpha |
Initial probabilities. |
S |
Sub-transition matrix. |
obs |
The observations. |
weight |
The weights for the observations. |
EM for discrete phase-type MoE
Description
EM for discrete phase-type MoE
Usage
EMstep_dph_MoE(alpha, S, obs, weight)
Arguments
alpha |
Initial probabilities. |
S |
Sub-transition matrix. |
obs |
The observations. |
weight |
The weights for the observations. |
EM for multivariate discrete phase-type
Description
EM for multivariate discrete phase-type
Usage
EMstep_mdph(alpha, S_list, obs, weight)
Arguments
alpha |
Initial probabilities. |
S_list |
List of marginal sub-transition matrices. |
obs |
The observations. |
weight |
The weights for the observations. |
EM for multivariate discrete phase-type MoE
Description
EM for multivariate discrete phase-type MoE
Usage
EMstep_mdph_MoE(alpha, S_list, obs, weight)
Arguments
alpha |
Initial probabilities. |
S_list |
List of marginal sub-transition matrices. |
obs |
The observations. |
weight |
The weights for the observations. |
New generic for obtaining the Fisher information of survival matrix distributions
Description
Methods are available for objects of class sph.
Usage
Fisher(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Fisher information method for sph class
Description
Fisher information method for sph class
Usage
## S4 method for signature 'sph'
Fisher(x, y, X, w = numeric(0))
Arguments
x |
An object of class sph. |
y |
Independent variate. |
X |
Matrix of covariates. |
w |
Weights. |
Value
A matrix.
New generic for likelihood ratio test between two matrix distribution models
Description
Methods are available for objects of class ph.
Usage
LRT(x, y, ...)
Arguments
x, y |
Objects of the model class. |
... |
Further parameters to be passed on. |
Value
A likelihood ratio test result.
LRT method for ph class
Description
LRT method for ph class
Usage
## S4 method for signature 'ph,ph'
LRT(x, y)
Arguments
x, y |
Objects of class ph. |
Value
LRT between the models.
Constructor function for multivariate phase-type distributions (MPH* class)
Description
Constructor function for multivariate phase-type distributions (MPH* class)
Usage
MPHstar(
alpha = NULL,
S = NULL,
structure = NULL,
dimension = 3,
R = NULL,
variables = 2
)
Arguments
alpha |
A probability vector. |
S |
A sub-intensity matrix. |
structure |
A valid ph structure. |
dimension |
The dimension of the ph structure (if provided). |
R |
A compatible (non-negative) reward matrix. |
variables |
The number of desired marginals. |
Value
An object of class MPHstar.
Examples
MPHstar(structure = "general", dimension = 4, variables = 3)
Multivariate phase-type distributions obtained by transformation via rewards
Description
Class of objects for multivariate phase type distributions.
Slots
nameName of the phase type distribution.
parsA list comprising of the parameters.
EM step using Uniformization for MPHstar class
Description
EM step using Uniformization for MPHstar class
Usage
MPHstar_EMstep_UNI(h, Rtol, alpha, S, R, mph_obs)
Arguments
h |
positive parameter for precision of uniformization method. |
Rtol |
The smallest value that a reward can take. |
alpha |
Vector of initial probabilities of the originating distribution. |
S |
The sub-intensity matrix of the originating distribution. |
R |
The reward matrix. |
mph_obs |
The list of summed, marginal observations with associated weights. |
Prepare data for the MPHstar_EMstep_UNI
Description
Prepare data for the MPHstar_EMstep_UNI
Usage
MPHstar_data_aggregation(y, w = numeric(0))
Arguments
y |
A matrix with marginal observations, each column corresponds to a marginal. |
w |
A matrix of weights, each column corresponds to a marginal. |
Value
For summed and marginal observations we have a list with matrices of unique observations and their associated weights, separated by uncensored and right-censored data.
New generic for mixture-of-experts regression with matrix distributions
Description
Methods are available for objects of class ph
Usage
MoE(x, y, ...)
Arguments
x |
An object of the model class. |
y |
A vector of data. |
... |
Further parameters to be passed on. |
Value
An object of the fitted model class.
MoE method for bivdph Class
Description
MoE method for bivdph Class
Usage
## S4 method for signature 'bivdph'
MoE(
x,
formula,
y,
data,
alpha_vecs = NULL,
weight = numeric(0),
stepsEM = 1000,
every = 10,
rand_init = TRUE
)
Arguments
x |
An object of class bivdph. |
formula |
A regression formula. |
y |
A matrix of observations. |
data |
A data frame of covariates. |
alpha_vecs |
Matrix of initial probabilities. |
weight |
Vector of weights. |
stepsEM |
Number of EM steps to be performed. |
every |
Number of iterations between likelihood display updates. |
rand_init |
Random initiation in the R-step. |
Value
An object of class sph.
Examples
x <- bivdph(dimensions = c(3, 3))
n <- 100
responses <- cbind(rpois(n, 3) + 1, rbinom(n, 5, 0.5))
covariates <- data.frame(age = sample(18:65, n, replace = TRUE) / 100, income = runif(n, 0, 0.99))
f <- responses ~ age + income
MoE(x = x, formula = f, y = responses, data = covariates, stepsEM = 20)
MoE method for dph Class
Description
MoE method for dph Class
Usage
## S4 method for signature 'dph'
MoE(
x,
formula,
data,
alpha_vecs = NULL,
weight = numeric(0),
stepsEM = 1000,
every = 10,
rand_init = TRUE,
maxWts = 1000
)
Arguments
x |
An object of class dph. |
formula |
A regression formula. |
data |
A data frame. |
alpha_vecs |
Matrix of initial probabilities. |
weight |
Vector of weights. |
stepsEM |
Number of EM steps to be performed. |
every |
Number of iterations between likelihood display updates. |
rand_init |
Random initiation in the R-step. |
maxWts |
Maximal number of weights in the nnet function. |
Value
An object of class sph.
Examples
x <- dph(structure = "general")
n <- 100
responses <- rpois(n, 3) + 1
covariate <- data.frame(age = sample(18:65, n, replace = TRUE) / 100, income = runif(n, 0, 0.99))
f <- responses ~ age + income # regression formula
MoE(x = x, formula = f, y = responses, data = covariate, stepsEM = 20)
MoE method for mdph Class
Description
MoE method for mdph Class
Usage
## S4 method for signature 'mdph'
MoE(
x,
formula,
y,
data,
alpha_vecs = NULL,
weight = numeric(0),
stepsEM = 1000,
every = 10,
rand_init = TRUE,
maxWts = 1000
)
Arguments
x |
An object of class mdph. |
formula |
A regression formula. |
y |
A matrix of observations. |
data |
A data frame of covariates. |
alpha_vecs |
Matrix of initial probabilities. |
weight |
Vector of weights. |
stepsEM |
Number of EM steps to be performed. |
every |
Number of iterations between likelihood display updates. |
rand_init |
Random initiation in the R-step. |
maxWts |
Maximal number of weights in the nnet function. |
Value
An object of class sph.
Examples
x <- mdph(structure = c("general", "general"))
n <- 100
responses <- cbind(rpois(n, 3) + 1, rbinom(n, 5, 0.5))
covariates <- data.frame(age = sample(18:65, n, replace = TRUE) / 100, income = runif(n, 0, 0.99))
f <- responses ~ age + income
MoE(x = x, formula = f, y = responses, data = covariates, stepsEM = 20)
Fit method for mph/miph class, using mixture-of-experts regression
Description
Fit method for mph/miph class, using mixture-of-experts regression
Usage
## S4 method for signature 'mph'
MoE(
x,
formula,
y,
data,
alpha_mat = NULL,
delta = numeric(0),
stepsEM = 1000,
r = 1,
maxit = 100,
reltol = 1e-08,
rand_init = T
)
Arguments
x |
An object of class mph. |
formula |
a regression formula. |
y |
A matrix of observations. |
data |
A data frame of covariates (they need to be scaled for the regression). |
alpha_mat |
Matrix with initial distribution vectors for each row of observations. |
delta |
Matrix with right-censoring indicators (1 uncensored, 0 right censored). |
stepsEM |
Number of EM steps to be performed. |
r |
Sub-sampling parameter, defaults to 1 (not supported for this method). |
maxit |
Maximum number of iterations when optimizing the g function (inhomogeneous likelihood). |
reltol |
Relative tolerance when optimizing g function. |
rand_init |
Random initiation in the R-step of the EM algorithm. |
Examples
under_mph <- mph(structure = c("general", "general"), dimension = 3)
x <- miph(under_mph, gfun = c("weibull", "weibull"), gfun_pars = list(c(2), c(3)))
n <- 100
responses <- cbind(rexp(n), rweibull(n, 2, 3))
covariates <- data.frame(age = sample(18:65, n, replace = TRUE) / 100, income = runif(n, 0, 0.99))
f <- responses ~ age + income
MoE(x = x, formula = f, y = responses, data = covariates, stepsEM = 20)
MoE method for ph Class
Description
MoE method for ph Class
Usage
## S4 method for signature 'ph'
MoE(
x,
formula,
data,
inhom = NULL,
alpha_vecs = NULL,
weight = numeric(0),
delta = numeric(0),
stepsEM = 1000,
optim_method = "BFGS",
maxit = 50,
reltol = 1e-08,
every = 10,
rand_init = TRUE
)
Arguments
x |
An object of class ph. |
formula |
A regression formula. |
data |
A data frame. |
inhom |
A list with the inhomogeneity functions. |
alpha_vecs |
Matrix of initial probabilities.s |
weight |
Vector of weights. |
delta |
Right-censoring indicator. |
stepsEM |
Number of EM steps to be performed. |
optim_method |
Method to use in gradient optimization. |
maxit |
Maximum number of iterations when optimizing g function. |
reltol |
Relative tolerance when optimizing g function. |
every |
Number of iterations between likelihood display updates. |
rand_init |
Random initiation in the R-step. |
Value
An object of class sph.
Examples
x <- iph(ph(structure = "general"), gfun = "weibull")
n <- 100
responses <- rweibull(n, 2, 3)
covariate <- data.frame(age = sample(18:65, n, replace = TRUE) / 100, income = runif(n, 0, 0.99))
f <- responses ~ age + income # regression formula
MoE(x = x, formula = f, y = responses, data = covariate, stepsEM = 20)
New generic for N-fold convolution of two matrix distributions
Description
Methods are available for objects of classes ph and dph.
Usage
Nfold(x1, x2, ...)
Arguments
x1 |
An object of the class dph. |
x2 |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
An object of the model class.
Nfold method for phase-type distributions
Description
Nfold method for phase-type distributions
Usage
## S4 method for signature 'dph'
Nfold(x1, x2)
Arguments
x1 |
An object of class ph. |
x2 |
An object of class dph. |
Value
An object of class ph.
Examples
dph1 <- dph(structure = "general", dimension = 3)
dph2 <- dph(structure = "general", dimension = 2)
ph0 <- ph(structure = "general", dimension = 2)
Nfold(dph1, ph0)
Nfold(dph1, dph2)
New generic for transformation via rewards of a matrix distribution
Description
Methods are available for objects of class ph
Usage
TVR(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
An object of the model class.
TVR Method for dph Class
Description
TVR Method for dph Class
Usage
## S4 method for signature 'dph'
TVR(x, rew)
Arguments
x |
An object of class dph. |
rew |
A vector of rewards. |
Value
An object of the of class dph.
Examples
obj <- dph(structure = "general")
TVR(obj, c(1, 0, 1))
TVR method for ph class
Description
TVR method for ph class
Usage
## S4 method for signature 'ph'
TVR(x, rew)
Arguments
x |
An object of class ph. |
rew |
A vector of rewards. |
Value
An object of the of class ph.
