Gompertz distribution — gompertz • RTMBdist

Density, distribution function, quantile function, and random generation for the Gompertz distribution.

Usage

dgompertz(x, eta = 1, b = 1, log = FALSE)

pgompertz(q, eta = 1, b = 1, lower.tail = TRUE, log.p = FALSE)

qgompertz(p, eta = 1, b = 1, lower.tail = TRUE, log.p = FALSE)

rgompertz(n, eta = 1, b = 1)

Arguments

x, q: vector of quantiles (non-negative)
eta: shape parameter, must be positive
b: rate parameter, must be positive
log, log.p: logical; if TRUE, probabilities/densities are returned as $\log(p)$.
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 density, pgompertz gives the distribution function, qgompertz gives the quantile function, and rgompertz generates random deviates.

Details

The Gompertz distribution with shape $\eta > 0$ and rate $b > 0$ has density $$f(x;\,\eta,b) = b\eta\,e^{bx}\exp\!\bigl(-\eta(e^{bx}-1)\bigr), \quad x \geq 0,$$ with CDF $F(x) = 1 - \exp(-\eta(e^{bx}-1))$ and quantile function $Q(p) = \log(1 - \log(1-p)/\eta)\,/\,b$.

References

https://en.wikipedia.org/wiki/Gompertz_distribution

Examples

x <- rgompertz(1, eta = 1, b = 1)
d <- dgompertz(x, eta = 1, b = 1)
p <- pgompertz(x, eta = 1, b = 1)
q <- qgompertz(p, eta = 1, b = 1)