Gompertz: The Gompertz distribution

In reliaR: Comprehensive Tools for some Probability Distributions

The Gompertz distribution

Description

Density, distribution function, quantile function and random generation for the Gompertz distribution with shape parameter alpha and scale parameter theta.

Usage

dgompertz(x, alpha, theta, log = FALSE)
pgompertz(q, alpha, theta, lower.tail = TRUE, log.p = FALSE)
qgompertz(p, alpha, theta, lower.tail = TRUE, log.p = FALSE)
rgompertz(n, alpha, theta)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
alpha	shape parameter.
theta	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 \le x] otherwise, P[X > x].

Details

The Gompertz distribution has density

f(x) = \theta e^{\alpha x} \exp\left\{\frac{\theta}{\alpha}\left(1 - e^{\alpha x}\right)\right\};\, x \ge 0, \theta > 0, -\infty < \alpha < \infty.

where \alpha and \theta are the shape and scale parameters, respectively.

Value

dgompertz gives the density, pgompertz gives the distribution function, qgompertz gives the quantile function, and rgompertz generates random deviates.

References

Marshall, A. W., Olkin, I. (2007). Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families, Springer, New York.

See Also

.Random.seed about random number; sgompertz for Gompertz survival / hazard etc. functions

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & theta for the data(sys2)
## Estimates of alpha & theta using 'maxLik' package
## alpha.est = 0.00121307, theta.est = 0.00173329

dgompertz(sys2, 0.00121307, 0.00173329, log = FALSE)
pgompertz(sys2, 0.00121307, 0.00173329, lower.tail = TRUE, log.p = FALSE)
qgompertz(0.25, 0.00121307, 0.00173329, lower.tail=TRUE, log.p = FALSE)
rgompertz(30, 0.00121307, 0.00173329)

reliaR documentation built on Nov. 5, 2025, 6:57 p.m.