eha (version 2.4-6)

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 shape1, shape2 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)

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.

shape, scale

Parameters: shape, a vector of length 2, defaulting to c(1, 1), and scale, defaulting to 1.

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, \(P(X > x)\).

Value

dmakeham gives the density, pmakeham gives the distribution function, qmakeham gives the quantile function, but is not yet implemented, 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.

Details

The Gompertz-Makeham distribution with shape parameters \(a_1\) and \(a_2\) and scale parameter \(\sigma\) has hazard function given by $$h(x) = a_2 + a_1 \exp(x / \sigma)$$ for \(x \ge 0\).