EW: The Exponentiated Weibull Distribution

In ousuga/reldist: Reliability and survival distributions

Description

Density, distribution function, quantile function, random generation and hazard function for the exponentiated weibull distribution with parameters alpha, theta and lambda.

Usage

dEW(x, alpha, theta, lambda, log = FALSE)

pEW(q, alpha, theta, lambda, lower.tail = TRUE, log.p = FALSE)

qEW(p, alpha, theta, lambda, lower.tail = TRUE, log.p = FALSE)

rEW(n, alpha, theta, lambda)

hEW(x, alpha, theta, lambda)

Arguments

x,q	vector of quantiles.
alpha	scale parameter.
theta,lambda	shape parameters.
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 Exponentiated Weibull Distribution with parameters alpha, theta and lambda has density given by

f(x)=lambda*alpha*theta*x^(theta-1)*exp(-alpha*(x^theta))*(1-exp(-alpha*(x^theta)))^(lambda-1)

for x > 0.

#'

Value

dEW gives the density, pEW gives the distribution function, qEW gives the quantile function, rEW generates random deviates and hEW gives the hazard function.

Examples

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

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pEW(x, alpha = 2, theta = 1.5, lambda = 0.5), from = 0, to = 2,  col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pEW(x, alpha = 2, theta = 1.5, lambda = 0.5, lower.tail = FALSE), from = 0, to = 2,  col = "red", las = 1, ylab = "The Reliability function")

## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qEW(p, alpha = 2, theta = 1.5, lambda = 0.5), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pEW(x, alpha = 2, theta = 1.5, lambda = 0.5),  from = 0, add = TRUE, col = "red")

## The random function
hist(rEW(n = 10000, alpha = 2, theta = 1.5, lambda = 0.5), freq = FALSE, xlab = "x", las = 1, main = "")
curve(dEW(x, alpha = 2, theta = 1.5, lambda = 0.5),  from = 0, add = TRUE, col = "red")

## The Hazard function
curve(hEW(x, alpha = 2,theta = 1.5, lambda = 0.5), from = 0, to = 2, ylim = c(0, 7), col = "red", ylab = "The Hazard function")

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