# Gompertz: Gompertz distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

Density, distribution function, quantile function and random generation for the Gompertz distribution.

## Usage

 ```1 2 3 4 5 6 7``` ```dgompertz(x, a = 1, b = 1, log = FALSE) pgompertz(q, a = 1, b = 1, lower.tail = TRUE, log.p = FALSE) qgompertz(p, a = 1, b = 1, lower.tail = TRUE, log.p = FALSE) rgompertz(n, a = 1, b = 1) ```

## Arguments

 `x, q` vector of quantiles. `a, b` positive valued scale and location 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. If `length(n) > 1`, the length is taken to be the number required.

## Details

Probability density function

f(x) = a*exp(b*x - a/b * (exp(b*x)-1))

Cumulative distribution function

F(x) = 1-exp(-a/b * (exp(b*x)-1))

Quantile function

F^-1(p) = 1/b * log(1 - b/a * log(1-p))

## References

Lenart, A. (2012). The Gompertz distribution and Maximum Likelihood Estimation of its parameters - a revision. MPIDR WORKING PAPER WP 2012-008. http://www.demogr.mpg.de/papers/working/wp-2012-008.pdf

## Examples

 ```1 2 3 4 5 6``` ```x <- rgompertz(1e5, 5, 2) hist(x, 100, freq = FALSE) curve(dgompertz(x, 5, 2), 0, 1, col = "red", add = TRUE) hist(pgompertz(x, 5, 2)) plot(ecdf(x)) curve(pgompertz(x, 5, 2), 0, 1, col = "red", lwd = 2, add = TRUE) ```

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.