Examples
obj <- ph(structure = "general")
TVR(obj, c(1, 2, 3))
Runge-Kutta for the calculation of the a vector in a EM step
Description
Runge-Kutta for the calculation of the a vector in a EM step
Usage
a_rungekutta(avector, dt, h, S)
Arguments
avector |
The a vector. |
dt |
Increment. |
h |
Step-length. |
S |
Sub-intensity matrix. |
Constructor function for bivariate discrete phase-type distributions
Description
Constructor function for bivariate discrete phase-type distributions
Usage
bivdph(alpha = NULL, S11 = NULL, S12 = NULL, S22 = NULL, dimensions = c(3, 3))
Arguments
alpha |
A probability vector. |
S11 |
A sub-transition matrix. |
S12 |
A matrix. |
S22 |
A sub-transition matrix. |
dimensions |
The dimensions of the bivariate discrete phase-type (if no parameters are provided). |
Value
An object of class bivdph.
Examples
bivdph(dimensions = c(3, 3))
S11 <- matrix(c(0.1, .5, .5, 0.1), 2, 2)
S12 <- matrix(c(.2, .3, .2, .1), 2, 2)
S22 <- matrix(c(0.2, 0, 0.1, 0.1), 2, 2)
bivdph(alpha = c(.5, .5), S11, S12, S22)
Bivariate discrete phase-type distributions
Description
Class of objects for bivariate discrete phase-type distributions.
Value
Class object.
Slots
nameName of the discrete phase-type distribution.
parsA list comprising of the parameters.
fitA list containing estimation information.
Bivariate discrete phase-type joint density of the feed forward type
Description
Bivariate discrete phase-type joint density of the feed forward type
Usage
bivdph_density(x, alpha, S11, S12, S22)
Arguments
x |
Matrix of values. |
alpha |
Vector of initial probabilities. |
S11 |
Sub-transition matrix. |
S12 |
Matrix. |
S22 |
Sub-transition matrix. |
Value
Joint density at x.
Bivariate discrete phase-type joint tail of the feed forward type
Description
Bivariate discrete phase-type joint tail of the feed forward type
Usage
bivdph_tail(x, alpha, S11, S12, S22)
Arguments
x |
Matrix of values. |
alpha |
Vector of initial probabilities. |
S11 |
Sub-transition matrix. |
S12 |
Matrix. |
S22 |
Sub-transition matrix. |
Value
Joint tail at x.
Constructor function for bivariate inhomogeneous phase-type distributions
Description
Constructor function for bivariate inhomogeneous phase-type distributions
Usage
biviph(
bivph = NULL,
gfun = NULL,
gfun_pars = NULL,
alpha = NULL,
S11 = NULL,
S12 = NULL,
S22 = NULL,
dimensions = c(3, 3)
)
Arguments
bivph |
An object of class bivph. |
gfun |
Vector of inhomogeneity transforms. |
gfun_pars |
List of parameters for the inhomogeneity functions. |
alpha |
A probability vector. |
S11 |
A sub-intensity matrix. |
S12 |
A matrix. |
S22 |
A sub-intensity matrix. |
dimensions |
The dimensions of the bivariate phase-type (if no parameters are provided). |
Value
An object of class biviph.
Examples
under_bivph <- bivph(dimensions = c(3, 3))
biviph(under_bivph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
Bivariate inhomogeneous phase-type distributions
Description
Class of objects for bivariate inhomogeneous phase-type distributions.
Value
Class object.
Slots
nameName of the phase type distribution.
gfunA list comprising of the parameters.
Constructor function for bivariate phase-type distributions
Description
Constructor function for bivariate phase-type distributions
Usage
bivph(alpha = NULL, S11 = NULL, S12 = NULL, S22 = NULL, dimensions = c(3, 3))
Arguments
alpha |
A probability vector. |
S11 |
A sub-intensity matrix. |
S12 |
A matrix. |
S22 |
A sub-intensity matrix. |
dimensions |
The dimensions of the bivariate phase-type (if no parameters are provided). |
Value
An object of class bivph.
Examples
bivph(dimensions = c(3, 3))
S11 <- matrix(c(-1, .5, .5, -1), 2, 2)
S12 <- matrix(c(.2, .4, .3, .1), 2, 2)
S22 <- matrix(c(-2, 0, 1, -1), 2, 2)
bivph(alpha = c(.5, .5), S11, S12, S22)
Bivariate phase-type distributions
Description
Class of objects for bivariate phase-type distributions.
Value
Class object.
Slots
nameName of the phase-type distribution.
parsA list comprising of the parameters.
fitA list containing estimation information.
Bivariate phase-type joint density of the feed forward type
Description
Bivariate phase-type joint density of the feed forward type
Usage
bivph_density(x, alpha, S11, S12, S22)
Arguments
x |
Matrix of values. |
alpha |
Vector of initial probabilities. |
S11 |
Sub-intensity matrix. |
S12 |
Matrix. |
S22 |
Sub-intensity matrix. |
Value
Joint density at x.
Bivariate phase-type joint Laplace
Description
Bivariate phase-type joint Laplace
Usage
bivph_laplace(r, alpha, S11, S12, S22)
Arguments
r |
Matrix of values. |
alpha |
Vector of initial probabilities. |
S11 |
Sub-intensity matrix. |
S12 |
Matrix. |
S22 |
Sub-intensity matrix. |
Value
Joint laplace at r.
Bivariate phase-type joint tail of the feed forward type
Description
Bivariate phase-type joint tail of the feed forward type
Usage
bivph_tail(x, alpha, S11, S12, S22)
Arguments
x |
Matrix of values. |
alpha |
Vector of initial probabilities. |
S11 |
Sub-intensity matrix. |
S12 |
Matrix. |
S22 |
Sub-intensity matrix. |
Value
Joint tail at x.
New generic for the distribution of matrix distributions
Description
Methods are available for objects of class ph.
Usage
cdf(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
CDF from the matrix distribution.
Distribution method for discrete phase-type distributions
Description
Distribution method for discrete phase-type distributions
Usage
## S4 method for signature 'dph'
cdf(x, q, lower.tail = TRUE)
Arguments
x |
An object of class dph. |
q |
A vector of locations. |
lower.tail |
Logical parameter specifying whether lower tail (CDF) or upper tail is computed. |
Value
A vector containing the CDF evaluations at the given locations.
Examples
obj <- dph(structure = "general")
cdf(obj, c(1, 2, 3))
Distribution method for inhomogeneous phase-type distributions
Description
Distribution method for inhomogeneous phase-type distributions
Usage
## S4 method for signature 'iph'
cdf(x, q, lower.tail = TRUE)
Arguments
x |
An object of class iph. |
q |
A vector of locations. |
lower.tail |
Logical parameter specifying whether lower tail (CDF) or upper tail is computed. |
Value
A vector containing the CDF evaluations at the given locations.
Examples
obj <- iph(ph(structure = "general"), gfun = "weibull", gfun_pars = 2)
cdf(obj, c(1, 2, 3))
Distribution method for multivariate inhomogeneous phase-type distributions
Description
Distribution method for multivariate inhomogeneous phase-type distributions
Usage
## S4 method for signature 'miph'
cdf(x, y, lower.tail = TRUE)
Arguments
x |
An object of class miph. |
y |
A matrix of observations. |
lower.tail |
Logical parameter specifying whether lower tail (CDF) or upper tail is computed. |
Value
A list containing the locations and corresponding CDF evaluations.
Examples
under_mph <- mph(structure = c("general", "general"))
obj <- miph(under_mph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
cdf(obj, c(1, 2))
Distribution method for multivariate phase-type distributions
Description
Distribution method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
cdf(x, y, lower.tail = TRUE)
Arguments
x |
An object of class mph. |
y |
A matrix of observations. |
lower.tail |
Logical parameter specifying whether lower tail (CDF) or upper tail is computed. |
Value
A list containing the locations and corresponding CDF evaluations.
Examples
obj <- mph(structure = c("general", "general"))
cdf(obj, matrix(c(0.5, 1), ncol = 2))
Distribution method for phase-type distributions
Description
Distribution method for phase-type distributions
Usage
## S4 method for signature 'ph'
cdf(x, q, lower.tail = TRUE)
Arguments
x |
An object of class ph. |
q |
A vector of locations. |
lower.tail |
Logical parameter specifying whether lower tail (CDF) or upper tail is computed. |
Value
A vector containing the CDF evaluations at the given locations.
Examples
obj <- ph(structure = "general")
cdf(obj, c(1, 2, 3))
Clone a matrix
Description
Clone a matrix
Usage
clone_matrix(m)
Arguments
m |
A matrix. |
Value
A clone of the matrix.
Clone a vector
Description
Clone a vector
Usage
clone_vector(v)
Arguments
v |
A vector. |
Value
A clone of the vector.
Coef method for bivdph class
Description
Coef method for bivdph class
Usage
## S4 method for signature 'bivdph'
coef(object)
Arguments
object |
An object of class bivdph. |
Value
Parameters of bivariate discrete phase-type model.
Examples
obj <- bivdph(dimensions = c(3, 3))
coef(obj)
Coef method for biviph class
Description
Coef method for biviph class
Usage
## S4 method for signature 'biviph'
coef(object)
Arguments
object |
An object of class biviph. |
Value
Parameters of bivariate inhomogeneous phase-type model.
Examples
under_bivph <- bivph(dimensions = c(3, 3))
obj <- biviph(under_bivph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
coef(obj)
Coef method for bivph class
Description
Coef method for bivph class
Usage
## S4 method for signature 'bivph'
coef(object)
Arguments
object |
An object of class bivph. |
Value
Parameters of bivariate phase-type model.
Examples
obj <- bivph(dimensions = c(3, 3))
coef(obj)
Coef method for dph Class
Description
Coef method for dph Class
Usage
## S4 method for signature 'dph'
coef(object)
Arguments
object |
An object of class dph. |
Value
Parameters of dph model.
Examples
obj <- dph(structure = "general", dim = 3)
coef(obj)
Coef method for iph class
Description
Coef method for iph class
Usage
## S4 method for signature 'iph'
coef(object)
Arguments
object |
An object of class iph. |
Value
Parameters of iph model.
Examples
obj <- iph(ph(structure = "general", dimension = 2), gfun = "lognormal", gfun_pars = 2)
coef(obj)
Coef method for mdph class
Description
Coef method for mdph class
Usage
## S4 method for signature 'mdph'
coef(object)
Arguments
object |
An object of class mdph. |
Value
Parameters of multivariate discrete phase-type model.
Examples
obj <- mdph(structure = c("general", "general"))
coef(obj)
Coef method for ph class
Description
Coef method for ph class
Usage
## S4 method for signature 'ph'
coef(object)
Arguments
object |
An object of class ph. |
Value
Parameters of ph model.
Examples
obj <- ph(structure = "general")
coef(obj)
Coef method for sph Class
Description
Coef method for sph Class
Usage
## S4 method for signature 'sph'
coef(object)
Arguments
object |
An object of class sph. |
Value
Parameters of sph model.
Cor method for MPHstar class
Description
Cor method for MPHstar class
Usage
## S4 method for signature 'MPHstar'
cor(x)
Arguments
x |
An object of class MPHstar. |
Value
The correlation matrix of the MPHstar distribution.
Examples
obj <- MPHstar(structure = "general")
cor(obj)
Cor method for bivdph class
Description
Cor method for bivdph class
Usage
## S4 method for signature 'bivdph'
cor(x)
Arguments
x |
An object of class bivdph. |
Value
The correlation matrix of the bivariate discrete phase-type distribution.
Examples
obj <- bivdph(dimensions = c(3, 3))
cor(obj)
Cor method for bivph class
Description
Cor method for bivph class
Usage
## S4 method for signature 'bivph'
cor(x)
Arguments
x |
An object of class bivph. |
Value
The correlation matrix of the bivariate phase-type distribution.
