new.dist (version 0.1.1)

kd: Kumaraswamy Distribution

Description

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)

Value

dkd gives the density, pkd gives the distribution function, qkd gives the quantile function and rkd generates random deviates.

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.

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)
pkd(0.5,lambda=2,alpha=3)
qkd(.8,lambda=2,alpha=3)
rkd(10,lambda=2,alpha=3)