RelDists (version 1.0.0)

dGGD: The Generalized Gompertz distribution

Description

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

Usage

dGGD(x, mu, sigma, nu, log = FALSE)
pGGD(q, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
qGGD(p, mu, sigma, nu, lower.tail = TRUE, log.p = FALSE)
rGGD(n, mu, sigma, nu)
hGGD(x, mu, sigma, nu)

Value

dGGD gives the density, pGGD gives the distribution function, qGGD gives the quantile function, rGGD

generates random deviates and hGGD gives the hazard function.

Arguments

x, q

vector of quantiles.

mu, nu

scale parameter.

sigma

shape parameters.

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.

Author

Johan David Marin Benjumea,

Details

The Generalized Gompertz Distribution with parameters mu, sigma and nu has density given by

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

for \(x \geq 0\), \(\mu > 0\), \(\sigma \geq 0\) and \(\nu > 0\).

References

el2013generalizedRelDists

Examples

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

## The probability density function 
par(mfrow = c(1, 1))
curve(dGGD(x, mu=1, sigma=0.3, nu=1.5), from = 0, to = 4, 
      col = "red", las = 1, ylab = "f(x)")

## The cumulative distribution and the Reliability function
par(mfrow = c(1, 2))
curve(pGGD(x, mu=1, sigma=0.3, nu=1.5), from = 0, to = 4, 
      ylim = c(0, 1), col = "red", las = 1, ylab = "F(x)")
curve(pGGD(x, mu=1, sigma=0.3, nu=1.5, lower.tail = FALSE), 
      from = 0, to = 4, 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 = qGGD(p=p, mu=1, sigma=0.3, nu=1.5), y = p, 
     xlab = "Quantile", las = 1, ylab = "Probability")
curve(pGGD(x, mu=1, sigma=0.3, nu=1.5), from = 0, add = TRUE, 
      col = "red")

## The random function
hist(rGGD(1000, mu=1, sigma=0.3, nu=1.5), freq = FALSE, xlab = "x", 
     las = 1, ylim = c(0, 0.7), main = "")
curve(dGGD(x,mu=1, sigma=0.3, nu=1.5), from = 0, to =8, add = TRUE, 
      col = "red")

## The Hazard function
par(mfrow=c(1,1))
curve(hGGD(x, mu=1, sigma=0.3, nu=1.5), from = 0, to = 3, col = "red",
      ylab = "The hazard function", las = 1)

par(old_par) # restore previous graphical parameters