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"))
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.
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).
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.