Base class for Distributions

Description

Represents a modifiable Distribution family

Active bindings

Methods

Public methods

• Distribution$new()

• Distribution$sample()

• Distribution$density()

• Distribution$tf_logdensity()

• Distribution$probability()

• Distribution$tf_logprobability()

• Distribution$quantile()

• Distribution$hazard()

• Distribution$diff_density()

• Distribution$diff_probability()

• Distribution$is_in_support()

• Distribution$is_discrete_at()

• Distribution$tf_is_discrete_at()

• Distribution$has_capability()

• Distribution$get_type()

• Distribution$get_components()

• Distribution$is_discrete()

• Distribution$is_continuous()

• Distribution$require_capability()

• Distribution$get_dof()

• Distribution$get_placeholders()

• Distribution$get_params()

• Distribution$tf_make_constants()

• Distribution$tf_compile_params()

• Distribution$get_param_bounds()

• Distribution$get_param_constraints()

• Distribution$export_functions()

• Distribution$clone()

Method new()

Usage

Distribution$new(type, caps, params, name, default_params)

Arguments

Details

Construct a Distribution instance

Used internally by the ⁠dist_*⁠ functions.

Method sample()

Usage

Distribution$sample(n, with_params = list())

Arguments

Details

Sample from a Distribution

Returns

A length n vector of i.i.d. random samples from the Distribution with the specified parameters.

Examples

dist_exponential(rate = 2.0)$sample(10)

Method density()

Usage

Distribution$density(x, log = FALSE, with_params = list())

Arguments

Details

Density of a Distribution

Returns

A numeric vector of (log-)densities

Examples

dist_exponential()$density(c(1.0, 2.0), with_params = list(rate = 2.0))

Method tf_logdensity()

Usage

Distribution$tf_logdensity()

Details

Compile a TensorFlow function for log-density evaluation

Returns

A tf_function taking arguments x and args returning the log-density of the Distribution evaluated at x with parameters args.

Method probability()

Usage

Distribution$probability(
  q,
  lower.tail = TRUE,
  log.p = FALSE,
  with_params = list()
)

Arguments

Details

Cumulative probability of a Distribution

Returns

A numeric vector of (log-)probabilities

Examples

dist_exponential()$probability(
  c(1.0, 2.0),
  with_params = list(rate = 2.0)
)

Method tf_logprobability()

Usage

Distribution$tf_logprobability()

Details

Compile a TensorFlow function for log-probability evaluation

Returns

A tf_function taking arguments qmin, qmax and args returning the log-probability of the Distribution evaluated over the closed interval [qmin, qmax] with parameters args.

Method quantile()

Usage

Distribution$quantile(
  p,
  lower.tail = TRUE,
  log.p = FALSE,
  with_params = list()
)

Arguments

Details

Quantile function of a Distribution

Returns

A numeric vector of quantiles

Examples

dist_exponential()$quantile(c(0.1, 0.5), with_params = list(rate = 2.0))

Method hazard()

Usage

Distribution$hazard(x, log = FALSE, with_params = list())

Arguments

Details

Hazard function of a Distribution

Returns

A numeric vector of (log-)hazards

Examples

dist_exponential(rate = 2.0)$hazard(c(1.0, 2.0))

Method diff_density()

Usage

Distribution$diff_density(x, log = FALSE, with_params = list())

Arguments

Details

Gradients of the density of a Distribution

Returns

A list structure containing the (log-)density gradients of all free parameters of the Distribution evaluated at x.

Examples

dist_exponential()$diff_density(
  c(1.0, 2.0),
  with_params = list(rate = 2.0)
)

Method diff_probability()

Usage

Distribution$diff_probability(
  q,
  lower.tail = TRUE,
  log.p = FALSE,
  with_params = list()
)

Arguments

Details

Gradients of the cumulative probability of a Distribution

Returns

A list structure containing the cumulative (log-)probability gradients of all free parameters of the Distribution evaluated at q.

Examples

dist_exponential()$diff_probability(
  c(1.0, 2.0),
  with_params = list(rate = 2.0)
)

Method is_in_support()

Usage

Distribution$is_in_support(x, with_params = list())

Arguments

Details

Determine if a value is in the support of a Distribution

Returns

A logical vector with the same length as x indicating whether x is part of the support of the distribution given its parameters.

Examples

dist_exponential(rate = 1.0)$is_in_support(c(-1.0, 0.0, 1.0))

Method is_discrete_at()

Usage

Distribution$is_discrete_at(x, with_params = list())

Arguments

Details

Determine if a value has positive probability

Returns

A logical vector with the same length as x indicating whether there is a positive probability mass at x given the Distribution parameters.

Examples

dist_dirac(point = 0.0)$is_discrete_at(c(0.0, 1.0))

Method tf_is_discrete_at()

Usage

Distribution$tf_is_discrete_at()

Details

Compile a TensorFlow function for discrete support checking

Returns

A tf_function taking arguments x and args returning whether the Distribution has a point mass at x given parameters args.

Method has_capability()

Usage

Distribution$has_capability(caps)

Arguments

Details

Check if a capability is present

Returns

A logical vector the same length as caps.

Examples

dist_exponential()$has_capability("density")

Method get_type()

Usage

Distribution$get_type()

Details

Get the type of a Distribution. Type can be one of discrete, continuous or mixed.

Returns

A string representing the type of the Distribution.

Examples

dist_exponential()$get_type()
dist_dirac()$get_type()

dist_mixture(list(dist_dirac(), dist_exponential()))$get_type()
dist_mixture(list(dist_dirac(), dist_binomial()))$get_type()

Method get_components()

Usage

Distribution$get_components()

Details

Get the component Distributions of a transformed Distribution.

Returns

A possibly empty list of Distributions

Examples

dist_trunc(dist_exponential())$get_components()
dist_dirac()$get_components()
dist_mixture(list(dist_exponential(), dist_gamma()))$get_components()

Method is_discrete()

Usage

Distribution$is_discrete()

Details

Check if a Distribution is discrete, i.e. it has a density with respect to the counting measure.

Returns

TRUE if the Distribution is discrete, FALSE otherwise. Note that mixed distributions are not discrete but can have point masses.

Examples

dist_exponential()$is_discrete()
dist_dirac()$is_discrete()

Method is_continuous()

Usage

Distribution$is_continuous()

Details

Check if a Distribution is continuous, i.e. it has a density with respect to the Lebesgue measure.

Returns

TRUE if the Distribution is continuous, FALSE otherwise. Note that mixed distributions are not continuous.

Examples

dist_exponential()$is_continuous()
dist_dirac()$is_continuous()

Method require_capability()

Usage

Distribution$require_capability(
  caps,
  fun_name = paste0(sys.call(-1)[[1]], "()")
)

Arguments

Details

Ensure that a Distribution has all required capabilities. Will throw an error if any capability is missing.

Returns

Invisibly TRUE.

Examples

dist_exponential()$require_capability("diff_density")

Method get_dof()

Usage

Distribution$get_dof()

Details

Get the number of degrees of freedom of a Distribution family. Only parameters without a fixed default are considered free.

Returns

An integer representing the degrees of freedom suitable e.g. for AIC calculations.

Examples

dist_exponential()$get_dof()
dist_exponential(rate = 1.0)$get_dof()

Method get_placeholders()

Usage

Distribution$get_placeholders()

Details

Get Placeholders of a Distribution family. Returns a list of free parameters of the family. Their values will be NULL.

If the Distribution has Distributions as parameters, placeholders will be computed recursively.

Returns

A named list containing any combination of (named or unnamed) lists and NULLs.

Examples

dist_exponential()$get_placeholders()
dist_mixture(list(dist_dirac(), dist_exponential()))$get_placeholders()

Method get_params()

Usage

Distribution$get_params(with_params = list())

Arguments

Details

Get a full list of parameters, possibly including placeholders.

Returns

A list representing the (recursive) parameter structure of the Distribution with values for specified parameters and NULL for free parameters that are missing both in the Distributions parameters and in with_params.

Examples

dist_mixture(list(dist_dirac(), dist_exponential()))$get_params(
  with_params = list(probs = list(0.5, 0.5))
)

Method tf_make_constants()

Usage

Distribution$tf_make_constants(with_params = list())

Arguments

Details

Get a list of constant TensorFlow parameters

Returns

A list representing the (recursive) constant parameters of the Distribution with values sprecified by parameters. Each constant is a TensorFlow Tensor of dtype floatx.

