dGGD function

The Generalized Gompertz distribution

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

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)

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.

Returns

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

generates random deviates and hGGD gives the hazard function.

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 $\nu > 0$.

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

References

Rdpack::insert_ref(key="el2013generalized",package="RelDists")

Author(s)

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