dgompertz(x, shape, rate = 1, log = FALSE)
pgompertz(q, shape, rate = 1, lower.tail = TRUE, log.p = FALSE)
qgompertz(p, shape, rate = 1, lower.tail = TRUE, log.p = FALSE)
rgompertz(n, shape, rate = 1)
hgompertz(x, shape, rate = 1, log=FALSE)
Hgompertz(x, shape, rate = 1, log=FALSE)length(n) > 1, the length
is taken to be the number required.dgompertz gives the density,
pgompertz gives the distribution function,
qgompertz gives the quantile function,
hgompertz gives the hazard function,
Hgompertz gives the cumulative hazard function, and
rgompertz generates random deviates.
shape parameter $a$ and
rate parameter $b$ has probability density function
$$f(x | a, b) = be^{ax}\exp(-b/a (e^{ax} - 1))$$and hazard
$$h(x | a, b) = b e^{ax}$$
The hazard is increasing for shape $a>0$ and decreasing for $a<0$. for="" $a="0$" the="" gompertz="" is="" equivalent="" to="" exponential="" distribution="" with="" constant="" hazard="" and="" rate="" $b$.="" <="" p="">
The probability distribution function is $$F(x | a, b) = 1 - \exp(-b/a (e^{ax} - 1))$$
Thus if $a$ is negative, letting $x$ tend to infinity
shows that there is a non-zero
probability $1 - exp(b/a)$ of living forever.
On these occasions qgompertz and rgompertz will return
Inf.
dexp