PL: The Power Lindley Distribution

In ousuga/reldist: Reliability and survival distributions

Description

Density, distribution function, quantile function, random generation and hazard function for the power Lindley distribution with parameters alpha and beta.

Usage

dPL(x, alpha, beta, log = FALSE)

pPL(q, alpha, beta, lower.tail = TRUE, log.p = FALSE)

qPL(p, alpha, beta, lower.tail = TRUE, log.p = FALSE)

rPL(n, alpha, beta)

hPL(x, alpha, beta)

Arguments

x,q	vector of quantiles.
alpha	shape parameter.
beta	scale parameter.
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 power Lindley distribution with parameters alpha and beta has density given by

f(x) = ((alpha*beta^2)/(beta+1))*(1+x^(alpha))*x^(alpha-1)*exp(-beta*(x^alpha))

for x > 0.

Value

dPL gives the density, pPL gives the distribution function, qPL gives the quantile function, rPL generates random deviates and hPL gives the hazard function.

Examples

## The probability density function
curve(dPL(x, alpha = 1, beta = 0.5), from = 0, to = 15, ylim = c(0, 0.25), col = "red", las = 1, ylab = "The probability density function")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pPL(x, alpha = 1, beta = 0.5), from = 0, to = 15,  ylim = c(0, 1), col = "red", las = 1, ylab = "The cumulative distribution function")
curve(pPL(x, alpha = 1, beta = 0.5, lower.tail = FALSE), from = 0, to = 15,  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=qPL(p=p, alpha = 1, beta = 0.5), y = p, xlab = "Quantile", las = 1, ylab = "Probability")
curve(pPL(x, alpha = 1, beta = 0.5), from = 0, add = TRUE, col = "red")

## The random function
hist(rPL(n = 1000, alpha = 1, beta = 0.5), freq = FALSE, , ylim = c(0, 0.25), xlab = "x", las = 1, main = "")
curve(dPL(x, alpha = 1, beta = 0.5),  from = 0, add = T, col = "red", ylim = c(0, 0.25))

## The Hazard function
curve(hPL(x, alpha = 1, beta = 0.5), from = 0, to = 10, ylim = c(0, 0.5), col = "red", las = 1, ylab = "The Hazard function")

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