Method tf_compile_params()

Usage

Distribution$tf_compile_params(input, name_prefix = "")

Arguments

Details

Compile distribution parameters into tensorflow outputs

Returns

A list with two elements

• outputs a flat list of keras output layers, one for each parameter.

• output_inflater a function taking keras output layers and transforming them into a list structure suitable for passing to the loss function returned by tf_compile_model()

Method get_param_bounds()

Usage

Distribution$get_param_bounds()

Details

Get Interval bounds on all Distribution parameters

Returns

A list representing the free (recursive) parameter structure of the Distribution with Interval objects as values representing the bounds of the respective free parameters.

Examples

dist_mixture(
  list(dist_dirac(), dist_exponential()),
  probs = list(0.5, 0.5)
)$get_param_bounds()

dist_mixture(
  list(dist_dirac(), dist_exponential())
)$get_param_bounds()

dist_genpareto()$get_param_bounds()
dist_genpareto1()$get_param_bounds()

Method get_param_constraints()

Usage

Distribution$get_param_constraints()

Details

Get additional (non-linear) equality constraints on Distribution parameters

Returns

NULL if the box constraints specified by dist$get_param_bounds() are sufficient, or a function taking full Distribution parameters and returning either a numeric vector (which must be 0 for valid parameter combinations) or a list with elements

• constraints: The numeric vector of constraints

• jacobian: The Jacobi matrix of the constraints with respect to the parameters

Examples

dist_mixture(
  list(dist_dirac(), dist_exponential())
)$get_param_constraints()

Method export_functions()

Usage

Distribution$export_functions(
  name,
  envir = parent.frame(),
  with_params = list()
)

Arguments

Details

Export sampling, density, probability and quantile functions to plain R functions

Creates new functions in envir named ⁠{r,d,p,q}<name>⁠ which implement dist$sample, dist$density, dist$probability and dist$quantile as plain functions with default arguments specified by with_params or the fixed parameters.

The resulting functions will have signatures taking all parameters as separate arguments.

Returns

Invisibly NULL.

Examples

tmp_env <- new.env(parent = globalenv())
dist_exponential()$export_functions(
  name = "exp",
  envir = tmp_env,
  with_params = list(rate = 2.0)
)
evalq(
  fitdistrplus::fitdist(rexp(100), "exp"),
  envir = tmp_env
)

Method clone()

The objects of this class are cloneable with this method.

Usage

Distribution$clone(deep = FALSE)

Arguments

See Also

Other Distributions: dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

# Example for param_bounds:

# Create an Exponential Distribution with rate constrained to (0, 2)
# instead of (0, Inf)
my_exp <- dist_exponential()
my_exp$param_bounds$rate <- interval(c(0, 2))
my_exp$get_param_bounds()

fit_dist(my_exp, rexp(100, rate = 3), start = list(rate = 1))$params$rate


## ------------------------------------------------
## Method `Distribution$sample`
## ------------------------------------------------

dist_exponential(rate = 2.0)$sample(10)

## ------------------------------------------------
## Method `Distribution$density`
## ------------------------------------------------

dist_exponential()$density(c(1.0, 2.0), with_params = list(rate = 2.0))

## ------------------------------------------------
## Method `Distribution$probability`
## ------------------------------------------------

dist_exponential()$probability(
  c(1.0, 2.0),
  with_params = list(rate = 2.0)
)

## ------------------------------------------------
## Method `Distribution$quantile`
## ------------------------------------------------

dist_exponential()$quantile(c(0.1, 0.5), with_params = list(rate = 2.0))

## ------------------------------------------------
## Method `Distribution$hazard`
## ------------------------------------------------

dist_exponential(rate = 2.0)$hazard(c(1.0, 2.0))

## ------------------------------------------------
## Method `Distribution$diff_density`
## ------------------------------------------------

dist_exponential()$diff_density(
  c(1.0, 2.0),
  with_params = list(rate = 2.0)
)

## ------------------------------------------------
## Method `Distribution$diff_probability`
## ------------------------------------------------

dist_exponential()$diff_probability(
  c(1.0, 2.0),
  with_params = list(rate = 2.0)
)

## ------------------------------------------------
## Method `Distribution$is_in_support`
## ------------------------------------------------

dist_exponential(rate = 1.0)$is_in_support(c(-1.0, 0.0, 1.0))

## ------------------------------------------------
## Method `Distribution$is_discrete_at`
## ------------------------------------------------

dist_dirac(point = 0.0)$is_discrete_at(c(0.0, 1.0))

## ------------------------------------------------
## Method `Distribution$has_capability`
## ------------------------------------------------

dist_exponential()$has_capability("density")

## ------------------------------------------------
## Method `Distribution$get_type`
## ------------------------------------------------

dist_exponential()$get_type()
dist_dirac()$get_type()

dist_mixture(list(dist_dirac(), dist_exponential()))$get_type()
dist_mixture(list(dist_dirac(), dist_binomial()))$get_type()

## ------------------------------------------------
## Method `Distribution$get_components`
## ------------------------------------------------

dist_trunc(dist_exponential())$get_components()
dist_dirac()$get_components()
dist_mixture(list(dist_exponential(), dist_gamma()))$get_components()

## ------------------------------------------------
## Method `Distribution$is_discrete`
## ------------------------------------------------

dist_exponential()$is_discrete()
dist_dirac()$is_discrete()

## ------------------------------------------------
## Method `Distribution$is_continuous`
## ------------------------------------------------

dist_exponential()$is_continuous()
dist_dirac()$is_continuous()

## ------------------------------------------------
## Method `Distribution$require_capability`
## ------------------------------------------------

dist_exponential()$require_capability("diff_density")

## ------------------------------------------------
## Method `Distribution$get_dof`
## ------------------------------------------------

dist_exponential()$get_dof()
dist_exponential(rate = 1.0)$get_dof()

## ------------------------------------------------
## Method `Distribution$get_placeholders`
## ------------------------------------------------

dist_exponential()$get_placeholders()
dist_mixture(list(dist_dirac(), dist_exponential()))$get_placeholders()

## ------------------------------------------------
## Method `Distribution$get_params`
## ------------------------------------------------

dist_mixture(list(dist_dirac(), dist_exponential()))$get_params(
  with_params = list(probs = list(0.5, 0.5))
)

## ------------------------------------------------
## Method `Distribution$get_param_bounds`
## ------------------------------------------------

dist_mixture(
  list(dist_dirac(), dist_exponential()),
  probs = list(0.5, 0.5)
)$get_param_bounds()

dist_mixture(
  list(dist_dirac(), dist_exponential())
)$get_param_bounds()

dist_genpareto()$get_param_bounds()
dist_genpareto1()$get_param_bounds()

## ------------------------------------------------
## Method `Distribution$get_param_constraints`
## ------------------------------------------------

dist_mixture(
  list(dist_dirac(), dist_exponential())
)$get_param_constraints()

## ------------------------------------------------
## Method `Distribution$export_functions`
## ------------------------------------------------

tmp_env <- new.env(parent = globalenv())
dist_exponential()$export_functions(
  name = "exp",
  envir = tmp_env,
  with_params = list(rate = 2.0)
)
evalq(
  fitdistrplus::fitdist(rexp(100), "exp"),
  envir = tmp_env
)

The Generalized Pareto Distribution (GPD)

Description

These functions provide information about the generalized Pareto distribution with threshold u. dgpd gives the density, pgpd gives the distribution function, qgpd gives the quantile function and rgpd generates random deviates.

Usage

rgpd(n = 1L, u = 0, sigmau = 1, xi = 0)

dgpd(x, u = 0, sigmau = 1, xi = 0, log = FALSE)

pgpd(q, u = 0, sigmau = 1, xi = 0, lower.tail = TRUE, log.p = FALSE)

qgpd(p, u = 0, sigmau = 1, xi = 0, lower.tail = TRUE, log.p = FALSE)

Arguments

Details

If u, sigmau or xi are not specified, they assume the default values of 0, 1 and 0 respectively.

The generalized Pareto distribution has density

f(x) = 1 / \sigma_u (1 + \xi z)^(- 1 / \xi - 1)

where z = (x - u) / \sigma_u and f(x) = exp(-z) if \xi is 0. The support is x \ge u for \xi \ge 0 and u \le x \le u - \sigma_u / \xi for \xi < 0.