Examples
obj <- bivph(dimensions = c(3, 3))
cor(obj)
Cor method for multivariate discrete phase-type distributions
Description
Cor method for multivariate discrete phase-type distributions
Usage
## S4 method for signature 'mdph'
cor(x)
Arguments
x |
An object of class mdph. |
Value
The correlation matrix of the multivariate discrete phase-type distribution.
Examples
obj <- mdph(structure = c("general", "general"))
cor(obj)
Cor method for multivariate phase-type distributions
Description
Cor method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
cor(x)
Arguments
x |
An object of class mph. |
Value
The correlation matrix of the multivariate phase-type distribution.
Examples
obj <- mph(structure = c("general", "general"))
cor(obj)
Cumulate matrix
Description
Creates a new matrix with entries the cumulated rows of A.
Usage
cumulate_matrix(A)
Arguments
A |
A matrix. |
Value
The cumulated matrix.
Cumulate vector
Description
Creates a new vector with entries the cumulated entries of A.
Usage
cumulate_vector(A)
Arguments
A |
A vector. |
Value
The cumulated vector.
Default size of the steps in the RK
Description
Computes the default step length for a matrix S to be employed in the
RK method.
Usage
default_step_length(S)
Arguments
S |
Sub-intensity matrix. |
Value
The step length for S.
New generic for the density of matrix distributions
Description
Methods are available for objects of class ph.
Usage
dens(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Density from the matrix distribution.
Density method for bivariate discrete phase-type distributions
Description
Density method for bivariate discrete phase-type distributions
Usage
## S4 method for signature 'bivdph'
dens(x, y)
Arguments
x |
An object of class bivdph. |
y |
A matrix of locations. |
Value
A vector containing the joint density evaluations at the given locations.
Examples
obj <- bivdph(dimensions = c(3, 3))
dens(obj, matrix(c(1, 2), ncol = 2))
Density method for bivariate inhomogeneous phase-type distributions
Description
Density method for bivariate inhomogeneous phase-type distributions
Usage
## S4 method for signature 'biviph'
dens(x, y)
Arguments
x |
An object of class biviph. |
y |
A matrix of locations. |
Value
A vector containing the joint density evaluations at the given locations.
Examples
under_bivph <- bivph(dimensions = c(3, 3))
obj <- biviph(under_bivph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
dens(obj, matrix(c(0.5, 1), ncol = 2))
Density method for bivariate phase-type distributions
Description
Density method for bivariate phase-type distributions
Usage
## S4 method for signature 'bivph'
dens(x, y)
Arguments
x |
An object of class bivph. |
y |
A matrix of locations. |
Value
A vector containing the joint density evaluations at the given locations.
Examples
obj <- bivph(dimensions = c(3, 3))
dens(obj, matrix(c(0.5, 1), ncol = 2))
Density method for discrete phase-type distributions
Description
Density method for discrete phase-type distributions
Usage
## S4 method for signature 'dph'
dens(x, y)
Arguments
x |
An object of class dph. |
y |
A vector of locations. |
Value
A vector containing the density evaluations at the given locations.
Examples
obj <- dph(structure = "general")
dens(obj, c(1, 2, 3))
Density method for inhomogeneous phase-type distributions
Description
Density method for inhomogeneous phase-type distributions
Usage
## S4 method for signature 'iph'
dens(x, y)
Arguments
x |
An object of class iph. |
y |
A vector of locations. |
Value
A vector containing the density evaluations at the given locations.
Examples
obj <- iph(ph(structure = "general"), gfun = "weibull", gfun_pars = 2)
dens(obj, c(1, 2, 3))
Density method for multivariate discrete phase-type distributions
Description
Density method for multivariate discrete phase-type distributions
Usage
## S4 method for signature 'mdph'
dens(x, y)
Arguments
x |
An object of class mdph. |
y |
A matrix of locations. |
Value
A vector containing the joint density evaluations at the given locations.
Examples
obj <- mdph(structure = c("general", "general"))
dens(obj, matrix(c(1, 1), ncol = 2))
Density method for multivariate inhomogeneous phase-type distributions
Description
Density method for multivariate inhomogeneous phase-type distributions
Usage
## S4 method for signature 'miph'
dens(x, y, delta = NULL)
Arguments
x |
An object of class miph. |
y |
A matrix of observations. |
delta |
Matrix with right-censoring indicators (1 uncensored, 0 right censored). |
Value
A list containing the locations and corresponding density evaluations.
Examples
under_mph <- mph(structure = c("general", "general"))
obj <- miph(under_mph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
dens(obj, c(1, 2))
Density method for multivariate phase-type distributions
Description
Density method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
dens(x, y, delta = NULL)
Arguments
x |
An object of class mph. |
y |
A matrix of observations. |
delta |
Matrix with right-censoring indicators (1 uncensored, 0 right censored). |
Value
A list containing the locations and corresponding density evaluations.
Examples
obj <- mph(structure = c("general", "general"))
dens(obj, matrix(c(0.5, 1), ncol = 2))
Density method for phase-type distributions
Description
Density method for phase-type distributions
Usage
## S4 method for signature 'ph'
dens(x, y)
Arguments
x |
An object of class ph. |
y |
A vector of locations. |
Value
A vector containing the density evaluations at the given locations.
Examples
obj <- ph(structure = "general")
dens(obj, c(1, 2, 3))
Constructor function for discrete phase-type distributions
Description
Constructor function for discrete phase-type distributions
Usage
dph(alpha = NULL, S = NULL, structure = NULL, dimension = 3)
Arguments
alpha |
A probability vector. |
S |
A sub-transition matrix. |
structure |
A valid dph structure: |
dimension |
The dimension of the dph structure (if structure is provided). |
Value
An object of class dph.
Examples
dph(structure = "general", dim = 5)
dph(alpha = c(0.5, 0.5), S = matrix(c(0.1, 0.5, 0.5, 0.2), 2, 2))
Discrete phase-type distributions
Description
Class of objects for discrete phase-type distributions.
Value
Class object.
Slots
nameName of the discrete phase-type distribution.
parsA list comprising of the parameters.
fitA list containing estimation information.
Pgf of a discrete phase-type distribution
Description
Computes the pgf at z of a discrete phase-type distribution with
parameters alpha and S.
Usage
dph_pgf(z, alpha, S)
Arguments
z |
Vector of real values. |
alpha |
Vector of initial probabilities. |
S |
Sub-transition matrix. |
Value
Laplace transform at r.
Discrete phase-type cdf
Description
Computes the cdf (tail) of a discrete phase-type distribution with parameters
alpha and S at x.
Usage
dphcdf(x, alpha, S, lower_tail = TRUE)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
lower_tail |
Cdf or tail. |
Value
The cdf (tail) at x.
Discrete phase-type density
Description
Computes the density of discrete phase-type distribution with parameters
alpha and S at x.
Usage
dphdensity(x, alpha, S)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-transition matrix. |
Value
The density at x.
Embedded Markov chain of a sub-intensity matrix
Description
Returns the transition probabilities of the embedded Markov chain determined the sub-intensity matrix.
Usage
embedded_mc(S)
Arguments
S |
A sub-intensity matrix. |
Value
The embedded Markov chain.
New generic for evaluating survival matrix distributions
Description
Methods are available for objects of class sph.
Usage
evaluate(x, subject, ...)
Arguments
x |
An object of the model class. |
subject |
A vector of data. |
... |
Further parameters to be passed on. |
Evaluation method for sph Class
Description
Evaluation method for sph Class
Usage
## S4 method for signature 'sph'
evaluate(x, subject)
Arguments
x |
An object of class sph. |
subject |
Covariates of a single subject. |
Value
A ph model.
expm terms of phase-type likelihood using uniformization
Description
expm terms of phase-type likelihood using uniformization
Usage
expm_terms(h, S, obs)
Arguments
h |
Positive parameter. |
S |
Sub-intensity matrix. |
obs |
The observations. |
Matrix exponential
Description
Armadillo matrix exponential implementation.
Usage
expmat(A)
Arguments
A |
A matrix. |
Value
exp(A).
Find n such that P(N > n) = h with N Poisson distributed
Description
Find n such that P(N > n) = h with N Poisson distributed
Usage
find_n(h, lambda)
Arguments
h |
Probability. |
lambda |
Mean of Poisson random variable. |
Value
Integer satisfying condition.
Find weight of observations
Description
Find weight of observations
Usage
find_weight(x)
Arguments
x |
A vector of observations from which we want to know their weights. |
Value
A matrix with unique observations as first column and associated weights for second column.
New generic for estimating matrix distributions
Description
Methods are available for objects of class ph.
Usage
fit(x, y, ...)
Arguments
x |
An object of the model class. |
y |
A vector of data. |
... |
Further parameters to be passed on. |
Value
An object of the fitted model class.
Fit method for mph class
Description
Fit method for mph class
Usage
## S4 method for signature 'MPHstar'
fit(
x,
y,
weight = numeric(0),
stepsEM = 1000,
uni_epsilon = 1e-04,
zero_tol = 1e-04,
every = 100,
plot = F,
r = 1,
replace = F
)
Arguments
x |
An object of class MPHstar. |
y |
A matrix of marginal data. |
weight |
A matrix of marginal weights. |
stepsEM |
The number of EM steps to be performed, defaults to 1000. |
uni_epsilon |
The epsilon parameter for the uniformization method, defaults to 1e-4. |
zero_tol |
The smallest value that a reward can take (to avoid numerical instability), defaults to 1e-4. |
every |
The number of iterations between likelihood display updates. The originating distribution is used, given that there is no explicit density. |
plot |
Boolean that determines if the plot of the loglikelihood evolution is plotted, defaults to False. |
r |
The sub-sampling proportion for stochastic EM, defaults to 1. |
replace |
Boolean that determines if sub-sampling is done with replacement or not, defaults to False. |
Value
An object of class MPHstar.
Examples
set.seed(123)
obj <- MPHstar(structure = "general")
data <- sim(obj, 100)
fit(obj, data, stepsEM = 20)
Fit method for bivdph Class
Description
Fit method for bivdph Class
Usage
## S4 method for signature 'bivdph'
fit(x, y, weight = numeric(0), stepsEM = 1000, every = 10)
Arguments
x |
An object of class bivdph. |
y |
A matrix with the data. |
weight |
Vector of weights. |
stepsEM |
Number of EM steps to be performed. |
every |
Number of iterations between likelihood display updates. |
Value
An object of class bivdph.
Examples
obj <- bivdph(dimensions = c(3, 3))
data <- sim(obj, n = 100)
fit(obj, data, stepsEM = 100, every = 50)
Fit method for bivph Class
Description
Fit method for bivph Class
Usage
## S4 method for signature 'bivph'
fit(
x,
y,
weight = numeric(0),
stepsEM = 1000,
maxit = 100,
reltol = 1e-08,
every = 10
)
Arguments
x |
An object of class bivph. |
y |
A matrix with the data. |
weight |
Vector of weights. |
stepsEM |
Number of EM steps to be performed. |
maxit |
Maximum number of iterations when optimizing g functions. |
reltol |
Relative tolerance when optimizing g functions. |
every |
Number of iterations between likelihood display updates. |
Value
An object of class bivph.
Examples
obj <- bivph(dimensions = c(3, 3))
data <- sim(obj, n = 100)
fit(obj, data, stepsEM = 100, every = 50)
Fit method for dph class
Description
Fit method for dph class
Usage
## S4 method for signature 'dph'
fit(x, y, weight = numeric(0), stepsEM = 1000, every = 100)
Arguments
x |
An object of class dph. |
y |
Vector or data. |
weight |
Vector of weights. |
stepsEM |
Number of EM steps to be performed. |
every |
Number of iterations between likelihood display updates. |
Value
An object of class dph.
