GPW: The Generalized Power Weibull Distribution

In ousuga/reldist: Reliability and survival distributions

Description

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

Usage

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

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

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

rGPW(n, alpha, theta, lambda)

hGPW(x, alpha, theta, lambda)

Arguments

x,q	vector of quantiles.
alpha	parameter one.
theta	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 generalized power weibull with parameters alpha, theta and lambda has density given by

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

for x > 0.

Value

dGPW gives the density, pGPW gives the distribution function, qGPW gives the quantile function, rGPW generates random deviates and hGPW gives the hazard function.

Examples

## The probability density function
curve(dGPW(x, alpha = 0.5, theta = 0.5, lambda = 0.25), from = 0, to = 2.5, ylim = c(0, 3), col = "red", las = 1, ylab = "The probability density function")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pGPW(x, alpha = 0.5, theta = 0.5, lambda = 0.25), from = 0, to = 2.5, col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pGPW(x, alpha = 0.5, theta = 0.5, lambda = 0.25, lower.tail = FALSE), from = 0, to = 2.5, col = "red", las = 1, ylab = "The Reliability function")

## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qGPW(p, alpha = 0.5, theta = 0.5, lambda = 0.25), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pGPW(x, alpha = 0.5, theta = 0.5, lambda = 0.25), from = 0, add = TRUE, col = "red")

## The random function
hist(rGPW(n = 10000, alpha = 0.5, theta = 0.5, lambda = 0.25), freq = FALSE, xlab = "x", las = 1, main = "")
curve(dGPW(x, alpha = 0.5, theta = 0.5, lambda = 0.25),  from = 0, add = TRUE, col = "red")

## The Hazard function
curve(hGPW(x, alpha = 0.5, theta = 0.5, lambda = 0.25), from = 0, to = 6, ylim = c(0, 13), col = "red", las = 1, ylab = "The Hazard function")

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