Gompertz distribution
Density, distribution function, quantile function and random generation for the Gompertz distribution.
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)
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 |
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))
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
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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.