The Expected value exists if \xi < 1 and is equal to

E(X) = u + \sigma_u / (1 - \xi)

k-th moments exist in general for k\xi < 1.

Value

rgpd generates random deviates.

dgpd gives the density.

pgpd gives the distribution function.

qgpd gives the quantile function.

References

https://en.wikipedia.org/wiki/Generalized_Pareto_distribution

Examples

x <- rgpd(1000, u = 1, sigmau = 0.5, xi = 0.1)
xx <- seq(-1, 10, 0.01)
hist(x, breaks = 100, freq = FALSE, xlim = c(-1, 10))
lines(xx, dgpd(xx, u = 1, sigmau = 0.5, xi = 0.1))

plot(xx, dgpd(xx, u = 1, sigmau = 1, xi = 0), type = "l")
lines(xx, dgpd(xx, u = 0.5, sigmau = 1, xi = -0.3), col = "blue", lwd = 2)
lines(xx, dgpd(xx, u = 1.5, sigmau = 1, xi = 0.3), col = "red", lwd = 2)

plot(xx, dgpd(xx, u = 1, sigmau = 1, xi = 0), type = "l")
lines(xx, dgpd(xx, u = 1, sigmau = 0.5, xi = 0), col = "blue", lwd = 2)
lines(xx, dgpd(xx, u = 1, sigmau = 2, xi = 0), col = "red", lwd = 2)

The Pareto Distribution

Description

These functions provide information about the Pareto distribution. dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function and rpareto generates random deviates.

Usage

rpareto(n = 1L, shape = 0, scale = 1)

dpareto(x, shape = 1, scale = 1, log = FALSE)

ppareto(q, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE)

qpareto(p, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

Details

If shape or scale are not specified, they assume the default values of 1.

The Pareto distribution with scale \theta and shape \xi has density

f(x) = \xi \theta^\xi / (x + \theta)^(\xi + 1)

The support is x \ge 0.

The Expected value exists if \xi > 1 and is equal to

E(X) = \theta / (\xi - 1)

k-th moments exist in general for k < \xi.

Value

rpareto generates random deviates.

dpareto gives the density.

ppareto gives the distribution function.

qpareto gives the quantile function.

References

https://en.wikipedia.org/wiki/Pareto_distribution - named Lomax therein.

Examples

x <- rpareto(1000, shape = 10, scale = 5)
xx <- seq(-1, 10, 0.01)
hist(x, breaks = 100, freq = FALSE, xlim = c(-1, 10))
lines(xx, dpareto(xx, shape = 10, scale = 5))

plot(xx, dpareto(xx, shape = 10, scale = 5), type = "l")
lines(xx, dpareto(xx, shape = 3, scale = 5), col = "red", lwd = 2)

plot(xx, dpareto(xx, shape = 10, scale = 10), type = "l")
lines(xx, dpareto(xx, shape = 10, scale = 5), col = "blue", lwd = 2)
lines(xx, dpareto(xx, shape = 10, scale = 20), col = "red", lwd = 2)

Convert TensorFlow tensors to distribution parameters recursively

Description

Convert TensorFlow tensors to distribution parameters recursively

Usage

as_params(x)

Arguments

Value

A nested list of vectors suitable as distribution parameters

Examples

if (interactive()) {
  tf_params <- list(
    probs = k_matrix(t(c(0.5, 0.3, 0.2))),
    shapes = k_matrix(t(c(1L, 2L, 3L)), dtype = "int32"),
    scale = keras3::as_tensor(1.0, keras3::config_floatx())
  )
  params <- as_params(tf_params)
  dist <- dist_erlangmix(vector("list", 3L))
  dist$sample(10L, with_params = params)
}

Transition functions for blended distributions

Description

Transition functions for blended distributions

Usage

blended_transition(x, u, eps, .gradient = FALSE, .extend_na = FALSE)

blended_transition_inv(x, u, eps, .component)

Arguments

Value

blended_transition returns a matrix with length(x) rows and length(u) + 1 columns containing the transformed values for each of the blending components. If .gradient is TRUE, an attribute "gradient" is attached with the same dimensions, containing the derivative of the respective transition component with respect to x.

blended_transition_inv returns a vector with length(x) values containing the inverse of the transformed values for the .componentth blending component.

Examples

library(ggplot2)
xx <- seq(from = 0, to = 20, length.out = 101)
blend_mat <- blended_transition(xx, u = 10, eps = 3, .gradient = TRUE)
ggplot(
  data.frame(
    x = rep(xx, 2L),
    fun = rep(c("p", "q"), each = length(xx)),
    y = as.numeric(blend_mat),
    relevant = c(xx <= 13, xx >= 7)
  ),
  aes(x = x, y = y, color = fun, linetype = relevant)
) %+%
  geom_line() %+%
  theme_bw() %+%
  theme(
    legend.position = "bottom", legend.box = "horizontal"
  ) %+%
  guides(color = guide_legend(direction = "horizontal", title = ""), linetype = guide_none()) %+%
  scale_linetype_manual(values = c("TRUE" = 1, "FALSE" = 3))

ggplot(
  data.frame(
    x = rep(xx, 2L),
    fun = rep(c("p'", "q'"), each = length(xx)),
    y = as.numeric(attr(blend_mat, "gradient")),
    relevant = c(xx <= 13, xx >= 7)
  ),
  aes(x = x, y = y, color = fun, linetype = relevant)
) %+%
  geom_line() %+%
  theme_bw() %+%
  theme(
    legend.position = "bottom", legend.box = "horizontal"
  ) %+%
  guides(color = guide_legend(direction = "horizontal", title = ""), linetype = guide_none()) %+%
  scale_linetype_manual(values = c("TRUE" = 1, "FALSE" = 3))

Keras Callback for adaptive learning rate with weight restoration

Description

Provides a keras callback similar to keras3::callback_reduce_lr_on_plateau() but which also restores the weights to the best seen so far whenever a learning rate reduction occurs, and with slightly more restrictive improvement detection.

Usage

callback_adaptive_lr(
  monitor = "val_loss",
  factor = 0.1,
  patience = 10L,
  verbose = 0L,
  mode = c("auto", "min", "max"),
  delta_abs = 1e-04,
  delta_rel = 0,
  cooldown = 0L,
  min_lr = 0,
  restore_weights = TRUE
)

Arguments

Details

Note that while keras3::callback_reduce_lr_on_plateau() automatically logs the learning rate as a metric 'lr', this is currently impossible from R. Thus, if you want to also log the learning rate, you should add keras3::callback_reduce_lr_on_plateau() with a high min_lr to effectively disable the callback but still monitor the learning rate.

Value

A KerasCallback suitable for passing to keras3::fit().

Examples

dist <- dist_exponential()
group <- sample(c(0, 1), size = 100, replace = TRUE)
x <- dist$sample(100, with_params = list(rate = group + 1))
global_fit <- fit(dist, x)

if (interactive()) {
  library(keras3)
  l_in <- layer_input(shape = 1L)
  mod <- tf_compile_model(
    inputs = list(l_in),
    intermediate_output = l_in,
    dist = dist,
    optimizer = optimizer_adam(),
    censoring = FALSE,
    truncation = FALSE
  )
  tf_initialise_model(mod, global_fit$params)
  fit_history <- fit(
    mod,
    x = as_tensor(group, config_floatx()),
    y = as_trunc_obs(x),
    epochs = 20L,
    callbacks = list(
      callback_adaptive_lr("loss", factor = 0.5, patience = 2L, verbose = 1L, min_lr = 1.0e-4),
      callback_reduce_lr_on_plateau("loss", min_lr = 1.0) # to track lr
    )
  )

  plot(fit_history)

  predicted_means <- predict(mod, data = as_tensor(c(0, 1), config_floatx()))
}

Callback to monitor likelihood gradient components

Description

Provides a keras callback to monitor the individual components of the censored and truncated likelihood. Useful for debugging TensorFlow implementations of Distributions.

Usage

callback_debug_dist_gradients(
  object,
  data,
  obs,
  keep_grads = FALSE,
  stop_on_na = TRUE,
  verbose = TRUE
)

Arguments

Value

A KerasCallback suitable for passing to keras3::fit().

