Density, distribution function, quantile function, hazard function,
cumulative hazard function, and random generation for the Gompertz
distribution with parameters shape and scale.
dgompertz(x, shape = 1, scale = 1, rate, log = FALSE,
param = c("default", "canonical", "rate"))
pgompertz(q, shape = 1, scale = 1, rate, lower.tail = TRUE, log.p = FALSE,
param = c("default", "canonical", "rate"))
qgompertz(p, shape = 1, scale = 1, rate, lower.tail = TRUE, log.p = FALSE,
param = c("default", "canonical", "rate"))
hgompertz(x, shape = 1, scale = 1, rate, log = FALSE,
param = c("default", "canonical", "rate"))
Hgompertz(x, shape = 1, scale = 1, rate, log.p = FALSE,
param = c("default", "canonical", "rate"))
rgompertz(n, shape = 1, scale = 1, rate,
param = c("default", "canonical", "rate"))shape and scale parameters, both defaulting to 1.
the rate parameter for that parametrization, replaces scale.
logical; if TRUE (default), probabilities are \(P(X \le x)\), otherwise, \(P(X > x)\).
default or canonical or rate.
vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length is
taken to be the number required.
logical; if TRUE, probabilities p are given as log(p).
dgompertz gives the density, pgompertz gives the distribution
function, qgompertz gives the quantile function, hgompertz gives the
hazard function, Hgompertz gives the cumulative hazard function, and
rgompertz generates random deviates.
Invalid arguments will result in return value NaN, with a warning.
The Gompertz distribution with scale parameter \(a\) and shape
parameter \(\sigma\) has hazard function given by
$$h(x) = a \exp(x/\sigma)$$
for \(x \ge 0\).
If param = "canonical", then then a --> a/b, so that b is a
true scale parameter (for any fixed a), and b is an 'AFT parameter'.
If param = "rate", then b --> 1/b.