kd {new.dist}

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)

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.

Value

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

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)