Examples

dist <- dist_exponential()
group <- sample(c(0, 1), size = 100, replace = TRUE)
x <- dist$sample(100, with_params = list(rate = group + 1))
global_fit <- fit(dist, x)

if (interactive()) {
  library(keras3)
  l_in <- layer_input(shape = 1L)
  mod <- tf_compile_model(
    inputs = list(l_in),
    intermediate_output = l_in,
    dist = dist,
    optimizer = optimizer_adam(),
    censoring = FALSE,
    truncation = FALSE
  )
  tf_initialise_model(mod, global_fit$params)
  gradient_tracker <- callback_debug_dist_gradients(
    mod,
    as_tensor(group, config_floatx()),
    x,
    keep_grads = TRUE
  )
  fit_history <- fit(
    mod,
    x = as_tensor(group, config_floatx()),
    y = x,
    epochs = 20L,
    callbacks = list(
      callback_adaptive_lr("loss", factor = 0.5, patience = 2L, verbose = 1L, min_lr = 1.0e-4),
      gradient_tracker,
      callback_reduce_lr_on_plateau("loss", min_lr = 1.0) # to track lr
    )
  )
  gradient_tracker$gradient_logs[[20]]$dens

  plot(fit_history)

  predicted_means <- predict(mod, data = as_tensor(c(0, 1), config_floatx()))
}

Construct a BDEGP-Family

Description

Constructs a BDEGP-Family distribution with fixed number of components and blending interval.

Usage

dist_bdegp(n, m, u, epsilon)

Arguments

Value

• A MixtureDistribution of

  • n DiracDistributions at 0 .. n - 1 and

  • a BlendedDistribution object with child Distributions

    • a TranslatedDistribution with offset n - 0.5 of an ErlangMixtureDistribution with m shapes

    • and a GeneralizedParetoDistribution with shape parameter restricted to [0, 1] and location parameter fixed at u With break u and bandwidth epsilon.

See Also

Other Distributions: Distribution, dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

dist <- dist_bdegp(n = 1, m = 2, u = 10, epsilon = 3)
params <- list(
  dists = list(
    list(),
    list(
      dists = list(
        list(
          dist = list(
            shapes = list(1L, 2L),
            scale = 1.0,
            probs = list(0.7, 0.3)
          )
        ),
        list(
          sigmau = 1.0,
          xi = 0.1
        )
      ),
      probs = list(0.1, 0.9)
    )
  ),
  probs = list(0.95, 0.05)
)
x <- dist$sample(100, with_params = params)

plot_distributions(
  theoretical = dist,
  empirical = dist_empirical(x),
  .x = seq(0, 20, length.out = 101),
  with_params = list(theoretical = params)
)

Beta Distribution

Description

See stats::Beta

Usage

dist_beta(shape1 = NULL, shape2 = NULL, ncp = NULL)

Arguments

Details

All parameters can be overridden with with_params = list(shape = ..., scale = ...).

Value

A BetaDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_beta <- dist_beta(shape1 = 2, shape2 = 2, ncp = 0)
x <- d_beta$sample(100)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_beta,
  estimated = d_beta,
  with_params = list(
    estimated = inflate_params(
      fitdistrplus::fitdist(x, distr = "beta")$estimate
    )
  ),
  .x = seq(0, 2, length.out = 100)
)

Binomial Distribution

Description

See stats::Binomial

Usage

dist_binomial(size = NULL, prob = NULL)

Arguments

Details

Both parameters can be overridden with with_params = list(size = ..., prob = ...).

Value

A BinomialDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_binom <- dist_binomial(size = 10, prob = 0.5)
x <- d_binom$sample(100)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_binom,
  estimated = d_binom,
  with_params = list(
    estimated = list(
      size = max(x),
      prob = mean(x) / max(x)
    )
  ),
  .x = 0:max(x)
)

Blended distribution

Description

Blended distribution

Usage

dist_blended(dists, probs = NULL, breaks = NULL, bandwidths = NULL)

Arguments

Value

A BlendedDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

bd <- dist_blended(
  list(
    dist_normal(mean = 0.0, sd = 1.0),
    dist_genpareto(u = 3.0, sigmau = 1.0, xi = 3.0)
  ),
  breaks = list(3.0),
  bandwidths = list(0.5),
  probs = list(0.9, 0.1)
)

plot_distributions(
  bd,
  .x = seq(-3, 10, length.out = 100),
  plots = c("d", "p")
)

Dirac (degenerate point) Distribution

Description

A degenerate distribution with all mass at a single point.

Usage

dist_dirac(point = NULL)

Arguments

Details

The parameter can be overridden with with_params = list(point = ...).

Value

A DiracDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_dirac <- dist_dirac(1.5)
d_dirac$sample(2L)
d_dirac$sample(2L, list(point = 42.0))

Discrete Distribution

Description

A full-flexibility discrete distribution with values from 1 to size.

Usage

dist_discrete(size = NULL, probs = NULL)

Arguments

Details

Parameters can be overridden with with_params = list(probs = ...).

Value

A DiscreteDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_discrete <- dist_discrete(probs = list(0.5, 0.25, 0.15, 0.1))
x <- d_discrete$sample(100)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_discrete,
  estimated = d_discrete,
  with_params = list(
    estimated = list(
      size = max(x),
      probs = as.list(unname(table(x)) / 100)
    )
  ),
  .x = 0:max(x)
)

Empirical distribution

Description

Creates an empirical distribution object from a sample. Assumes iid. samples. with_params should not be used with this distribution because estimation of the relevant indicators happens during construction.

Usage

dist_empirical(sample, positive = FALSE, bw = "nrd0")

Arguments

Details

• sample() samples iid. from sample. This approach is similar to bootstrapping.

• density() evaluates a kernel density estimate, approximating with zero outside of the known support. This estimate is either obtained using stats::density or logKDE::logdensity_fft, depending on positive.

• probability() evaluates the empirical cumulative density function obtained by stats::ecdf.

• quantile() evaluates the empirical quantiles using stats::quantile

• hazard() estimates the hazard rate using the density estimate and the empirical cumulative density function: h(t) = df(t) / (1 - cdf(t)).

Value

An EmpiricalDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

x <- rexp(20, rate = 1)
dx <- dist_empirical(sample = x, positive = TRUE)

y <- rnorm(20)
dy <- dist_empirical(sample = y)

plot_distributions(
  exponential = dx,
  normal = dy,
  .x = seq(-3, 3, length.out = 100)
)

Erlang Mixture distribution

Description

Erlang Mixture distribution

Usage

dist_erlangmix(shapes, scale = NULL, probs = NULL)

Arguments

Value

An ErlangMixtureDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

params <- list(scale = 1.0, probs = list(0.5, 0.3, 0.2), shapes = list(1L, 2L, 3L))
dist <- dist_erlangmix(vector("list", 3L))
x <- dist$sample(20, with_params = params)
d_emp <- dist_empirical(x, positive = TRUE)

plot_distributions(
  empirical = d_emp,
  theoretical = dist,
  with_params = list(
    theoretical = params
  ),
  .x = seq(1e-4, 5, length.out = 100)
)

Exponential distribution

Description

See stats::Exponential.

Usage

dist_exponential(rate = NULL)

Arguments

Details

The parameter can be overridden with with_params = list(rate = ...).

Value

An ExponentialDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

rate <- 1
d_exp <- dist_exponential()
x <- d_exp$sample(20, with_params = list(rate = rate))
d_emp <- dist_empirical(x, positive = TRUE)

plot_distributions(
  empirical = d_emp,
  theoretical = d_exp,
  estimated = d_exp,
  with_params = list(
    theoretical = list(rate = rate),
    estimated = list(rate = 1 / mean(x))
  ),
  .x = seq(1e-4, 5, length.out = 100)
)

Gamma distribution

Description

See stats::GammaDist.

Usage

dist_gamma(shape = NULL, rate = NULL)

Arguments

Details

Both parameters can be overridden with with_params = list(shape = ..., rate = ...).