Examples
obj <- dph(structure = "general", dimension = 2)
data <- sim(obj, n = 100)
fit(obj, data, stepsEM = 100, every = 20)
Fit method for mdph Class
Description
Fit method for mdph Class
Usage
## S4 method for signature 'mdph'
fit(x, y, weight = numeric(0), stepsEM = 1000, every = 10)
Arguments
x |
An object of class mdph. |
y |
A matrix with the data. |
weight |
Vector of weights. |
stepsEM |
Number of EM steps to be performed. |
every |
Number of iterations between likelihood display updates. |
Value
An object of class mdph.
Examples
obj <- mdph(structure = c("general", "general"))
data <- sim(obj, n = 100)
fit(obj, data, stepsEM = 100, every = 50)
Fit method for mph Class
Description
Fit method for mph Class
Usage
## S4 method for signature 'mph'
fit(
x,
y,
delta = numeric(0),
stepsEM = 1000,
equal_marginals = FALSE,
r = 1,
maxit = 100,
reltol = 1e-08
)
Arguments
x |
An object of class mph. |
y |
Matrix of data. |
delta |
Matrix with right-censoring indicators (1 uncensored, 0 right censored). |
stepsEM |
Number of EM steps to be performed. |
equal_marginals |
Logical. If |
r |
Sub-sampling parameter, defaults to 1. |
maxit |
Maximum number of iterations when optimizing g function. |
reltol |
Relative tolerance when optimizing g function. |
Examples
obj <- mph(structure = c("general", "coxian"))
data <- sim(obj, 100)
fit(x = obj, y = data, stepsEM = 20)
Fit method for ph class
Description
Fit method for ph class
Usage
## S4 method for signature 'ph'
fit(
x,
y,
weight = numeric(0),
rcen = numeric(0),
rcenweight = numeric(0),
stepsEM = 1000,
methods = c("RK", "RK"),
rkstep = NA,
uni_epsilon = NA,
maxit = 100,
reltol = 1e-08,
every = 100,
r = 1
)
Arguments
x |
An object of class ph. |
y |
Vector or data. |
weight |
Vector of weights. |
rcen |
Vector of right-censored observations. |
rcenweight |
Vector of weights for right-censored observations. |
stepsEM |
Number of EM steps to be performed. |
methods |
Methods to use for matrix exponential calculation: RM, UNI or PADE. |
rkstep |
Runge-Kutta step size (optional). |
uni_epsilon |
Epsilon parameter for uniformization method. |
maxit |
Maximum number of iterations when optimizing g function. |
reltol |
Relative tolerance when optimizing g function. |
every |
Number of iterations between likelihood display updates. |
r |
Sub-sampling proportion for stochastic EM, defaults to 1. |
Value
An object of class ph.
Examples
obj <- iph(ph(structure = "general", dimension = 2), gfun = "weibull", gfun_pars = 2)
data <- sim(obj, n = 100)
fit(obj, data, stepsEM = 100, every = 20)
New generic for the hazard rate of matrix distributions
Description
Methods are available for objects of class ph.
Usage
haz(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Hazard rate from the matrix distribution.
Hazard rate method for phase-type distributions
Description
Hazard rate method for phase-type distributions
Usage
## S4 method for signature 'ph'
haz(x, y)
Arguments
x |
An object of class ph. |
y |
A vector of locations. |
Value
A vector containing the hazard rate evaluations at the given locations.
Examples
obj <- ph(structure = "general")
haz(obj, c(1, 2, 3))
L inf norm of a matrix
Description
Computes the L inf norm of a matrix A, which is defined as:
L_inf(A) = max(1 <= i <= M) sum(1 <= j <= N) abs(A(i,j)).
Usage
inf_norm(A)
Arguments
A |
A matrix. |
Value
The L inf norm.
Initial state of Markov jump process
Description
Given the accumulated values of the initial probabilities alpha and a
uniform value u, it returns the initial state of a Markov jump process.
This corresponds to the states satisfying cum_alpha_(k-1) < u < cum_alpha_(k).
Usage
initial_state(cum_alpha, u)
Arguments
cum_alpha |
A cummulated vector of initial probabilities. |
u |
Random value in (0,1). |
Value
Initial state of the Markov jump process.
Constructor function for inhomogeneous phase-type distributions
Description
Constructor function for inhomogeneous phase-type distributions
Usage
iph(
ph = NULL,
gfun = NULL,
gfun_pars = NULL,
alpha = NULL,
S = NULL,
structure = NULL,
dimension = 3,
scale = 1
)
Arguments
ph |
An object of class ph. |
gfun |
Inhomogeneity transform. |
gfun_pars |
The parameters of the inhomogeneity function. |
alpha |
A probability vector. |
S |
A sub-intensity matrix. |
structure |
A valid ph structure. |
dimension |
The dimension of the ph structure (if provided). |
scale |
Scale. |
Value
An object of class iph.
Examples
iph(ph(structure = "coxian", dimension = 4), gfun = "pareto", gfun_pars = 3)
Inhomogeneous phase-type distributions
Description
Class of objects for inhomogeneous phase-type distributions.
Value
Class object.
Slots
nameName of the phase-type distribution.
gfunA list comprising of the parameters.
scaleScale.
New generic for Laplace transform of matrix distributions
Description
Methods are available for objects of class ph.
Usage
laplace(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Laplace transform of the matrix distribution.
Laplace method for bivph class
Description
Laplace method for bivph class
Usage
## S4 method for signature 'bivph'
laplace(x, r)
Arguments
x |
An object of class mph. |
r |
A matrix of real values. |
Value
A vector containing the corresponding Laplace transform evaluations.
Examples
obj <- bivph(dimensions = c(3, 3))
laplace(obj, matrix(c(0.5, 1), ncol = 2))
Laplace method for multivariate phase-type distributions
Description
Laplace method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
laplace(x, r)
Arguments
x |
An object of class mph. |
r |
A matrix of real values. |
Value
A vector containing the corresponding Laplace transform evaluations.
Examples
set.seed(123)
obj <- mph(structure = c("general", "general"))
laplace(obj, matrix(c(0.5, 1), ncol = 2))
Laplace method for phase-type distributions
Description
Laplace method for phase-type distributions
Usage
## S4 method for signature 'ph'
laplace(x, r)
Arguments
x |
An object of class ph. |
r |
A vector of real values. |
Value
The Laplace transform of the ph (or underlying ph) object at the given locations.
Examples
set.seed(123)
obj <- ph(structure = "general", dimension = 3)
laplace(obj, 3)
New generic for linear combinations of multivariate matrix distributions
Description
Methods are available for objects of multivariate classes.
Usage
linCom(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Marginal of the matrix distribution.
Linear combination method for MPHstar class
Description
Linear combination method for MPHstar class
Usage
## S4 method for signature 'MPHstar'
linCom(x, w)
Arguments
x |
An object of class MPHstar. |
w |
A vector with non-negative entries. |
Value
An object of class ph.
Examples
obj <- MPHstar(structure = "general")
linCom(obj, c(1, 0))
Linear combination method for bivariate phase-type distributions
Description
Linear combination method for bivariate phase-type distributions
Usage
## S4 method for signature 'bivph'
linCom(x, w = c(1, 1))
Arguments
x |
An object of class bivph. |
w |
A vector with non-negative entries. |
Value
An object of class ph.
Examples
obj <- bivph(dimensions = c(3, 3))
linCom(obj, c(1, 0))
Computes PH parameters of a linear combination of vector from MPHstar
Description
Computes PH parameters of a linear combination of vector from MPHstar
Usage
linear_combination(w, alpha, S, R)
Arguments
w |
Vector with weights. |
alpha |
Initial distribution vector. |
S |
Sub-intensity matrix. |
R |
Reward matrix. |
Value
A list of PH parameters.
Loglikelihood method for ph class
Description
Loglikelihood method for ph class
Usage
## S4 method for signature 'ph'
logLik(object)
Arguments
object |
An object of class ph. |
Value
An object of class logLik.
Examples
obj <- iph(ph(structure = "general", dimension = 2), gfun = "weibull", gfun_pars = 2)
data <- sim(obj, n = 100)
fitted_ph <- fit(obj, data, stepsEM = 10)
logLik(fitted_ph)
Loglikelihood for discrete phase-type
Description
Loglikelihood for discrete phase-type
Usage
logLikelihoodDPH(alpha, S, obs, weight)
Arguments
alpha |
Initial probabilities. |
S |
Sub-transition matrix. |
obs |
The observations. |
weight |
The weights of the observations. |
Loglikelihood for discrete phase-type MoE
Description
Loglikelihood for discrete phase-type MoE
Usage
logLikelihoodDPH_MoE(alpha, S, obs, weight)
Arguments
alpha |
Initial probabilities. |
S |
Sub-transition matrix. |
obs |
The observations. |
weight |
The weights of the observations. |
Loglikelihood of matrix-GEV using Pade
Description
Loglikelihood for a sample
Usage
logLikelihoodMgev_PADE(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
Loglikelihood of matrix-GEV using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMgev_RK(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of matrix-GEV using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMgev_UNI(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of matrix-Gompertz using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMgompertz_PADE(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
Loglikelihood of PI with matrix-Gompertz using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMgompertz_PADEs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-Gompertz using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMgompertz_RK(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-Gompertz using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMgompertz_RKs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-Gompertz using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMgompertz_UNI(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-Gompertz using Uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMgompertz_UNIs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-loglogistic using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMloglogistic_PADE(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
Loglikelihood of PI with matrix-loglogistic using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMloglogistic_PADEs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-loglogistic using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMloglogistic_RK(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameters of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-loglogistic using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMloglogistic_RKs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameters of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-loglogistic using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMloglogistic_UNI(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-loglogistic using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMloglogistic_UNIs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-lognormal using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMlognormal_PADE(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
Loglikelihood of PI with matrix-lognormal using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMlognormal_PADEs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-lognormal using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMlognormal_RK(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI matrix-lognormal using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMlognormal_RKs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-lognormal using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMlognormal_UNI(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-lognormal using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMlognormal_UNIs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-Pareto using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMpareto_PADE(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
Loglikelihood of PI with matrix-Pareto using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMpareto_PADEs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-Pareto using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMpareto_RK(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-Pareto using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMpareto_RKs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-Pareto using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMpareto_UNI(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-Pareto using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMpareto_UNIs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-Weibull using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMweibull_PADE(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
Loglikelihood of PI with matrix-Weibull using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodMweibull_PADEs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Inhomogeneity parameter. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-Weibull using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMweibull_RK(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-Weibull using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodMweibull_RKs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of matrix-Weibull using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMweibull_UNI(h, alpha, S, beta, obs, weight, rcens, rcweight)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with matrix-Weibull using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodMweibull_UNIs(
h,
alpha,
S,
beta,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of transformation. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood for PH-MoE
Description
Loglikelihood for PH-MoE
Usage
logLikelihoodPH_MoE(alpha1, alpha2, S, obs, weight, rcens, rcweight)
Arguments
alpha1 |
Initial probabilities for non-censored data. |
alpha2 |
Initial probabilities for censored data. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
Loglikelihood of phase-type using Pade approximation
Description
Loglikelihood for a sample.
Usage
logLikelihoodPH_PADE(h, alpha, S, obs, weight, rcens, rcweight)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
Loglikelihood of PI with phase-type using Pade
Description
Loglikelihood for a sample.
Usage
logLikelihoodPH_PADEs(
h,
alpha,
S,
obs,
weight,
rcens,
rcweight,
scale1,
scale2
)
Arguments
h |
Nuisance parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
The weights of the observations. |
rcens |
Censored observations. |
rcweight |
The weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of phase-type using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodPH_RK(h, alpha, S, obs, weight, rcens, rcweight)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with phase-type using Runge-Kutta
Description
Loglikelihood for a sample.
