makeham: The Gompertz-Makeham Distribution

Description

Density, distribution function, quantile function, hazard function, cumulative hazard function, and random generation for the Gompertz-Makeham distribution with parameters shape and scale.

Usage

dmakeham(x, shape = c(1, 1), scale = 1, log = FALSE)
pmakeham(q, shape = c(1, 1), scale = 1, lower.tail = TRUE, log.p = FALSE)
qmakeham(p, shape = c(1, 1), scale = 1, lower.tail = TRUE, log.p = FALSE)
hmakeham(x, shape = c(1, 1), scale = 1, log = FALSE)
Hmakeham(x, shape = c(1, 1), scale = 1, log.p = FALSE)
rmakeham(n, shape = c(1, 1), scale = 1)

Value

dmakeham gives the density, pmakeham gives the distribution function, qmakeham gives the quantile function, hmakeham gives the hazard function, Hmakeham gives the cumulative hazard function, and rmakeham generates random deviates.

Invalid arguments will result in return value NaN, with a warning.

Arguments

shape: A vector, default value c(1, 1).
scale: defaulting to 1.
lower.tail: logical; if TRUE (default), probabilities are $P(X \le x)$, otherwise, $P(X > x)$.
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.
log, log.p: logical; if TRUE, probabilities p are given as log(p).

Details

The Gompertz-Makeham distribution with shape parameter $a$ and scale parameter $\sigma$ has hazard function given by $$h(x) = a[2] + a[1] \exp(x/\sigma)$$ for $x \ge 0$.