Value

A GammaDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

alpha <- 2
beta <- 2

d_gamma <- dist_gamma(shape = alpha, rate = beta)
x <- d_gamma$sample(100)
d_emp <- dist_empirical(x, positive = TRUE)

plot_distributions(
  empirical = d_emp,
  theoretical = d_gamma,
  estimated = d_gamma,
  with_params = list(
    estimated = inflate_params(
      fitdistrplus::fitdist(x, distr = "gamma")$estimate
    )
  ),
  .x = seq(1e-3, max(x), length.out = 100)
)

Generalized Pareto Distribution

Description

See evmix::gpd

Usage

dist_genpareto(u = NULL, sigmau = NULL, xi = NULL)

dist_genpareto1(u = NULL, sigmau = NULL, xi = NULL)

Arguments

Details

All parameters can be overridden with with_params = list(u = ..., sigmau = ..., xi = ...).

dist_genpareto1 is equivalent to dist_genpareto but enforces bound constraints on xi to ⁠[0, 1]⁠. This ensures unboundedness and finite expected value unless xi == 1.0.

Value

A GeneralizedParetoDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_genpareto <- dist_genpareto(u = 0, sigmau = 1, xi = 1)
x <- d_genpareto$sample(100)
d_emp <- dist_empirical(x)

d_genpareto$export_functions("gpd") # so fitdistrplus finds it

plot_distributions(
  empirical = d_emp,
  theoretical = d_genpareto,
  estimated = d_genpareto,
  with_params = list(
    estimated = fit(dist_genpareto(), x)$params
  ),
  .x = seq(0, 5, length.out = 100)
)

Log Normal distribution

Description

See stats::Lognormal.

Usage

dist_lognormal(meanlog = NULL, sdlog = NULL)

Arguments

Details

Both parameters can be overridden with with_params = list(meanlog = ..., sdlog = ...).

Value

A LognormalDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

mu <- 0
sigma <- 1

d_lnorm <- dist_lognormal(meanlog = mu, sdlog = sigma)
x <- d_lnorm$sample(20)
d_emp <- dist_empirical(x, positive = TRUE)

plot_distributions(
  empirical = d_emp,
  theoretical = d_lnorm,
  estimated = d_lnorm,
  with_params = list(
    estimated = inflate_params(
      fitdistrplus::fitdist(x, distr = "lnorm")$estimate
    )
  ),
  .x = seq(1e-3, 5, length.out = 100)
)

Mixture distribution

Description

Parameters of mixing components can be overridden with with_params = list(dists = list(..., ..., ...)). #' Mixing probabilites can be overridden with with_params = list(probs = list(..., ..., ...)). The number of components cannot be overridden.

Usage

dist_mixture(dists = list(), probs = NULL)

Arguments

Details

Does not support the quantile() capability!

Value

A MixtureDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

# A complicated way to define a uniform distribution on \[0, 2\]
dist_mixture(
  dists = list(
    dist_uniform(min = 0, max = 1),
    dist_uniform(min = 1, max = 2)
  ),
  probs = list(0.5, 0.5)
)

Negative binomial Distribution

Description

See stats::NegBinomial

Usage

dist_negbinomial(size = NULL, mu = NULL)

Arguments

Details

Both parameters can be overridden with with_params = list(size = ..., prob = ...).

Value

A NegativeBinomialDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_nbinom <- dist_negbinomial(size = 3.5, mu = 8.75)
x <- d_nbinom$sample(100)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_nbinom,
  estimated = d_nbinom,
  with_params = list(
    estimated = inflate_params(
      fitdistrplus::fitdist(x, distr = "nbinom")$estimate
    )
  ),
  .x = 0:max(x)
)

Normal distribution

Description

See stats::Normal.

Usage

dist_normal(mean = NULL, sd = NULL)

Arguments

Details

Both parameters can be overridden with with_params = list(mean = ..., sd = ...).

Value

A NormalDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

mu <- 0
sigma <- 1

d_norm <- dist_normal(mean = mu, sd = sigma)
x <- d_norm$sample(20)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_norm,
  estimated = d_norm,
  with_params = list(
    estimated = list(mean = mean(x), sd = sd(x))
  ),
  .x = seq(-3, 3, length.out = 100)
)

Pareto Distribution

Description

See Pareto

Usage

dist_pareto(shape = NULL, scale = NULL)

Arguments

Details

Both parameters can be overridden with with_params = list(shape = ..., scale = ...).

Value

A ParetoDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_pareto <- dist_pareto(shape = 3, scale = 1)
x <- d_pareto$sample(100)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_pareto,
  estimated = d_pareto,
  with_params = list(
    estimated = inflate_params(
      fitdistrplus::fitdist(x, distr = "pareto")$estimate
    )
  ),
  .x = seq(0, 2, length.out = 100)
)

Poisson Distribution

Description

See stats::Poisson

Usage

dist_poisson(lambda = NULL)

Arguments

Details

The parameter can be overridden with with_params = list(lambda = ...).

Value

A PoissonDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_translate(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_pois <- dist_poisson(lambda = 5.0)
x <- d_pois$sample(100)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_pois,
  estimated = d_pois,
  with_params = list(
    estimated = inflate_params(
      fitdistrplus::fitdist(x, distr = "pois")$estimate
    )
  ),
  .x = 0:max(x)
)

Tranlsated distribution

Description

Tranlsated distribution

Usage

dist_translate(dist = NULL, offset = NULL, multiplier = 1)

Arguments

Value

A TranslatedDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_trunc(), dist_uniform(), dist_weibull()

Examples

d_norm <- dist_normal(mean = 0, sd = 1)
d_tnorm <- dist_translate(dist = d_norm, offset = 1)
plot_distributions(d_norm, d_tnorm, .x = seq(-2, 3, length.out = 100))

Truncated distribution

Description

Truncated distribution

Usage

dist_trunc(dist = NULL, min = NULL, max = NULL, offset = 0, max_retry = 100)

Arguments

Value

A TruncatedDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_uniform(), dist_weibull()

Examples

d_norm <- dist_normal(mean = 0, sd = 1)
d_tnorm <- dist_trunc(dist = d_norm, min = -2, max = 2, offset = 1)
plot_distributions(d_norm, d_tnorm, .x = seq(-2, 3, length.out = 100))

Uniform distribution

Description

See stats::Uniform

Usage

dist_uniform(min = NULL, max = NULL)

Arguments

Details

Both parameters can be overridden with with_params = list(min = ..., max = ...).

Value

A UniformDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_weibull()

Examples

d_unif <- dist_uniform(min = 0, max = 1)
x <- d_unif$sample(100)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_unif,
  estimated = d_unif,
  with_params = list(
    estimated = inflate_params(
      fitdistrplus::fitdist(x, distr = "unif")$estimate
    )
  ),
  .x = seq(0, 1, length.out = 100)
)

Weibull Distribution

Description

See stats::Weibull

Usage

dist_weibull(shape = NULL, scale = NULL)

Arguments

Details

Both parameters can be overridden with with_params = list(shape = ..., scale = ...).

Value

A WeibullDistribution object.

See Also

Other Distributions: Distribution, dist_bdegp(), dist_beta(), dist_binomial(), dist_blended(), dist_dirac(), dist_discrete(), dist_empirical(), dist_erlangmix(), dist_exponential(), dist_gamma(), dist_genpareto(), dist_lognormal(), dist_mixture(), dist_negbinomial(), dist_normal(), dist_pareto(), dist_poisson(), dist_translate(), dist_trunc(), dist_uniform()

Examples

d_weibull <- dist_weibull(shape = 3, scale = 1)
x <- d_weibull$sample(100)
d_emp <- dist_empirical(x)

plot_distributions(
  empirical = d_emp,
  theoretical = d_weibull,
  estimated = d_weibull,
  with_params = list(
    estimated = inflate_params(
      fitdistrplus::fitdist(x, distr = "weibull")$estimate
    )
  ),
  .x = seq(0, 2, length.out = 100)
)

Fit a neural network based distribution model to data

Description

This function delegates most work to keras3::fit.keras.src.models.model.Model() and performs additional consistency checks to make sure tf_compile_model() was called with the appropriate options to support fitting the observations y as well as automatically converting y to a n x 6 matrix needed by the compiled loss function.

Usage

## S3 method for class 'reservr_keras_model'
fit(
  object,
  x,
  y,
  batch_size = NULL,
  epochs = 10,
  verbose = getOption("keras.fit_verbose", default = 1),
  callbacks = NULL,
  view_metrics = getOption("keras.view_metrics", default = "auto"),
  validation_split = 0,
  validation_data = NULL,
  shuffle = TRUE,
  class_weight = NULL,
  sample_weight = NULL,
  initial_epoch = 0,
  steps_per_epoch = NULL,
  validation_steps = NULL,
  ...
)

Arguments

Details

Additionally, the default batch_size is min(nrow(y), 10000) instead of keras default of 32 because the latter is a very bad choice for fitting most distributions since the involved loss is much less stable than typical losses used in machine learning, leading to divergence for small batch sizes.