Usage
logLikelihoodPH_RKs(h, alpha, S, obs, weight, rcens, rcweight, scale1, scale2)
Arguments
h |
Step-length. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood of phase-type using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodPH_UNI(h, alpha, S, obs, weight, rcens, rcweight)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
Loglikelihood of PI with phase-type using uniformization
Description
Loglikelihood for a sample.
Usage
logLikelihoodPH_UNIs(h, alpha, S, obs, weight, rcens, rcweight, scale1, scale2)
Arguments
h |
Positive parameter. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
obs |
The observations. |
weight |
Weights of the observations. |
rcens |
Censored observations. |
rcweight |
Weights of the censored observations. |
scale1 |
Scale for observations. |
scale2 |
Scale for censored observations. |
Loglikelihood for bivariate discrete phase-type
Description
Loglikelihood for bivariate discrete phase-type
Usage
logLikelihoodbivDPH(alpha, S11, S12, S22, obs, weight)
Arguments
alpha |
Initial probabilities. |
S11 |
Sub-transition matrix. |
S12 |
Matrix. |
S22 |
Sub-transition matrix. |
obs |
The observations. |
weight |
The weights of the observations. |
Loglikelihood for bivariate discrete phase-type MoE
Description
Loglikelihood for bivariate discrete phase-type MoE
Usage
logLikelihoodbivDPH_MoE(alpha, S11, S12, S22, obs, weight)
Arguments
alpha |
Initial probabilities. |
S11 |
Sub-transition matrix. |
S12 |
Matrix. |
S22 |
Sub-transition matrix. |
obs |
The observations. |
weight |
The weights of the observations. |
Loglikelihood for Bivariate PH
Description
Loglikelihood for Bivariate PH
Usage
logLikelihoodbivPH(alpha, S11, S12, S22, obs, weight)
Arguments
alpha |
Vector of initial probabilities. |
S11 |
Sub-intensity matrix. |
S12 |
Matrix. |
S22 |
Sub-intensity matrix. |
obs |
The observations. |
weight |
The weights of the observations. |
Loglikelihood for multivariate discrete phase-type
Description
Loglikelihood for multivariate discrete phase-type
Usage
logLikelihoodmDPH(alpha, S_list, obs, weight)
Arguments
alpha |
Initial probabilities. |
S_list |
List of marginal sub-transition matrices. |
obs |
The observations. |
weight |
The weights of the observations. |
Loglikelihood for multivariate discrete phase-type MoE
Description
Loglikelihood for multivariate discrete phase-type MoE
Usage
logLikelihoodmDPH_MoE(alpha, S_list, obs, weight)
Arguments
alpha |
Initial probabilities. |
S_list |
List of marginal sub-transition matrices. |
obs |
The observations. |
weight |
The weights of the observations. |
Computes exp(Sx) via series representation
Description
Computes exp(Sx) via series representation
Usage
m_exp_sum(x, n, pow_vector, a)
Arguments
x |
A number. |
n |
An integer. |
pow_vector |
A vector. |
a |
A number. |
New generic for the marginals of multivariate matrix distributions
Description
Methods are available for objects of multivariate classes.
Usage
marginal(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Marginal of the matrix distribution.
Marginal method for MPHstar class
Description
Marginal method for MPHstar class
Usage
## S4 method for signature 'MPHstar'
marginal(x, mar = 1)
Arguments
x |
An object of class MPHstar. |
mar |
Indicator of which marginal. |
Value
An object of the of class ph.
Examples
obj <- MPHstar(structure = "general")
marginal(obj, 1)
Marginal method for bivdph class
Description
Marginal method for bivdph class
Usage
## S4 method for signature 'bivdph'
marginal(x, mar = 1)
Arguments
x |
An object of class bivdph. |
mar |
Indicator of which marginal. |
Value
An object of the of class dph.
Examples
obj <- bivdph(dimensions = c(3, 3))
marginal(obj, 1)
Marginal method for biviph class
Description
Marginal method for biviph class
Usage
## S4 method for signature 'biviph'
marginal(x, mar = 1)
Arguments
x |
An object of class biviph. |
mar |
Indicator of which marginal. |
Value
An object of the of class iph.
Examples
under_bivph <- bivph(dimensions = c(3, 3))
obj <- biviph(under_bivph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
marginal(obj, 1)
Marginal method for bivph class
Description
Marginal method for bivph class
Usage
## S4 method for signature 'bivph'
marginal(x, mar = 1)
Arguments
x |
An object of class bivph. |
mar |
Indicator of which marginal. |
Value
An object of the of class ph.
Examples
obj <- bivph(dimensions = c(3, 3))
marginal(obj, 1)
Marginal method for mdph class
Description
Marginal method for mdph class
Usage
## S4 method for signature 'mdph'
marginal(x, mar = 1)
Arguments
x |
An object of class mdph. |
mar |
Indicator of which marginal. |
Value
An object of the of class dph.
Examples
obj <- mdph(structure = c("general", "general"))
marginal(obj, 1)
Marginal method for multivariate inhomogeneous phase-type distributions
Description
Marginal method for multivariate inhomogeneous phase-type distributions
Usage
## S4 method for signature 'miph'
marginal(x, mar = 1)
Arguments
x |
An object of class miph. |
mar |
Indicator of which marginal. |
Value
An object of the of class iph.
Examples
under_mph <- mph(structure = c("general", "general"))
obj <- miph(under_mph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
marginal(obj, 1)
Marginal method for multivariate phase-type distributions
Description
Marginal method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
marginal(x, mar = 1)
Arguments
x |
An object of class mph. |
mar |
Indicator of which marginal. |
Value
An object of the of class ph.
Examples
obj <- mph(structure = c("general", "general"))
marginal(obj, 1)
Marginal conditional expectations
Description
Marginal conditional expectations
Usage
marginal_expectation(rew, pos, N, alpha, S, obs, weight)
Arguments
rew |
Column of the reward matrix corresponding to its marginal. |
pos |
Vector that indicates which state is associated to a positive reward. |
N |
Uniformization parameter. |
alpha |
Marginal initial distribution vector. |
S |
Marginal sub-intensity matrix. |
obs |
Marginal observations. |
weight |
Marginal weights. |
Value
A vector with the expected time spent in each state by the marginal, conditional on the observations.
Matrix exponential
Description
MATLAB's built-in algorithm for matrix exponential - Pade approximation.
Usage
matrix_exponential(A)
Arguments
A |
A matrix. |
Value
exp(A).
Inverse of a matrix
Description
Inverse of a matrix
Usage
matrix_inverse(A)
Arguments
A |
A matrix. |
Value
Inverse of A.
Computes A^n
Description
Computes A^n
Usage
matrix_power(n, A)
Arguments
n |
An integer. |
A |
A matrix. |
Value
A^n.
Product of two matrices
Description
Product of two matrices
Usage
matrix_product(A1, A2)
Arguments
A1 |
A matrix. |
A2 |
A matrix. |
Value
Computes A1 * A2.
Creates the matrix (A1, B1 ; 0, A2)
Description
Creates the matrix (A1, B1 ; 0, A2)
Usage
matrix_vanloan(A1, A2, B1)
Arguments
A1 |
Matrix. |
A2 |
Matrix. |
B1 |
Matrix. |
Value
Computes (A1, B1 ; 0, A2).
Maximum diagonal element of a matrix
Description
Maximum diagonal element of a matrix
Usage
max_diagonal(A)
Arguments
A |
Matrix. |
Value
The maximum value in the diagonal.
New generic for maximum of two matrix distributions
Description
Methods are available for objects of class ph.
Usage
maximum(x1, x2, ...)
Arguments
x1 |
An object of the model class. |
x2 |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
An object of the model class.
Maximum method for discrete phase-type distributions
Description
Maximum method for discrete phase-type distributions
Usage
## S4 method for signature 'dph,dph'
maximum(x1, x2)
Arguments
x1 |
An object of class dph. |
x2 |
An object of class dph. |
Value
An object of class dph.
Examples
dph1 <- dph(structure = "general", dimension = 3)
dph2 <- dph(structure = "general", dimension = 5)
dph_max <- maximum(dph1, dph2)
dph_max
Maximum method for inhomogeneous phase-type distributions
Description
Maximum method for inhomogeneous phase-type distributions
Usage
## S4 method for signature 'iph,iph'
maximum(x1, x2)
Arguments
x1 |
An object of class iph. |
x2 |
An object of class iph. |
Value
An object of class iph.
Examples
iph1 <- iph(ph(structure = "general", dimension = 3), gfun = "weibull", gfun_pars = 2)
iph2 <- iph(ph(structure = "gcoxian", dimension = 5), gfun = "weibull", gfun_pars = 2)
iph_min <- maximum(iph1, iph2)
iph_min
Maximum method for phase-type distributions
Description
Maximum method for phase-type distributions
Usage
## S4 method for signature 'ph,ph'
maximum(x1, x2)
Arguments
x1 |
An object of class ph. |
x2 |
An object of class ph. |
Value
An object of class ph.
Examples
ph1 <- ph(structure = "general", dimension = 3)
ph2 <- ph(structure = "gcoxian", dimension = 5)
ph_max <- maximum(ph1, ph2)
ph_max
Constructor function for multivariate discrete phase-type distributions
Description
Constructor function for multivariate discrete phase-type distributions
Usage
mdph(alpha = NULL, S = NULL, structure = NULL, dimension = 3, variables = NULL)
Arguments
alpha |
A probability vector. |
S |
A list of sub-transition matrices. |
structure |
A vector of valid ph structures. |
dimension |
The dimension of the dph structure (if provided). |
variables |
The dimension of the multivariate discrete phase-type. |
Value
An object of class mdph.
Examples
mdph(structure = c("general", "general"), dimension = 5)
Multivariate discrete phase-type distributions
Description
Class of objects for multivariate discrete phase-type distributions.
Value
Class object.
Slots
nameName of the discrete phase-type distribution.
parsA list comprising of the parameters.
fitA list containing estimation information.
Multivariate discrete phase-type density
Description
Computes the density of multivariate discrete phase-type distribution with
parameters alpha and S at x.
Usage
mdphdensity(x, alpha, S_list)
Arguments
x |
Matrix of positive integer values. |
alpha |
Initial probabilities. |
S_list |
List of marginal sub-transition matrices. |
Value
The density at x.
Mean method for MPHstar class
Description
Mean method for MPHstar class
Usage
## S4 method for signature 'MPHstar'
mean(x)
Arguments
x |
An object of class MPHstar. |
Value
The mean of MPHstar distribution.
Examples
obj <- MPHstar(structure = "general")
mean(obj)
Mean method for bivdph class
Description
Mean method for bivdph class
Usage
## S4 method for signature 'bivdph'
mean(x)
Arguments
x |
An object of class bivdph. |
Value
The mean of the bivariate discrete phase-type distribution.
Examples
obj <- bivdph(dimensions = c(3, 3))
mean(obj)
Mean Method for bivph class
Description
Mean Method for bivph class
Usage
## S4 method for signature 'bivph'
mean(x)
Arguments
x |
An object of class bivph. |
Value
The mean of the bivariate phase-type distribution.
Examples
obj <- bivph(dimensions = c(3, 3))
mean(obj)
Mean method for discrete phase-type distributions
Description
Mean method for discrete phase-type distributions
Usage
## S4 method for signature 'dph'
mean(x)
Arguments
x |
An object of class dph. |
Value
The raw first moment of the dph object.
Examples
set.seed(123)
obj <- dph(structure = "general", dimension = 3)
mean(obj)
Mean method for multivariate discrete phase-type distributions
Description
Mean method for multivariate discrete phase-type distributions
Usage
## S4 method for signature 'mdph'
mean(x)
Arguments
x |
An object of class mdph. |
Value
The mean of the multivariate discrete phase-type distribution.
