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.
Value
dgompertz gives the (log) probability function, pgompertz gives the (log) distribution function, qgompertz gives the quantile function, and rgompertz generates random deviates.
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 \(\gamma>0\).