Value

A history object that contains all information collected during training. The model object will be updated in-place as a side-effect.

See Also

predict.reservr_keras_model tf_compile_model keras3::fit.keras.src.models.model.Model

Examples

dist <- dist_exponential()
params <- list(rate = 1.0)
N <- 100L
rand_input <- runif(N)
x <- dist$sample(N, with_params = params)

if (interactive()) {
  tf_in <- keras3::layer_input(1L)
  mod <- tf_compile_model(
    inputs = list(tf_in),
    intermediate_output = tf_in,
    dist = dist,
    optimizer = keras3::optimizer_adam(),
    censoring = FALSE,
    truncation = FALSE
  )

  tf_fit <- fit(
    object = mod,
    x = k_matrix(rand_input),
    y = x,
    epochs = 10L,
    callbacks = list(
      callback_debug_dist_gradients(mod, k_matrix(rand_input), x, keep_grads = TRUE)
    )
  )
}

Fit a Blended mixture using an ECME-Algorithm

Description

Fit a Blended mixture using an ECME-Algorithm

Usage

fit_blended(
  dist,
  obs,
  start,
  min_iter = 0L,
  max_iter = 100L,
  skip_first_e = FALSE,
  tolerance = 1e-05,
  trace = FALSE,
  ...
)

Arguments

Value

A list with elements

• params the fitted parameters in the same structure as init.

• params_hist (if trace is TRUE) the history of parameters (after each e- and m- step)

• iter the number of outer EM-iterations

• logLik the final log-likelihood

See Also

Other distribution fitting functions: fit_dist(), fit_erlang_mixture(), fit_mixture()

Examples

dist <- dist_blended(
   list(
     dist_exponential(),
     dist_genpareto()
   )
 )

params <- list(
  probs = list(0.9, 0.1),
  dists = list(
    list(rate = 2.0),
    list(u = 1.5, xi = 0.2, sigmau = 1.0)
  ),
  breaks = list(1.5),
  bandwidths = list(0.3)
)

x <- dist$sample(100L, with_params = params)

dist$default_params$breaks <- params$breaks
dist$default_params$bandwidths <- params$bandwidths
if (interactive()) {
  fit_blended(dist, x)
}

Fit a general distribution to observations

Description

The default implementation performs maximum likelihood estimation on all placeholder parameters.

Usage

fit_dist(dist, obs, start, ...)

fit_dist_direct(dist, obs, start, ..., .start_with_default = FALSE)

## S3 method for class 'Distribution'
fit(object, obs, start, ...)

Arguments

Details

For Erlang mixture distributions and for Mixture distributions, an EM-Algorithm is instead used to improve stability.

fit() and fit_dist() will chose an optimisation method optimized for the specific distribution given. fit_dist_direct() can be used to force direct maximisation of the likelihood.

Value

A list with at least the elements

• params the fitted parameters in the same structure as init.

• logLik the final log-likelihood

Additional information may be provided depending on dist.

See Also

Other distribution fitting functions: fit_blended(), fit_erlang_mixture(), fit_mixture()

Other distribution fitting functions: fit_blended(), fit_erlang_mixture(), fit_mixture()

Examples

x <- rexp(100)
lambda_hat <- 1 / mean(x)
lambda_hat2 <- fit_dist(dist_exponential(), x)$params$rate
identical(lambda_hat, lambda_hat2)
dist <- dist_mixture(list(dist_normal(), dist_translate(dist_exponential(), offset = 6)))
params <- list(
  dists = list(list(mean = 5, sd = 1), list(dist = list(rate = 1))), probs = list(0.95, 0.05)
)
set.seed(2000)
u <- runif(100, 10, 20)
x <- dist$sample(100, with_params = params)
obs <- trunc_obs(x = x[x <= u], tmin = -Inf, tmax = u[x <= u])

default_fit <- fit_dist(dist, obs)
direct_fit <- fit_dist_direct(dist, obs)
# NB: direct optimisation steps with pre-run take a few seconds

direct_fit_init <- fit_dist_direct(dist, obs, start = default_fit$params)
direct_fit_auto_init <- fit_dist_direct(dist, obs, .start_with_default = TRUE)

stopifnot(direct_fit_init$logLik == direct_fit_auto_init$logLik)

c(default_fit$logLik, direct_fit$logLik, direct_fit_init$logLik)

Find starting values for distribution parameters

Description

Find starting values for distribution parameters

Usage

## S3 method for class 'MixtureDistribution'
fit_dist_start(dist, obs, dists_start = NULL, ...)

fit_dist_start(dist, obs, ...)

Arguments

Value

A list of initial parameters suitable for passing to fit_dist().

Examples

fit_dist_start(dist_exponential(), rexp(100))

Fit an Erlang mixture using an ECME-Algorithm

Description

Fit an Erlang mixture using an ECME-Algorithm

Usage

fit_erlang_mixture(
  dist,
  obs,
  start,
  min_iter = 0L,
  max_iter = 100L,
  skip_first_e = FALSE,
  tolerance = 1e-05,
  trace = FALSE,
  parallel = FALSE,
  ...
)

Arguments

Value

A list with elements

• params the fitted parameters in the same structure as init.

• params_hist (if trace is TRUE) the history of parameters (after each e- and m- step). Otherwise an empty list.

• iter the number of outer EM-iterations

• logLik the final log-likelihood

See Also

Other distribution fitting functions: fit_blended(), fit_dist(), fit_mixture()

Examples

dist <- dist_erlangmix(list(NULL, NULL, NULL))
params <- list(
  shapes = list(1L, 4L, 12L),
  scale = 2.0,
  probs = list(0.5, 0.3, 0.2)
)
x <- dist$sample(100L, with_params = params)
fit_erlang_mixture(dist, x, init = "kmeans")

Fit a generic mixture using an ECME-Algorithm

Description

Fit a generic mixture using an ECME-Algorithm

Usage

fit_mixture(
  dist,
  obs,
  start,
  min_iter = 0L,
  max_iter = 100L,
  skip_first_e = FALSE,
  tolerance = 1e-05,
  trace = FALSE,
  ...
)

Arguments

Value

A list with elements

• params the fitted parameters in the same structure as init.

• params_hist (if trace is TRUE) the history of parameters (after each e- and m- step)

• iter the number of outer EM-iterations

• logLik the final log-likelihood

See Also

Other distribution fitting functions: fit_blended(), fit_dist(), fit_erlang_mixture()

Examples

dist <- dist_mixture(
  list(
    dist_dirac(0.0),
    dist_exponential()
  )
)

params <- list(
  probs = list(0.1, 0.9),
  dists = list(
    list(),
    list(rate = 1.0)
  )
)

x <- dist$sample(100L, with_params = params)

fit_mixture(dist, x)

Flatten / Inflate parameter lists / vectors

Description

Flatten / Inflate parameter lists / vectors

Usage

flatten_params(params)

flatten_params_matrix(params)

flatten_bounds(bounds)

inflate_params(flat_params)

Arguments

Value

flatten_params returns a 'flattened' vector of parameters. It is intended as an adapter for multi-dimensional optimisation functions to distribution objects.

flatten_params_matrix returns a 'flattened' matrix of parameters. It is intended as an adapter for multi-dimensional optimisation functions to distribution objects. Each column corresponds to one input element.

flatten_bounds returns a named list of vectors with names lower and upper. Containing the upper and lower bounds of each parameter.

inflate_params returns an 'inflated' list of parameters. This can be passed as the with_params argument to most distribution functions.

