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survstan (version 0.0.7.1)

Gompertz: 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, ...)

Value

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

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 \(\gamma>0\).