| Title: | Kumaraswamy Complementary Weibull Geometric (Kw-CWG) Probability Distribution |
| Version: | 1.0.0 |
| Description: | Density, distribution function, quantile function and random generation for the Kumaraswamy Complementary Weibull Geometric (Kw-CWG) lifetime probability distribution proposed in Afify, A.Z. et al (2017) <doi:10.1214/16-BJPS322>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| LazyData: | true |
| URL: | https://github.com/matheushjs/elfDistr |
| BugReports: | https://github.com/matheushjs/elfDistr/issues |
| RoxygenNote: | 6.1.1 |
| Depends: | R (≥ 3.1.0) |
| LinkingTo: | Rcpp |
| Imports: | Rcpp |
| SystemRequirements: | C++11 |
| NeedsCompilation: | yes |
| Suggests: | testthat |
| Packaged: | 2019-10-06 05:23:46 UTC; mathjs |
| Author: | Matheus H. J. Saldanha [aut, cre], Adriano K. Suzuki [aut] |
| Maintainer: | Matheus H. J. Saldanha <mhjsaldanha@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2019-10-07 18:00:02 UTC |
Kumaraswamy Complementary Weibull Geometric (Kw-CWG) Probability Distribution
Description
Density, distribution function, quantile function and random generation for the Kumaraswamy Complementary Weibull Geometric probability distribution (Kw-CWG) lifetime distribution.
Details
This package follows naming convention that is consistent with base R,
where density (or probability mass) functions, distribution functions,
quantile functions and random generation functions names are followed by
d, p, q, and r prefixes.
Behaviour of the functions is consistent with base R, where for
not valid parameters values NaN's are returned, while
for values beyond function support 0's are returned
(e.g. for non-integers in discrete distributions, or for
negative values in functions with non-negative support).
All the functions vectorized and coded in C++ using Rcpp.
Kumaraswamy Complementary Weibull Geometric Probability Distribution
Description
Density, distribution function, quantile function and random generation for the Kumaraswamy Complementary Weibull Geometric (Kw-CWG) probability distribution.
Usage
dkwcwg(x, alpha, beta, gamma, a, b, log = FALSE)
pkwcwg(q, alpha, beta, gamma, a, b, lower.tail = TRUE, log.p = FALSE)
qkwcwg(p, alpha, beta, gamma, a, b, lower.tail = TRUE, log.p = FALSE)
rkwcwg(n, alpha, beta, gamma, a, b)
Arguments
x, q |
vector of quantiles. |
alpha, beta, gamma, a, b |
Parameters of the distribution. 0 < alpha < 1, and the other parameters mustb e positive. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of observations. If |
Details
Probability density function
f(x) = \alpha^a \beta \gamma a b (\gamma x)^{\beta - 1} \exp[-(\gamma x)^\beta] \cdot
\frac{\{1 - \exp[-(\gamma x)^\beta]\}^{a-1}}{\{ \alpha + (1 - \alpha) \exp[-(\gamma x)^\beta] \}^{a+1}} \cdot
\cdot \bigg\{ 1 - \frac{\alpha^a[1 - \exp[-(\gamma x)^\beta]]^a}{\{ \alpha + (1 - \alpha) \exp[-(\gamma x)^\beta] \}^a} \bigg\}
Cumulative density function
F(x) = 1 - \bigg\{ 1 - \bigg[ \frac{\alpha (1 - \exp[-(\gamma x)^\beta]) }{ \alpha + (1 - \alpha) \exp[-(\gamma x)^\beta] } \bigg]^a \bigg\}^b
Quantile function
Q(u) = \gamma^{-1} \bigg\{
\log\bigg[\frac{
\alpha + (1 - \alpha) \sqrt[a]{1 - \sqrt[b]{1 - u} }
}{
\alpha (1 - \sqrt[a]{1 - \sqrt[b]{1 - u} } )
}\bigg]
\bigg\}^{1/\beta}, 0 < u < 1
References
Afify, A.Z., Cordeiro, G.M., Butt, N.S., Ortega, E.M. and Suzuki, A.K. (2017). A new lifetime model with variable shapes for the hazard rate. Brazilian Journal of Probability and Statistics