Examples

library(ggplot2)

mm <- dist_mixture(list(
  dist_exponential(NULL),
  dist_lognormal(0.5, NULL)
), list(NULL, 1))

ph <- mm$get_placeholders()
ph_flat <- flatten_params(ph)
ph_reinflated <- inflate_params(ph_flat)
ph_flat[] <- c(1, 1, 6)
ph_sample <- inflate_params(ph_flat)

x <- mm$sample(
  100,
  with_params = ph_sample
)

emp_cdf <- ecdf(x)

ggplot(data.frame(t = seq(from = min(x), to = max(x), length.out = 100))) %+%
  geom_point(aes(x = t, y = emp_cdf(t))) %+%
  geom_line(aes(x = t, y = mm$probability(t, with_params = ph_sample)),
            linetype = 2)

Adaptive Gauss-Kronrod Quadrature for multiple limits

Description

Integrates fun over the bounds [ lower, upper ] vectorized over lower and upper. Vectorized list structures of parameters can also be passed.

Usage

integrate_gk(
  fun,
  lower,
  upper,
  params = list(),
  .tolerance = .Machine$double.eps^0.25,
  .max_iter = 100L
)

Arguments

Details

The integration error is estimated by the Gauss-Kronrod quadrature as the absolute difference between the 7-point quadrature and the 15-point quadrature. Integrals that did not converge will be bisected at the midpoint. The params object will be recursively subsetted on all numeric vectors with the same length as the number of observations.

Value

A vector of integrals with the i-th entry containing an approximation of the integral of fun(t, pick_params_at(params, i)) dt over the interval lower[i] to upper[i]

Examples

# Argument recycling and parallel integration of two intervals
integrate_gk(sin, 0, c(pi, 2 * pi))

dist <- dist_exponential()
integrate_gk(
  function(x, p) dist$density(x, with_params = p),
  lower = 0, upper = 1:10,
  params = list(rate = 1 / 1:10)
)
dist$probability(1:10, with_params = list(rate = 1 / 1:10))

Intervals

Description

Intervals

Usage

interval(
  range = c(-Inf, Inf),
  ...,
  include_lowest = closed,
  include_highest = closed,
  closed = FALSE,
  integer = FALSE,
  read_only = FALSE
)

is.Interval(x)

Arguments

Value

interval returns an Interval. is.Interval returns TRUE if x is an Interval, FALSE otherwise.

See Also

interval-operations

Examples

# The real line
interval()

# Closed unit interval
interval(c(0, 1), closed = TRUE)
# Alternative form
interval(0, 1, closed = TRUE)

# Non-negative real line
interval(c(0, Inf), include_lowest = TRUE)

Convex union and intersection of intervals

Description

Convex union and intersection of intervals

Usage

interval_union(..., intervals = list())

interval_intersection(..., intervals = list())

Arguments

Value

interval_union returns the convex union of all intervals in intervals. This is the smallest interval completely containing all intervals.

interval_intersection returns the set intersection of all intervals in intervals. The empty set is represented by the open interval (0, 0).

See Also

interval

Examples

interval_union(
  interval(c(0, 1), closed = TRUE),
  interval(c(1, 2))
)

interval_union(
  interval(c(0, 5)),
  interval(c(1, 4), closed = TRUE)
)

# Convex union is not equal to set union:
interval_union(
  interval(c(0, 1)),
  interval(c(2, 3))
)

# The empty union is {}
interval_union()

interval_intersection(
  interval(c(0, 1)),
  interval(c(0.5, 2))
)

interval_intersection(
  interval(c(0, Inf)),
  interval(c(-Inf, 0))
)

interval_intersection(
  interval(c(0, Inf), include_lowest = TRUE),
  interval(c(-Inf, 0), include_highest = TRUE)
)

interval_intersection(
  interval(c(0, 5)),
  interval(c(1, 6), closed = TRUE)
)

# The empty intersection is (-Inf, Inf)
interval_intersection()

Test if object is a Distribution

Description

Test if object is a Distribution

Usage

is.Distribution(object)

Arguments

Value

TRUE if object is a Distribution, FALSE otherwise.

Examples

is.Distribution(dist_dirac())

Cast to a TensorFlow matrix

Description

Cast to a TensorFlow matrix

Usage

k_matrix(x, dtype = NULL)

Arguments

Value

A two-dimensional tf.Tensor with values from x. The shape will be ⁠(nrow(x), ncol(x))⁠ where x is first converted to an R matrix via as.matrix().

Examples

if (interactive()) {
  k_matrix(diag(1:3))
  k_matrix(diag(1:3), dtype = "int32")
  # Vectors are converted to columns:
  k_matrix(1:3)
}

Plot several distributions

Description

Plot several distributions

Usage

plot_distributions(
  ...,
  distributions = list(),
  .x,
  plots = c("density", "probability", "hazard"),
  with_params = list(),
  as_list = FALSE
)

Arguments

Value

A stacked patchwork of the requested ggplots

Examples

rate <- 1
x <- rexp(20, rate)
d_emp <- dist_empirical(x, positive = TRUE)
d_exp <- dist_exponential()
plot_distributions(
  empirical = d_emp,
  theoretical = d_exp,
  estimated = d_exp,
  with_params = list(
    theoretical = list(rate = rate),
    estimated = list(rate = 1 / mean(x))
  ),
  .x = seq(1e-4, 5, length.out = 100)
)

Predict individual distribution parameters

Description

Predict individual distribution parameters

Usage

## S3 method for class 'reservr_keras_model'
predict(object, data, as_matrix = FALSE, ...)

Arguments

Value

A parameter list suitable for the with_params argument of the distribution family used for the model. Contains one set of parameters per row in data.

Examples

if (interactive()) {
  dist <- dist_exponential()
  params <- list(rate = 1.0)
  N <- 100L
  rand_input <- runif(N)
  x <- dist$sample(N, with_params = params)

  tf_in <- keras3::layer_input(1L)
  mod <- tf_compile_model(
    inputs = list(tf_in),
    intermediate_output = tf_in,
    dist = dist,
    optimizer = keras3::optimizer_adam(),
    censoring = FALSE,
    truncation = FALSE
  )

  tf_fit <- fit(
    object = mod,
    x = k_matrix(rand_input),
    y = x,
    epochs = 10L,
    callbacks = list(
      callback_debug_dist_gradients(mod, k_matrix(rand_input), x)
    )
  )

  tf_preds <- predict(mod, data = k_matrix(rand_input))
}

Determine probability of reporting under a Poisson arrival Process

Description

Determines the probability that claims occuring under a Poisson process with arrival intensity expo and reporting delay distribution dist during the time between t_min and t_max are reported between tau_min and tau_max.

Usage

prob_report(
  dist,
  intervals,
  expo = NULL,
  with_params = list(),
  .tolerance = .Machine$double.eps^0.5,
  .max_iter = 100L,
  .try_compile = TRUE
)

Arguments

Details

The reporting probability is given by

P(x + d in [tmin, tmax] | x in [xmin, xmax]) = E(P(x + d in [tmin, tmax] | x) | x in [xmin, xmax]) / P(x in [xmin, xmax]) = int_[xmin, xmax] expo(x) P(x + d in [tmin, tmax]) dx = int_[xmin, xmax] expo(x) P(d in [tmin - x, tmax - x]) dx / int_[xmin, xmax] expo(x) dx

prob_report uses integrate_gk() to compute the two integrals.

Value

A vector of reporting probabilities, with one entry per row of intervals.

Examples

dist <- dist_exponential()
ints <- data.frame(
  xmin = 0,
  xmax = 1,
  tmin = seq_len(10) - 1.0,
  tmax = seq_len(10)
)
params <- list(rate = rep(c(1, 0.5), each = 5))

prob_report(dist, ints, with_params = params)

Quantiles of Distributions

Description

Produces quantiles corresponding to the given probabilities with configurable distribution parameters.

Usage

## S3 method for class 'Distribution'
quantile(x, probs = seq(0, 1, 0.25), with_params = list(), ..., .start = 0)

Arguments

Details

If x$has_capability("quantile") is true, this returns the same as x$quantile(probs, with_params = with_params). In this case, with_params may contain separate sets of parameters for each quantile to be determined.

Otherwise, a numerical estimation of the quantiles is done using the density and probability function. This method assumes with_params to cantain only one set of parameters. The strategy uses two steps:

1. Find the smallest and largest quantiles in probs using a newton method starting from .start.

2. Find the remaining quantiles with bisection using stats::uniroot().

Value

The quantiles of x corresponding to probs with parameters with_params.

