MW: The Modified Weibull Distribution

In ousuga/reldist: Reliability and survival distributions

Description

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

Usage

dMW(x, beta, gamma, lambda, log = FALSE)

pMW(q, beta, gamma, lambda, lower.tail = TRUE, log.p = FALSE)

qMW(p, beta, gamma, lambda, lower.tail = TRUE, log.p = FALSE)

rMW(n, beta, gamma, lambda)

hMW(x, beta, gamma, lambda)

Arguments

x,q	vector of quantiles.
beta	shape parameter one.
gamma	parameter two.
lambda	scale 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 distribution with parameters beta, gamma and lambda has density given by

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

for x > 0.

Value

dMW gives the density, pMW gives the distribution function, qMW gives the quantile function, rMW generates random deviates and hMW gives the hazard function.

Examples

## The probability density function
curve(dMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from=0, to=2, 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(pMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from = 0, to = 2, ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pMW(x, beta = 2, gamma = 1.5, lambda = 0.2, lower.tail = FALSE), from = 0, to = 2, 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 = qMW(p = p, beta = 2, gamma = 1.5, lambda = 0.2), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from = 0, add = TRUE, col = "red")

## The random function
hist(rMW(n = 1000, beta = 2, gamma = 1.5, lambda = 0.2), freq = FALSE, , ylim=c(0,1.5),xlab = "x", las = 1, main = "")
curve(dMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from = 0, , ylim=c(0,1.5), add = T, col = "red")

## The Hazard function
curve(hMW(x, beta = 2, gamma = 1.5, lambda = 0.2), from = 0, to = 1.5, ylim = c(0, 5), col = "red", las = 1, ylab = "The Hazard function")

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