Probability function, distribution function, quantile function and random generation for the distribution with parameters alpha and gamma.
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, ...)
dgompertz gives the (log) probability function, pgompertz gives the (log) distribution function, qgompertz gives the quantile function, and rgompertz generates random deviates.
vector of (non-negative integer) quantiles.
shape parameter of the distribution (alpha > 0).
scale parameter of the distribution (gamma > 0).
logical; if TRUE, probabilities p are given as log(p).
further arguments passed to other methods.
vector of quantiles.
logical; if TRUE (default), probabilities are \(P[X \le x]\); otherwise, \(P[X > x]\).
vector of probabilities.
number of random values to return.
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 \(\gamma>0\).