Examples

# With quantiles available
dist <- dist_normal(sd = 1)
qqs <- quantile(dist, probs = rep(0.5, 3), with_params = list(mean = 1:3))
stopifnot(all.equal(qqs, 1:3))

# Without quantiles available
dist <- dist_erlangmix(shapes = list(1, 2, 3), scale = 1.0)
my_probs <- c(0, 0.01, 0.25, 0.5, 0.75, 1)
qqs <- quantile(
  dist, probs = my_probs,
  with_params = list(probs = list(0.5, 0.3, 0.2)), .start = 2
)

all.equal(dist$probability(qqs, with_params = list(probs = list(0.5, 0.3, 0.2))), my_probs)
# Careful: Numerical estimation of extreme quantiles can result in out-of-bounds values.
# The correct 0-quantile would be 0 in this case, but it was estimated < 0.
qqs[1L]

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

generics

fit

Soft-Max function

Description

Softmax for a vector x is defined as

Usage

softmax(x)

dsoftmax(x)

Arguments

Details

s_i = \exp(x_i) / \sum_k \exp(x_k)

It satisfies sum(s) == 1.0 and can be used to smoothly enforce a sum constraint.

Value

softmax returns the softmax of x; rowwise if x is a matrix.

dsoftmax returns the Jacobi-matrix of softmax(x) at x. x must be a vector.

Examples

softmax(c(5, 5))
softmax(diag(nrow = 5, ncol = 6))

Compile a Keras model for truncated data under dist

Description

Compile a Keras model for truncated data under dist

Usage

tf_compile_model(
  inputs,
  intermediate_output,
  dist,
  optimizer,
  censoring = TRUE,
  truncation = TRUE,
  metrics = NULL,
  weighted_metrics = NULL
)

Arguments

Value

A reservr_keras_model that can be used to train truncated and censored observations from dist based on input data from inputs.

Examples

dist <- dist_exponential()
params <- list(rate = 1.0)
N <- 100L
rand_input <- runif(N)
x <- dist$sample(N, with_params = params)

if (interactive()) {
  tf_in <- keras3::layer_input(1L)
  mod <- tf_compile_model(
    inputs = list(tf_in),
    intermediate_output = tf_in,
    dist = dist,
    optimizer = keras3::optimizer_adam(),
    censoring = FALSE,
    truncation = FALSE
  )
}

Initialise model weights to a global parameter fit

Description

Initialises a compiled reservr_keras_model weights such that the predictions are equal to, or close to, the distribution parameters given by params.

Usage

tf_initialise_model(
  model,
  params,
  mode = c("scale", "perturb", "zero", "none")
)

Arguments

Value

Invisibly model with changed weights

Examples

dist <- dist_exponential()
group <- sample(c(0, 1), size = 100, replace = TRUE)
x <- dist$sample(100, with_params = list(rate = group + 1))
global_fit <- fit(dist, x)

if (interactive()) {
  library(keras3)
  l_in <- layer_input(shape = 1L)
  mod <- tf_compile_model(
    inputs = list(l_in),
    intermediate_output = l_in,
    dist = dist,
    optimizer = optimizer_adam(),
    censoring = FALSE,
    truncation = FALSE
  )
  tf_initialise_model(mod, global_fit$params)
  fit_history <- fit(
    mod,
    x = group,
    y = x,
    epochs = 200L
  )

  predicted_means <- predict(mod, data = as_tensor(c(0, 1), config_floatx()))
}

Define a set of truncated observations

Description

If x is missing, both xmin and xmax must be specified.

Usage

trunc_obs(x, xmin = x, xmax = x, tmin = -Inf, tmax = Inf, w = 1)

as_trunc_obs(.data)

truncate_obs(.data, tmin_new = -Inf, tmax_new = Inf, .partial = FALSE)

repdel_obs(.data, accident, delay, time, .truncate = FALSE)

Arguments

Details

Uncensored observations must satisfy tmin <= xmin = x = xmax <= tmax. Censored observations must satisfy ⁠tmin <= xmin < xmax <= tmax⁠ and x = NA.

Value

trunc_obs: A trunc_obs tibble with columns x, xmin, xmax, tmin and tmax describing possibly interval-censored observations with truncation

as_trunc_obs returns a trunc_obs tibble.

truncate_obs returns a trunc_obs tibble with possibly fewer observations than .data and updated truncation bounds.

repdel_obs returns a trunc_obs tibble corresponding to the reporting delay observations of each claim. If .truncate is FALSE, the result is guaranteed to have the same number of rows as .data.

Examples

N <- 100
x <- rexp(N, 0.5)

# Random, observation dependent truncation intervals
tmin <- runif(N, 0, 1)
tmax <- tmin + runif(N, 1, 2)

oob <- x < tmin | x > tmax
x <- x[!oob]
tmin <- tmin[!oob]
tmax <- tmax[!oob]

# Number of observations after truncation
N <- length(x)

# Randomly interval censor 30% of observations
cens <- rbinom(N, 1, 0.3) == 1L
xmin <- x
xmax <- x
xmin[cens] <- pmax(tmin[cens], floor(x[cens]))
xmax[cens] <- pmin(tmax[cens], ceiling(x[cens]))
x[cens] <- NA

trunc_obs(x, xmin, xmax, tmin, tmax)

as_trunc_obs(c(1, 2, 3))
as_trunc_obs(data.frame(x = 1:3, tmin = 0, tmax = 10))
as_trunc_obs(data.frame(x = c(1, NA), xmin = c(1, 2), xmax = c(1, 3)))
truncate_obs(1:10, tmin_new = 2.0, tmax_new = 8.0)

Truncate claims data subject to reporting delay

Description

Truncate claims data subject to reporting delay

Usage

truncate_claims(data, accident, delay, time, .report_col = "report")

Arguments

Value

Truncated data. The reporting time is stored in a colnumn named by .report_col unless .report_col is NULL. If both .report_col is NULL and time contains only Infs, a warning will be issued since data will be returned unchanged and no work will be done.

Examples

claims_full <- data.frame(
  acc = runif(100),
  repdel = rexp(100)
)
tau <- 2.0
truncate_claims(claims_full, acc, repdel, tau)

Compute weighted moments

Description

Compute weighted moments

Usage

weighted_moments(x, w, n = 2L, center = TRUE)

Arguments

Value

A vector of length n where the kth entry is the kth weighted moment of x with weights w. If center is TRUE the moments are centralized, i.e. E((X - E(X))^k). The first moment is never centralized. The moments are scaled with 1 / sum(w), so they are not de-biased.

e.g. the second central weighted moment weighted_moment(x, w)[2L] is equal to var(rep(x, w)) * (sum(w) - 1) / sum(w) for integer w

See Also

Other weighted statistics: weighted_quantile(), weighted_tabulate()

Examples

weighted_moments(rexp(100))
weighted_moments(c(1, 2, 3), c(1, 2, 3))
c(mean(rep(1:3, 1:3)), var(rep(1:3, 1:3)) * 5 / 6)

Compute weighted quantiles

Description

Compute weighted quantiles

Usage

weighted_quantile(x, w, probs)

weighted_median(x, w)

Arguments

Value

A vector the same length as probs with the corresponding weighted quantiles of x with weight w. For integer weights, this is equivalent to quantile(rep(x, w), probs)

The weighted median of x with weights w. For integer weights, this is equivalent to median(rep(x, w))

See Also

Other weighted statistics: weighted_moments(), weighted_tabulate()

Examples

weighted_median(1:6)
weighted_median(1:3, c(1, 4, 9))
weighted_median(1:3, c(9, 4, 1))

weighted_quantile(1:3, c(1, 4, 9), seq(0.0, 1.0, by = 0.25))
quantile(rep(1:3, c(1, 4, 9)), seq(0.0, 1.0, by = 0.25))

Compute weighted tabulations

Description

Computes the sum of w grouped by bin. If w is missing the result is equivalent to tabulate(bin, nbins)

Usage

weighted_tabulate(bin, w, nbins = max(1L, bin, na.rm = TRUE))

Arguments

Value

A vector with length nbins where the ith result is equal to sum(w[bin == i]) or sum(bin == i) if w is missing. For integer weights, this is equivalent to tabulate(rep(bin, w), nbins).

See Also

Other weighted statistics: weighted_moments(), weighted_quantile()

Examples

weighted_tabulate(c(1, 1, 2))
weighted_tabulate(c(1, 1, 2), nbins = 3L)
weighted_tabulate(c(1, 1, 2), w = c(0.5, 0.5, 1), nbins = 3L)