Examples
obj <- mdph(structure = c("general", "general"))
mean(obj)
Mean method for multivariate phase-type distributions
Description
Mean method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
mean(x)
Arguments
x |
An object of class mph. |
Value
The mean of the multivariate phase-type distribution.
Examples
obj <- mph(structure = c("general", "general"))
mean(obj)
Mean method for phase-type distributions
Description
Mean method for phase-type distributions
Usage
## S4 method for signature 'ph'
mean(x)
Arguments
x |
An object of class ph. |
Value
The raw first moment of the ph (or underlying ph) object.
Examples
set.seed(123)
obj <- ph(structure = "general", dimension = 3)
mean(obj)
Merges the matrices S11, S12 and S22 into a sub-intensity matrix
Description
Merges the matrices S11, S12 and S22 into a sub-intensity matrix
Usage
merge_matrices(S11, S12, S22)
Arguments
S11 |
A sub-intensity matrix. |
S12 |
A matrix. |
S22 |
A sub-intensity matrix. |
Value
A sub-intensity matrix.
Matrix-GEV cdf
Description
Computes the cdf (tail) of a matrix-GEV distribution with parameters
alpha, S and beta at x.
Usage
mgevcdf(x, alpha, S, beta, lower_tail = TRUE)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Transformation parameters. |
lower_tail |
Cdf or tail. |
Value
The cdf (tail) at x.
Matrix-GEV density
Description
Computes the density of a matrix-GEV distribution with parameters
alpha, S and beta at x.
Does not allow for atoms in zero.
Usage
mgevden(x, alpha, S, beta)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Transformation parameters. |
Value
The density at x.
New generic for mgf of matrix distributions
Description
Methods are available for objects of class ph.
Usage
mgf(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Mgf of the matrix distribution.
Mgf method for bivph class
Description
Mgf method for bivph class
Usage
## S4 method for signature 'bivph'
mgf(x, r)
Arguments
x |
An object of class mph. |
r |
A matrix of real values. |
Value
A vector containing the corresponding mgf evaluations.
Examples
set.seed(123)
obj <- bivph(dimensions = c(3, 3))
mgf(obj, matrix(c(0.5, 0.1), ncol = 2))
Mgf method for multivariate phase-type distributions
Description
Mgf method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
mgf(x, r)
Arguments
x |
An object of class mph. |
r |
A matrix of real values. |
Value
A vector containing the corresponding mgf evaluations.
Examples
set.seed(124)
obj <- mph(structure = c("general", "general"))
mgf(obj, matrix(c(0.5, 0.3), ncol = 2))
Mgf method for phase-type distributions
Description
Mgf method for phase-type distributions
Usage
## S4 method for signature 'ph'
mgf(x, r)
Arguments
x |
An object of class ph. |
r |
A vector of real values. |
Value
The mgf of the ph (or underlying ph) object at the given locations.
Examples
set.seed(123)
obj <- ph(structure = "general", dimension = 3)
mgf(obj, 0.4)
Matrix-Gompertz cdf
Description
Computes the cdf (tail) of a matrix-Gompertz distribution with parameters
alpha, S and beta at x.
Usage
mgompertzcdf(x, alpha, S, beta, lower_tail = TRUE)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Shape parameter. |
lower_tail |
Cdf or tail. |
Value
The cdf (tail) at x.
Matrix-Gompertz density
Description
Computes the density of a matrix-Gompertz distribution with parameters
alpha, S and beta at x.
Usage
mgompertzden(x, alpha, S, beta)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Shape parameter. |
Value
The density at x.
New generic for minimum of two matrix distributions
Description
Methods are available for objects of class ph.
Usage
minimum(x1, x2, ...)
Arguments
x1 |
An object of the model class. |
x2 |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
An object of the model class.
Minimum method for discrete phase-type distributions
Description
Minimum method for discrete phase-type distributions
Usage
## S4 method for signature 'dph,dph'
minimum(x1, x2)
Arguments
x1 |
An object of class dph. |
x2 |
An object of class dph. |
Value
An object of class dph.
Examples
dph1 <- dph(structure = "general", dimension = 3)
dph2 <- dph(structure = "general", dimension = 5)
dph_min <- minimum(dph1, dph2)
dph_min
Minimum method for inhomogeneous phase-type distributions
Description
Minimum method for inhomogeneous phase-type distributions
Usage
## S4 method for signature 'iph,iph'
minimum(x1, x2)
Arguments
x1 |
An object of class iph. |
x2 |
An object of class iph. |
Value
An object of class iph.
Examples
iph1 <- iph(ph(structure = "general", dimension = 3), gfun = "weibull", gfun_pars = 2)
iph2 <- iph(ph(structure = "gcoxian", dimension = 5), gfun = "weibull", gfun_pars = 2)
iph_min <- minimum(iph1, iph2)
iph_min
Minimum method for phase-type distributions
Description
Minimum method for phase-type distributions
Usage
## S4 method for signature 'ph,ph'
minimum(x1, x2)
Arguments
x1 |
An object of class ph. |
x2 |
An object of class ph. |
Value
An object of class ph.
Examples
ph1 <- ph(structure = "general", dimension = 3)
ph2 <- ph(structure = "gcoxian", dimension = 5)
ph_min <- minimum(ph1, ph2)
ph_min
Constructor function for multivariate inhomogeneous phase-type distributions
Description
Constructor function for multivariate inhomogeneous phase-type distributions
Usage
miph(
mph = NULL,
gfun = NULL,
gfun_pars = NULL,
alpha = NULL,
S = NULL,
structure = NULL,
dimension = 3,
variables = NULL,
scale = 1
)
Arguments
mph |
An object of class mph. |
gfun |
Vector of inhomogeneity transforms. |
gfun_pars |
List of parameters for the inhomogeneity functions. |
alpha |
A probability vector. |
S |
A list of sub-intensity matrices. |
structure |
A vector of valid ph structures. |
dimension |
The dimension of the ph structure (if provided). |
variables |
Number of marginals. |
scale |
Scale. |
Value
An object of class iph.
Examples
under_mph <- mph(structure = c("gcoxian", "general"), dimension = 4)
miph(under_mph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
Multivariate inhomogeneous phase-type distributions
Description
Class of objects for multivariate inhomogeneous phase-type distributions.
Value
Class object.
Slots
nameName of the phase type distribution.
gfunA list comprising of the parameters.
scaleScale.
New generic for mixture of two matrix distributions
Description
Methods are available for objects of classes ph and dph.
Usage
mixture(x1, x2, ...)
Arguments
x1 |
An object of the model class. |
x2 |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
An object of the model class.
Mixture method for phase-type distributions
Description
Mixture method for phase-type distributions
Usage
## S4 method for signature 'dph,dph'
mixture(x1, x2, prob)
Arguments
x1 |
An object of class dph. |
x2 |
An object of class dph. |
prob |
Probability for first object. |
Value
An object of class dph.
Examples
dph1 <- dph(structure = "general", dimension = 3)
dph2 <- dph(structure = "general", dimension = 5)
dph_mix <- mixture(dph1, dph2, 0.5)
dph_mix
Mixture method for phase-type distributions
Description
Mixture method for phase-type distributions
Usage
## S4 method for signature 'ph,ph'
mixture(x1, x2, prob)
Arguments
x1 |
An object of class ph. |
x2 |
An object of class ph. |
prob |
Probability for first object. |
Value
An object of class ph.
Examples
ph1 <- ph(structure = "general", dimension = 3)
ph2 <- ph(structure = "gcoxian", dimension = 5)
ph_mix <- mixture(ph1, ph2, 0.5)
ph_mix
Matrix-loglogistic cdf
Description
Computes the cdf (tail) of a matrix-loglogistic distribution with parameters
alpha, S and beta at x.
Usage
mloglogisticcdf(x, alpha, S, beta, lower_tail = TRUE)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Transformation parameters. |
lower_tail |
Cdf or tail. |
Value
The cdf (tail) at x.
Matrix-loglogistic density
Description
Computes the density of a matrix-loglogistic distribution with parameters
alpha, S and beta at x.
Usage
mloglogisticden(x, alpha, S, beta)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Transformation parameters. |
Value
The density at x.
Matrix-lognormal cdf
Description
Computes the cdf (tail) of a matrix-lognormal distribution with parameters
alpha, S and beta at x.
Usage
mlognormalcdf(x, alpha, S, beta, lower_tail = TRUE)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Shape parameter. |
lower_tail |
Cdf or tail. |
Value
The cdf (tail) at x.
Matrix-lognormal density
Description
Computes the density of a matrix-lognormal distribution with parameters
alpha, S and beta at x.
Usage
mlognormalden(x, alpha, S, beta)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Shape parameter. |
Value
The density at x.
New generic for moments of matrix distributions
Description
Methods are available for objects of class ph.
Usage
moment(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Moment of the matrix distribution.
Moment method for bivdph class
Description
Moment method for bivdph class
Usage
## S4 method for signature 'bivdph'
moment(x, k = c(1, 1))
Arguments
x |
An object of class bivdph. |
k |
A vector with the location. |
Value
An real value.
Examples
obj <- bivdph(dimensions = c(3, 3))
moment(obj, c(1, 1))
Moment method for bivph class
Description
Moment method for bivph class
Usage
## S4 method for signature 'bivph'
moment(x, k = c(1, 1))
Arguments
x |
An object of class bivph. |
k |
A vector with the location. |
Value
An real value.
Examples
obj <- bivph(dimensions = c(3, 3))
moment(obj, c(1, 1))
Moment method for discrete phase-type distributions
Description
Moment method for discrete phase-type distributions
Usage
## S4 method for signature 'dph'
moment(x, k = 1)
Arguments
x |
An object of class dph. |
k |
A positive integer (moment order). |
Value
The factional moment of the dph object.
Examples
set.seed(123)
obj <- dph(structure = "general", dimension = 3)
moment(obj, 2)
Moment method for multivariate discrete phase-type distributions
Description
Moment method for multivariate discrete phase-type distributions
Usage
## S4 method for signature 'mdph'
moment(x, k)
Arguments
x |
An object of class mdph. |
k |
A vector of positive integer values. |
Value
The corresponding joint factorial moment evaluation.
Examples
obj <- mdph(structure = c("general", "general"))
moment(obj, c(2, 1))
Moment method for multivariate phase-type distributions
Description
Moment method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
moment(x, k)
Arguments
x |
An object of class mph. |
k |
A vector of non-negative integer values. |
Value
The corresponding joint moment evaluation.
Examples
obj <- mph(structure = c("general", "general"))
moment(obj, c(2, 1))
Moment method for phase-type distributions
Description
Moment method for phase-type distributions
Usage
## S4 method for signature 'ph'
moment(x, k = 1)
Arguments
x |
An object of class ph. |
k |
A positive integer (moment order). |
Value
The raw moment of the ph (or underlying ph) object.
Examples
set.seed(123)
obj <- ph(structure = "general", dimension = 3)
moment(obj, 2)
Matrix-Pareto cdf
Description
Computes the cdf (tail) of a matrix-Pareto distribution with parameters
alpha, S and beta at x.
Usage
mparetocdf(x, alpha, S, beta, lower_tail = TRUE)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Scale parameter. |
lower_tail |
Cdf or tail. |
Value
The cdf (tail) at x.
Matrix-Pareto density
Description
Computes the density of a matrix-Pareto distribution with parameters
alpha, S and beta at x.
Usage
mparetoden(x, alpha, S, beta)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Scale parameter. |
Value
The density at x.
Constructor function for multivariate phase-type distributions
Description
Constructor function for multivariate phase-type distributions
Usage
mph(alpha = NULL, S = NULL, structure = NULL, dimension = 3, variables = NULL)
Arguments
alpha |
A probability vector. |
S |
A list of sub-intensity matrices. |
structure |
A vector of valid ph structures. |
dimension |
The dimension of the ph structure (if provided). |
variables |
The dimension of the multivariate phase-type. |
Value
An object of class mph.
