dWG function

The Weibull Geometric distribution

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

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.

Returns

dWG gives the density, pWG gives the distribution function, qWG gives the quantile function, rWG

generates random deviates and hWG gives the hazard function.

Details

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

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

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

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

References

Rdpack::insert_ref(key="barreto2011weibull",package="RelDists")

Author(s)

Johan David Marin Benjumea, johand.marin@udea.edu.co