dWG {RelDists}

The Weibull Geometric distribution

Description

Density, distribution function, quantile function, random generation and hazard function for the weibull geometric distribution with parameters mu, sigma and nu.

Usage

dWG(x, mu, sigma, nu, log = FALSE)

pWG(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)

qWG(p, sigma, mu, nu, lower.tail = TRUE, log.p = FALSE)

rWG(n, mu, sigma, nu)

hWG(x, mu, sigma, nu)

Arguments

x, q

vector of quantiles.

mu

scale parameter.

sigma

shape parameter.

nu

parameter of geometric random variable.

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 Weibull geometric distribution with parameters mu, sigma and nu has density given by

f(x) = (\sigma \mu^\sigma (1-\nu) x^(\sigma - 1) \exp(-(\mu x)^\sigma)) (1- \nu \exp(-(\mu x)^\sigma))^{-2},

for x > 0, \mu > 0, \sigma > 0 and 0 < \nu < 1.

Value

dWG gives the density, pWG gives the distribution function, qWG gives the quantile function, rWG generates random deviates and hWG gives the hazard function.

Author(s)

Johan David Marin Benjumea, [e-mail]

References

Barreto-Souza W, de Morais AL, Cordeiro GM (2011). “The Weibull-geometric distribution.” Journal of Statistical Computation and Simulation, 81(5), 645–657.

Examples

old_par <- par(mfrow = c(1, 1)) # save previous graphical parameters

## The probability density function 
curve(dWG(x, mu = 0.9, sigma = 2, nu = 0.5), from = 0, to = 3, 
ylim = c(0, 1.1), col = "red", las = 1, ylab = "f(x)")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pWG(x, mu = 0.9, sigma = 2, nu = 0.5), from = 0, to = 3, 
ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)")
curve(pWG(x, mu = 0.9, sigma = 2, nu = 0.5, lower.tail = FALSE), 
from = 0, to = 3, ylim = c(0, 1), col = "red", las = 1, ylab = "R(x)")

## The quantile function
p <- seq(from = 0, to = 0.99999, length.out = 100)
plot(x = qWG(p = p, mu = 0.9, sigma = 2, nu = 0.5), y = p, 
xlab = "Quantile", las = 1, ylab = "Probability")
curve(pWG(x,mu = 0.9, sigma = 2, nu = 0.5), from = 0, add = TRUE, 
col = "red")

## The random function
hist(rWG(1000, mu = 0.9, sigma = 2, nu = 0.5), freq = FALSE, xlab = "x", 
ylim = c(0, 1.8), las = 1, main = "")
curve(dWG(x, mu = 0.9, sigma = 2, nu = 0.5),  from = 0, add = TRUE, 
col = "red", ylim = c(0, 1.8))

## The Hazard function(
par(mfrow=c(1,1))
curve(hWG(x, mu = 0.9, sigma = 2, nu = 0.5), from = 0, to = 8, 
ylim = c(0, 12), col = "red", ylab = "Hazard function", las = 1)

par(old_par) # restore previous graphical parameters