Examples
mph(structure = c("gcoxian", "general"), dimension = 5)
Multivariate phase-type distributions
Description
Class of objects for multivariate phase-type distributions.
Value
Class object.
Slots
nameName of the phase type distribution.
parsA list comprising of the parameters.
fitA list containing estimation information.
Matrix-Weibull cdf
Description
Computes the cdf (tail) of a matrix-Weibull distribution with parameters
alpha, S and beta at x.
Usage
mweibullcdf(x, alpha, S, beta, lower_tail = TRUE)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Shape parameter. |
lower_tail |
Cdf or tail. |
Value
The cdf (tail) at x.
Matrix-Weibull density
Description
Computes the density of a matrix-Weibull distribution with parameters
alpha, S and beta at x.
Usage
mweibullden(x, alpha, S, beta)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Shape parameter. |
Value
The density at x.
Find how many states have positive reward
Description
Find how many states have positive reward
Usage
n_pos(R)
Arguments
R |
reward vector |
Value
The number of states with positive rewards
New state in a Markov jump process
Description
Given a transition matrix Q, a uniform value u, and a previous
state k, it returns the new state of a Markov jump process.
Usage
new_state(prev_state, cum_embedded_mc, u)
Arguments
prev_state |
Previous state of the Markov jump process. |
cum_embedded_mc |
Transition matrix. |
u |
Random value in (0,1). |
Value
Next state of the Markov jump process.
New generic for pgf of matrix distributions
Description
Methods are available for objects of class dph.
Usage
pgf(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Pgf of the matrix distribution.
Pgf method for bivariate discrete phase-type distributions
Description
Pgf method for bivariate discrete phase-type distributions
Usage
## S4 method for signature 'bivdph'
pgf(x, z)
Arguments
x |
An object of class bivdph. |
z |
A vector of real values. |
Value
The joint pdf of the dph object at the given location.
Examples
obj <- bivdph(dimensions = c(3, 3))
pgf(obj, c(0.5, 0.2))
Pgf Method for discrete phase-type distributions
Description
Pgf Method for discrete phase-type distributions
Usage
## S4 method for signature 'dph'
pgf(x, z)
Arguments
x |
An object of class dph. |
z |
A vector of real values. |
Value
The probability generating of the dph object at the given locations.
Examples
set.seed(123)
obj <- dph(structure = "general", dimension = 3)
pgf(obj, 0.5)
Pgf method for multivariate discrete phase-type distributions
Description
Pgf method for multivariate discrete phase-type distributions
Usage
## S4 method for signature 'mdph'
pgf(x, z)
Arguments
x |
An object of class mdph. |
z |
A matrix of real values. |
Value
A vector containing the corresponding pgf evaluations.
Examples
obj <- mdph(structure = c("general", "general"))
pgf(obj, matrix(c(0.5, 1), ncol = 2))
Constructor function for phase-type distributions
Description
Constructor function for phase-type distributions
Usage
ph(alpha = NULL, S = NULL, structure = NULL, dimension = 3)
Arguments
alpha |
A probability vector. |
S |
A sub-intensity matrix. |
structure |
A valid ph structure: |
dimension |
The dimension of the ph structure (if structure is provided). |
Value
An object of class ph.
Examples
ph(structure = "gcoxian", dimension = 5)
ph(alpha = c(.5, .5), S = matrix(c(-1, .5, .5, -1), 2, 2))
Phase-type distributions
Description
Class of objects for phase-type distributions.
Value
Class object.
Slots
nameName of the phase-type distribution.
parsA list comprising of the parameters.
fitA list containing estimation information.
Laplace transform of a phase-type distribution
Description
Computes the Laplace transform at r of a phase-type distribution with
parameters alpha and S.
Usage
ph_laplace(r, alpha, S)
Arguments
r |
Vector of real values. |
alpha |
Vector of initial probabilities. |
S |
Sub-intensity matrix. |
Value
Laplace transform at r.
Phase-type cdf
Description
Computes the cdf (tail) of a phase-type distribution with parameters
alpha and S at x.
Usage
phcdf(x, alpha, S, lower_tail = TRUE)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
lower_tail |
Cdf or tail. |
Value
The cdf (tail) at x.
Phase-type density
Description
Computes the density of a phase-type distribution with parameters
alpha and S at x.
Usage
phdensity(x, alpha, S)
Arguments
x |
Non-negative value. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
Value
The density at x.
Find which states have positive reward
Description
Find which states have positive reward
Usage
plus_states(R)
Arguments
R |
reward vector |
Value
A vector with the states (number) that are associated with positive rewards
Computes A^(2^n)
Description
Computes A^(2^n)
Usage
pow2_matrix(n, A)
Arguments
n |
An integer. |
A |
A matrix. |
Value
A^(2^n).
New generic for the quantile of matrix distributions
Description
Methods are available for objects of class ph.
Usage
quan(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
Quantile from the matrix distribution.
Quantile method for phase-type distributions
Description
Quantile method for phase-type distributions
Usage
## S4 method for signature 'ph'
quan(x, p)
Arguments
x |
An object of class ph. |
p |
A vector of probabilities. |
Value
A vector containing the quantile evaluations at the given locations.
Examples
obj <- ph(structure = "general")
quan(obj, c(0.5, 0.9, 0.99))
Simulate MDPH*
Description
Generates a sample of size n from a MDPH* distribution with
parameters alpha, S, and R.
Usage
rMDPHstar(n, alpha, S, R)
Arguments
n |
Sample size. |
alpha |
Vector of initial probabilities. |
S |
Sub-transition matrix. |
R |
Reward matrix. |
Value
Simulated sample.
Simulate a MIPH* random vector
Description
Generates a sample of size n from a MIPH* distribution with parameters
alpha, S and R.
Usage
rMIPHstar(n, alpha, S, R, gfun, gfun_par)
Arguments
n |
Sample size. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
R |
Reward matrix. |
gfun |
Vector with transformations names. |
gfun_par |
List with transformations parameters. |
Value
The simulated sample.
Simulate a MPH* random vector
Description
Generates a sample of size n from a MPH* distribution with parameters
alpha, S and R.
Usage
rMPHstar(n, alpha, S, R)
Arguments
n |
Sample size. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
R |
Reward matrix. |
Value
The simulated sample.
Random reward matrix
Description
Generates a random reward matrix for a multivariate phase-type distribution with p states and d marginals.
Usage
random_reward(p, d)
Arguments
p |
Number of transient states in the sub-intensity matrix. |
d |
Number of marginals. |
Value
A random reward matrix.
Random structure of a phase-type
Description
Generates random parameters alpha and S of a phase-type
distribution of dimension p with chosen structure.
Usage
random_structure(p, structure = "general", scale_factor = 1)
Arguments
p |
Dimension of the phase-type. |
structure |
Type of structure: "general", "hyperexponential", "gerlang", "coxian" or "gcoxian". |
scale_factor |
A factor that multiplies the sub-intensity matrix. |
Value
Random parameters alpha and S of a phase-type.
Random structure of a bivariate phase-type
Description
Generates random parameters alpha, S11, S12, and S22
of a bivariate phase-type distribution of dimension p = p1 + p2.
Usage
random_structure_bivph(p1, p2, scale_factor = 1)
Arguments
p1 |
Dimension of the first block. |
p2 |
Dimension of the second block. |
scale_factor |
A factor that multiplies the sub-intensity matrix. |
Value
Random parameters alpha, S11, S12, and S22
of a bivariate phase-type.
Simulate discrete phase-type
Description
Generates a sample of size n from a discrete phase-type distribution with
parameters alpha and S.
Usage
rdphasetype(n, alpha, S)
Arguments
n |
Sample size. |
alpha |
Vector of initial probabilities. |
S |
Sub-transition matrix. |
Value
Simulated sample.
New generic for regression with matrix distributions
Description
Methods are available for objects of class ph.
Usage
reg(x, y, ...)
Arguments
x |
An object of the model class. |
y |
A vector of data. |
... |
Further parameters to be passed on. |
Value
An object of the fitted model class.
Regression method for ph Class
Description
Regression method for ph Class
Usage
## S4 method for signature 'ph'
reg(
x,
y,
weight = numeric(0),
rcen = numeric(0),
rcenweight = numeric(0),
X = numeric(0),
B0 = numeric(0),
stepsEM = 1000,
methods = c("RK", "UNI"),
rkstep = NA,
uni_epsilon = NA,
optim_method = "BFGS",
maxit = 50,
reltol = 1e-08,
every = 10
)
Arguments
x |
An object of class ph. |
y |
Vector or data. |
weight |
Vector of weights. |
rcen |
Vector of right-censored observations. |
rcenweight |
Vector of weights for right-censored observations. |
X |
Model matrix (no intercept needed). |
B0 |
Initial regression coefficients (optional). |
stepsEM |
Number of EM steps to be performed. |
methods |
Methods to use for matrix exponential calculation: |
rkstep |
Runge-Kutta step size (optional). |
uni_epsilon |
Epsilon parameter for uniformization method. |
optim_method |
Method to use in gradient optimization. |
maxit |
Maximum number of iterations when optimizing g function. |
reltol |
Relative tolerance when optimizing g function. |
every |
Number of iterations between likelihood display updates. |
Value
An object of class sph.
Examples
set.seed(1)
obj <- iph(ph(structure = "general", dimension = 2), gfun = "weibull", gfun_pars = 2)
data <- sim(obj, n = 100)
X <- runif(100)
reg(x = obj, y = data, X = X, stepsEM = 10)
Applies the inverse of the GEV transformation but giving back the resulting vector in reverse order
Description
Used for EM step in RK.
Usage
revers_data_trans(obs, weights, beta)
Arguments
obs |
The observations. |
weights |
Weights of the observations. |
beta |
Parameters of the GEV. |
Transform a reward matrix with very small rewards to avoid numerical problems
Description
Transform a reward matrix with very small rewards to avoid numerical problems
Usage
rew_sanity_check(R, tol)
Arguments
R |
Reward matrix |
tol |
Lower bound considered for a reward |
Value
A reward matrix that does not cause issues with uniformization
Random inhomogeneous phase-type
Description
Generates a sample of size n from an inhomogeneous phase-type
distribution with parameters alpha, S and beta.
Usage
riph(n, dist_type, alpha, S, beta)
Arguments
n |
Sample size. |
dist_type |
Type of IPH. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
beta |
Parameter of the transformation. |
Value
The simulated sample.
Random matrix GEV
Description
Generates a sample of size n from an inhomogeneous phase-type
distribution with parameters alpha, S and beta.
Usage
rmatrixgev(n, alpha, S, mu, sigma, xi = 0)
Arguments
n |
Sample size. |
alpha |
Initial probabilities. |
S |
Sub-intensity matrix. |
mu |
Location parameter. |
sigma |
Scale parameter. |
xi |
Shape parameter: Default 0 which corresponds to the Gumbel case. |
Value
The simulated sample.
Simulate phase-type
Description
Generates a sample of size n from a phase-type distribution with
parameters alpha and S.
Usage
rphasetype(n, alpha, S)
Arguments
n |
Sample size. |
alpha |
Vector of initial probabilities. |
S |
Sub-intensity matrix. |
Value
Simulated sample.
Runge-Kutta for the calculation of the a and b vectors and the c matrix in a EM step
Description
Performs the Runge-Kutta method of fourth order.
