Gompertz {survstan}

The Gompertz Distribution

Description

Probability function, distribution function, quantile function and random generation for the distribution with parameters alpha and gamma.

Usage

dgompertz(x, alpha = 1, gamma = 1, log = FALSE, ...)

pgompertz(q, alpha = 1, gamma = 1, lower.tail = TRUE, log.p = FALSE, ...)

qgompertz(p, alpha = 1, gamma = 1, lower.tail = FALSE, log.p = FALSE, ...)

rgompertz(n, alpha = 1, gamma = 1, ...)

Arguments

x

vector of (non-negative integer) quantiles.

alpha

shape parameter of the distribution (alpha > 0).

gamma

scale parameter of the distribution (gamma > 0).

log, log.p

logical; if TRUE, probabilities p are given as log(p).

...

further arguments passed to other methods.

q

vector of quantiles.

lower.tail

logical; if TRUE (default), probabilities are P[X \le x]; otherwise, P[X > x].

p

vector of probabilities.

n

number of random values to return.

Details

Probability density function:

f(x|\alpha, \gamma) = \alpha\gamma \exp\{\gamma x - \alpha(e^{\gamma x} - 1)\}I_{[0, \infty)}(x),

for \alpha>0 and \gamma>0.

Distribution function:

F(x|\alpha, \gamma) = 1 - \exp\{- \alpha(e^{\gamma x} - 1)\},

for x>0, \alpha>0 and \gamma>0.

Value

dgompertz gives the (log) probability function, pgompertz gives the (log) distribution function, qgompertz gives the quantile function, and rgompertz generates random deviates.