RW: The Reflected Weibull Distribution

In ousuga/reldist: Reliability and survival distributions

Description

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

Usage

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

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

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

rRW(n, alpha, theta)

hRW(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 reflected weibull distribution with parameters alpha and theta has density given by

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

for - inf < x < 0.

Value

dRW gives the density, pRW gives the distribution function, qRW gives the quantile function, rRW generates random deviates and hRW gives the hazard function.

Examples

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

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pRW(x, alpha = 1, theta = 1), from = -5, to = 0, ylim = c(0, 1), col = "red", las = 1, ylab ="The cumulative distribution function")
curve(pRW(x, alpha = 1, theta = 1, lower.tail = FALSE), from = -5, to = 0, ylim = c(0, 1), col = "red", las = 1, ylab = "The Reliability function")

## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x=qRW(p=p,alpha = 1, theta = 1), y=p, xlab="Quantile", las=1, ylab="Probability")
curve(pRW(x, alpha = 1, theta = 1), from = -5, add = TRUE, col = "red")

## The random function
hist(rRW(n = 10000, alpha = 1, theta = 1), freq = FALSE,xlab = "x", las = 1, main = "")
curve(dRW(x, alpha = 1, theta = 1),  from = -5, to = 0, add = TRUE, col = "red")

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

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