IW: The Inverse Weibull Distribution

In ousuga/reldist: Reliability and survival distributions

Description

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

Usage

dIW(x, alpha, theta, log = FALSE)

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

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

rIW(n, alpha, theta)

hIW(x, alpha, theta)

Arguments

x,q	vector of quantiles.
alpha	parameter one.
theta	parameter two.
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 inverse weibull distribution with parameters alpha and theta has density given by

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

for x > 0.

Value

dIW gives the density, pIW gives the distribution function, qIW gives the quantile function, rIW generates random deviates and hIW gives the hazard function.

Examples

## The probability density function
curve(dIW(x, alpha = 5, theta = 2.5), from = 0, to = 10, ylim = c(0, 0.55), col = "red", las = 1, ylab = "The probability density function")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pIW(x, alpha = 5, theta = 2.5), from = 0, to = 10, ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pIW(x, alpha = 5, theta = 2.5, lower.tail = FALSE), from = 0, to = 10, 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 = qIW(p, alpha = 5, theta = 2.5), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pIW(x, alpha = 5, theta = 2.5),  from = 0, add = TRUE, col = "red")

## The random function
hist(rIW(n = 1000, alpha = 5, theta = 2.5), freq = FALSE, xlab = "x", ylim = c(0, 0.55), las = 1, main = "")
curve(dIW(x, alpha = 5, theta = 2.5),  from = 0, to = 10, add = TRUE, ylim = c(0, 0.55), col = "red")

## The Hazard function
curve(hIW(x, alpha = 5, theta = 2.5), from = 0, to = 15, ylim = c(0, 1), col = "red", las = 1, ylab = "The Hazard function")

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