chen: Chen distribption

In dmi3kno/qpd: Tools for Quantile-Parametrized Distribiutions

Chen distribption

Description

Defines quantile function (ICDF), and quantile density function as well as probability function (CDF) for Chen distribution Distribution range is 0<x<\infty Chen distribution QF, QDF, CDF and PDF are

Q(u)=\left[\ln\left(1-\frac{\ln(1-u)}{\lambda}\right)\right]^{1/\beta}

q(u)=\frac{\ln\left(1-\frac{\ln(1-u)}{\lambda}\right)^{\frac{1}{\beta}-1}}{\beta(\ln(1-u)-\lambda)(u-1)}

F(x)=1-\exp(\lambda(1-\exp(x^\beta)))

f(x)=\lambda\beta x^{\beta-1}\exp[\lambda(1-\exp(x^\beta)+x^\beta)]

Usage

qchen(p, lambda, beta)

fchen(x, lambda, beta, log = FALSE)

dqchen(p, lambda, beta, log = FALSE)

pchen(x, lambda, beta)

fchen(x, lambda, beta, log = FALSE)

rchen(n, lambda, beta)

Arguments

p	vector of probabilities
lambda	shape parameter of Chen distribution, must be positive
beta	shape parameter of Chen distribution, must be positive
x	numeric observations
log	logical; if TRUE, log density is returnes. Default is FALSE
n	numeric; number of samples to draw from Tukey Lambda distribution

Value

vector

References

Chen Z (2000) A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics & Probability Letters, Volume 49, Issue 2, https://doi.org/10.1016/S0167-7152(00)00044-4.

Examples

qchen(0.1, 0.5, 1)
p <- runif(1e4)
x <- qchen(p, 0.5, 1)+qchen(p, 1, 0.5)
hist(x,30)

dmi3kno/qpd documentation built on Sept. 29, 2024, 6:39 p.m.