Gompertz {DescTools} | R Documentation |

## The Gompertz distribution

### Description

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

### Usage

```
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 = 1, rate = 1)
```

### Arguments

`x` , `q` |
vector of quantiles. |

`shape` , `rate` |
vector of shape and rate parameters. |

`log` , `log.p` |
logical; if TRUE, probabilities p are given as log(p). |

`lower.tail` |
logical; if TRUE (default), probabilities are |

`p` |
vector of probabilities. |

`n` |
number of observations. If |

### Details

The Gompertz distribution with `shape`

parameter `a`

and
`rate`

parameter `b`

has probability density function

`f(x | a, b) = be^{ax}\exp(-b/a (e^{ax} - 1))`

For `a=0`

the Gompertz is equivalent to the exponential distribution
with constant hazard and rate `b`

.

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`

.

### Value

`dGompertz`

gives the density, `pGompertz`

gives the
distribution function, `qGompertz`

gives the quantile function,
and `rGompertz`

generates random deviates.

### Note

Some implementations of the Gompertz restrict `a`

to be strictly
positive, which ensures that the probability of survival decreases to zero
as `x`

increases to infinity. The more flexible implementation given
here is consistent with `streg`

in Stata.

The functions `dGompertz`

and similar available in the
package eha label the parameters the other way round, so that what is
called the `shape`

there is called the `rate`

here, and what is
called `1 / scale`

there is called the `shape`

here. The
terminology here is consistent with the exponential `dexp`

and
Weibull `dweibull`

distributions in R.

### Author(s)

Christopher Jackson <chris.jackson@mrc-bsu.cam.ac.uk>

### References

Stata Press (2007) Stata release 10 manual: Survival analysis and epidemiological tables.

### See Also

*DescTools*version 0.99.55 Index]