Density, distribution function, quantile function and random generation for
Kumaraswamy distribution with shape parameters.
Usage
dkd(x, lambda, alpha, log = FALSE)
pkd(q, lambda, alpha, lower.tail = TRUE, log.p = FALSE)
qkd(p, lambda, alpha, lower.tail = TRUE)
rkd(n, lambda, alpha)Arguments
- x, q
vector of quantiles.
- alpha, lambda
are non-negative shape parameters.
- log, log.p
logical; if TRUE, probabilities p are given as log(p).
- lower.tail
logical; if TRUE (default), probabilities are \(P\left[ X\leq x\right]\), otherwise, \(P\left[ X>x\right] \).
- p
vector of probabilities.
- n
number of observations. If
length(n) > 1, the length is taken to be the number required.
Value
dkd gives the density, pkd gives the distribution
function, qkd gives the quantile function and rkd generates
random deviates.
Details
Kumaraswamy distribution with non-negative shape parameters \(\alpha\) and \(\lambda\) has density $$f\left( x\right) =\alpha \lambda x^{\lambda -1}\left( 1-x^{\lambda } \right)^{\alpha -1},$$ where $$0<x<1,~~\alpha ,\lambda >0.$$
References
Kohansal, A. ve Bakouch, H. S., 2021, Estimation procedures for Kumaraswamy distribution parameters under adaptive type-II hybrid progressive censoring, Communications in Statistics-Simulation and Computation, 50 (12), 4059-4078.
Examples
library("new.dist")
dkd(0.1,lambda=2,alpha=3)
#> [1] 0.58806
pkd(0.5,lambda=2,alpha=3)
#> [1] 0.578125
qkd(.8,lambda=2,alpha=3)
#> [1] 0.6443574
rkd(10,lambda=2,alpha=3)
#> [1] 0.8008176 0.4227315 0.4386099 0.6428988 0.6342509 0.5038876 0.7964932
#> [8] 0.7012778 0.3052778 0.5131865