MWEx: The Modified Weibull Extension Distribution

In ousuga/reldist: Reliability and survival distributions

Description

Density, distribution function, quantile function, random generation and hazard function for the modified weibull extension distribution with parameters alpha, beta and lambda.

Usage

dMWEx(x, alpha, beta, lambda, log = FALSE)

pMWEx(q, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)

qMWEx(p, alpha, beta, lambda, lower.tail = TRUE, log.p = FALSE)

rMWEx(n, alpha, beta, lambda)

hMWEx(x, alpha, beta, lambda)

Arguments

x,q	vector of quantiles.
alpha	parameter one.
beta	parameter two.
lambda	parameter three.
log,log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
p	vector of probabilities.
n	number of observations.

Details

The modified weibull extension distribution with parameters alpha, beta and lambda has density given by

f(x) = lambda*beta*((x/alpha)^(beta-1))*exp((x/alpha)^beta + lambda*alpha*(1-exp((x/alpha)^beta)))

for x > 0.

Value

dMWEx gives the density, pMWEx gives the distribution function, qMWEx gives the quantile function, rMWEx generates random deviates and hMWEx gives the hazard function.

Examples

## The probability density function
curve(dMWEx(x, alpha = 1/0.5, beta = 3, lambda = 2), from = 0, to = 2.5, ylim = c(0, 1.5), col = "red", las = 1, ylab = "The probability density function")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pMWEx(x, alpha = 1/0.5, beta = 3, lambda = 2), from = 0, to = 2.5, ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pMWEx(x, alpha = 1/0.5, beta = 3, lambda = 2,  lower.tail = FALSE), from = 0, to = 2.5, ylim = c(0, 1), col = "red", las = 1, ylab = "The Reliability function")

## The quantile function
p <- seq(from = 0, to = 0.998, length.out = 100)
plot(x = qMWEx(p, alpha = 1/0.5, beta = 3, lambda = 2), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pMWEx(x, alpha = 1/0.5, beta = 3, lambda = 2), from = 0, add = TRUE, col = "red")

## The random function
hist(rMWEx(n = 10000, alpha = 1/0.5, beta = 3, lambda = 2), freq = FALSE, ylim = c(0, 1.5), xlab = "x", las = 1, main = "")
curve(dMWEx(x, alpha = 1/0.5, beta = 3, lambda = 2),  from = 0, ylim = c(0, 2.5), add = T, col = "red")

## The Hazard function
curve(hMWEx(x, alpha = 1/0.5, beta = 3, lambda = 2), from = 0, to = 1.7, ylim = c(0, 12), col = "red", ylab = "The hazard function", las = 1)

ousuga/reldist documentation built on May 24, 2019, 5:54 p.m.