Usage
runge_kutta(avector, bvector, cmatrix, dt, h, S, s)
Arguments
avector |
The a vector. |
bvector |
The b vector. |
cmatrix |
The c matrix. |
dt |
The increment. |
h |
Step-length. |
S |
Sub-intensity matrix. |
s |
Exit rates. |
Show method for multivariate phase-type distributions
Description
Show method for multivariate phase-type distributions
Usage
## S4 method for signature 'MPHstar'
show(object)
Arguments
object |
An object of class MPHstar. |
Show method for bivariate discrete phase-type distributions
Description
Show method for bivariate discrete phase-type distributions
Usage
## S4 method for signature 'bivdph'
show(object)
Arguments
object |
An object of class bivdph. |
Show method for bivariate inhomogeneous phase-type distributions
Description
Show method for bivariate inhomogeneous phase-type distributions
Usage
## S4 method for signature 'biviph'
show(object)
Arguments
object |
An object of class biviph. |
Show method for bivariate phase-type distributions
Description
Show method for bivariate phase-type distributions
Usage
## S4 method for signature 'bivph'
show(object)
Arguments
object |
An object of class bivph. |
Show method for discrete phase-type distributions
Description
Show method for discrete phase-type distributions
Usage
## S4 method for signature 'dph'
show(object)
Arguments
object |
An object of class dph. |
Show method for inhomogeneous phase-type distributions
Description
Show method for inhomogeneous phase-type distributions
Usage
## S4 method for signature 'iph'
show(object)
Arguments
object |
An object of class iph. |
Show method for multivariate discrete phase-type distributions
Description
Show method for multivariate discrete phase-type distributions
Usage
## S4 method for signature 'mdph'
show(object)
Arguments
object |
An object of class mdph. |
Show method for multivariate inhomogeneous phase-type distributions
Description
Show method for multivariate inhomogeneous phase-type distributions
Usage
## S4 method for signature 'miph'
show(object)
Arguments
object |
An object of class miph. |
Show method for multivariate phase-type distributions
Description
Show method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
show(object)
Arguments
object |
An object of class mph. |
Show method for phase-type distributions
Description
Show method for phase-type distributions
Usage
## S4 method for signature 'ph'
show(object)
Arguments
object |
An object of class ph. |
Show method for survival phase-type objects
Description
Show method for survival phase-type objects
Usage
## S4 method for signature 'sph'
show(object)
Arguments
object |
An object of class sph. |
New generic for simulating matrix distributions
Description
Methods are available for objects of class ph.
Usage
sim(x, ...)
Arguments
x |
An object of the model class. |
... |
Further parameters to be passed on. |
Value
A realization from the matrix distribution.
Simulation method for multivariate phase-type distributions
Description
Simulation method for multivariate phase-type distributions
Usage
## S4 method for signature 'MPHstar'
sim(x, n = 1000)
Arguments
x |
An object of class MPHstar. |
n |
Desired sample size for each marginal. |
Value
A matrix of sample data for each marginal.
Examples
obj <- MPHstar(structure = "general")
sim(obj, 100)
Simulation method for bivariate discrete phase-type distributions
Description
Simulation method for bivariate discrete phase-type distributions
Usage
## S4 method for signature 'bivdph'
sim(x, n = 1000)
Arguments
x |
An object of class bivdph. |
n |
An integer of length of realization. |
Value
A realization of independent and identically distributed bivariate discrete phase-type vector.
Examples
obj <- bivdph(dimensions = c(3, 3))
sim(obj, n = 100)
Simulation method for bivariate inhomogeneous phase-type distributions
Description
Simulation method for bivariate inhomogeneous phase-type distributions
Usage
## S4 method for signature 'biviph'
sim(x, n = 1000)
Arguments
x |
An object of class biviph. |
n |
An integer of length of realization. |
Value
A realization of independent and identically distributed bivariate inhomogeneous phase-type vector.
Examples
under_bivph <- bivph(dimensions = c(3, 3))
obj <- biviph(under_bivph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
sim(obj, n = 100)
Simulation method for bivariate phase-type distributions
Description
Simulation method for bivariate phase-type distributions
Usage
## S4 method for signature 'bivph'
sim(x, n = 1000)
Arguments
x |
An object of class bivph. |
n |
An integer of length of realization. |
Value
A realization of independent and identically distributed bivariate phase-type vector.
Examples
obj <- bivph(dimensions = c(3, 3))
sim(obj, n = 100)
Simulation method for phase-type distributions
Description
Simulation method for phase-type distributions
Usage
## S4 method for signature 'dph'
sim(x, n = 1000)
Arguments
x |
An object of class dph. |
n |
An integer of length of realization. |
Value
A realization of independent and identically distributed discrete phase-type variables.
Examples
obj <- dph(structure = "general")
sim(obj, n = 100)
Simulation method for inhomogeneous phase-type distributions
Description
Simulation method for inhomogeneous phase-type distributions
Usage
## S4 method for signature 'iph'
sim(x, n = 1000)
Arguments
x |
An object of class iph. |
n |
An integer of length of realization. |
Value
A realization of independent and identically distributed inhomogeneous phase-type variables.
Examples
obj <- iph(ph(structure = "general"), gfun = "lognormal", gfun_pars = 2)
sim(obj, n = 100)
Simulation method for multivariate discrete phase-type distributions
Description
Simulation method for multivariate discrete phase-type distributions
Usage
## S4 method for signature 'mdph'
sim(x, n = 1000, equal_marginals = 0)
Arguments
x |
An object of class mdph. |
n |
Length of realization. |
equal_marginals |
Non-negative integer. If positive, it specifies the number of marginals to simulate from, all from the first matrix. |
Value
A realization of a multivariate discrete phase-type distribution.
Examples
obj <- mdph(structure = c("general", "general"))
sim(obj, 100)
Simulation method for inhomogeneous multivariate phase-type distributions
Description
Simulation method for inhomogeneous multivariate phase-type distributions
Usage
## S4 method for signature 'miph'
sim(x, n = 1000)
Arguments
x |
An object of class miph. |
n |
An integer of length of realization. |
Value
A realization of independent and identically distributed inhomogeneous multivariate phase-type variables. If x is a MoE miph an array of dimension c(n,d,m) is returned, with d the number of marginals and m the number of initial distribution vectors.
Examples
under_mph <- mph(structure = c("general", "general"))
obj <- miph(under_mph, gfun = c("weibull", "pareto"), gfun_pars = list(c(2), c(3)))
sim(obj, 100)
Simulation method for multivariate phase-type distributions
Description
Simulation method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
sim(x, n = 1000, equal_marginals = 0)
Arguments
x |
An object of class mph. |
n |
Length of realization. |
equal_marginals |
Non-negative integer. If positive, it specifies the number of marginals to simulate from, all from the first matrix. |
Value
A realization of a multivariate phase-type distribution.
Examples
obj <- mph(structure = c("general", "general"))
sim(obj, 100)
Simulation method for phase-type distributions
Description
Simulation method for phase-type distributions
Usage
## S4 method for signature 'ph'
sim(x, n = 1000)
Arguments
x |
An object of class ph. |
n |
An integer of length of realization. |
Value
A realization of independent and identically distributed phase-type variables.
Examples
obj <- ph(structure = "general")
sim(obj, n = 100)
Constructor function for survival phase-type objects
Description
Constructor function for survival phase-type objects
Usage
sph(x = NULL, coefs = list(B = numeric(0), C = numeric(0)), type = "reg")
Arguments
x |
An object of class ph. |
coefs |
Coefficients of the survival regression object. |
type |
Type of survival object. |
Value
An object of class sph.
Survival analysis for phase-type distributions
Description
Class of objects for inhomogeneous phase-type distributions
Value
Class object
Slots
coefsCoefficients of the survival regression object.
typeType of survival object.
Computes the initial distribution and sub-intensity of the sum of two discrete phase-type distributed random variables
Description
Computes the initial distribution and sub-intensity of the sum of two discrete phase-type distributed random variables
Usage
sum_dph(alpha1, S1, alpha2, S2)
Arguments
alpha1 |
Initial distribution. |
S1 |
Sub-transition matrix. |
alpha2 |
Initial distribution. |
S2 |
Sub-transition matrix. |
Computes the initial distribution and sub-intensity of the sum of two phase-type distributed random variables.
Description
Computes the initial distribution and sub-intensity of the sum of two phase-type distributed random variables.
Usage
sum_ph(alpha1, S1, alpha2, S2)
Arguments
alpha1 |
Initial distribution. |
S1 |
Sub-intensity matrix. |
alpha2 |
Initial distribution. |
S2 |
Sub-intensity matrix. |
Performs TVR for discrete phase-type distributions
Description
Performs TVR for discrete phase-type distributions
Usage
tvr_dph(alpha, S, R)
Arguments
alpha |
Initial distribution vector. |
S |
Sub-intensity matrix. |
R |
Reward vector. |
Value
A list of PH parameters.
Performs TVR for phase-type distributions
Description
Performs TVR for phase-type distributions
Usage
tvr_ph(alpha, S, R)
Arguments
alpha |
Initial distribution vector. |
S |
Sub-intensity matrix. |
R |
Reward vector. |
Value
A list of phase-type parameters.
Var method for MPHstar class
Description
Var method for MPHstar class
Usage
## S4 method for signature 'MPHstar'
var(x)
Arguments
x |
An object of class MPHstar. |
Value
The covariance matrix of the MPHstar distribution.
Examples
obj <- MPHstar(structure = "general")
var(obj)
Var method for bivdph class
Description
Var method for bivdph class
Usage
## S4 method for signature 'bivdph'
var(x)
Arguments
x |
An object of class bivdph. |
Value
The covariance matrix of the bivariate discrete phase-type distribution.
Examples
obj <- bivdph(dimensions = c(3, 3))
var(obj)
Var method for bivph class
Description
Var method for bivph class
Usage
## S4 method for signature 'bivph'
var(x)
Arguments
x |
An object of class bivph. |
Value
The covariance matrix of the bivariate phase-type distribution.
Examples
obj <- bivph(dimensions = c(3, 3))
var(obj)
Var method for discrete phase-type distributions
Description
Var method for discrete phase-type distributions
Usage
## S4 method for signature 'dph'
var(x)
Arguments
x |
An object of class dph. |
Value
The variance of the dph object.
Examples
set.seed(123)
obj <- dph(structure = "general", dimension = 3)
var(obj)
Var method for multivariate discrete phase-type distributions
Description
Var method for multivariate discrete phase-type distributions
Usage
## S4 method for signature 'mdph'
var(x)
Arguments
x |
An object of class mdph. |
Value
The covariance matrix of the multivariate discrete phase-type distribution.
Examples
obj <- mdph(structure = c("general", "general"))
var(obj)
Var method for multivariate phase-type distributions
Description
Var method for multivariate phase-type distributions
Usage
## S4 method for signature 'mph'
var(x)
Arguments
x |
An object of class mph. |
Value
The covariance matrix of the multivariate phase-type distribution.
Examples
obj <- mph(structure = c("general", "general"))
var(obj)
Var method for phase-type distributions
Description
Var method for phase-type distributions
Usage
## S4 method for signature 'ph'
var(x)
Arguments
x |
An object of class ph. |
Value
The variance of the ph (or underlying ph) object.
Examples
set.seed(123)
obj <- ph(structure = "general", dimension = 3)
var(obj)
Computes the elements S^n / n! until the a given size
Description
Computes the elements S^n / n! until the a given size
Usage
vector_of_matrices(vect, S, a, vect_size)
Arguments
vect |
A vector. |
S |
Sub-intensity matrix. |
a |
A number. |
vect_size |
Size of vector. |
Computes the elements S^n / n! until given value of n
Description
Computes the elements S^n / n! until given value of n
Usage
vector_of_matrices_2(vect, S, vect_size)
Arguments
vect |
A vector. |
S |
Sub-intensity matrix. |
vect_size |
Size of vector. |
Computes elements A^n until the given size
Description
Computes elements A^n until the given size
Usage
vector_of_powers(A, vect_size)
Arguments
A |
A matrix. |
vect_size |
Size of vector. |