# gompertz: Gompertz distribution In VaRES: Computes value at risk and expected shortfall for over 100 parametric distributions

## Description

Computes the pdf, cdf, value at risk and expected shortfall for the Gompertz distribution due to Gompertz (1825) given by

\begin{array}{ll} &\displaystyle f(x) = b η \exp (bx) \exp ≤ft[ η - η \exp (bx) \right], \\ &\displaystyle F (x) = 1 - \exp ≤ft[ η - η \exp (bx) \right], \\ &\displaystyle {\rm VaR}_p (X) = \frac {1}{b} \log ≤ft[ 1 - \frac {1}{η} \log (1 - p) \right], \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{p b} \int_0^p \log ≤ft[ 1 - \frac {1}{η} \log (1 - v) \right] dv \end{array}

for x > 0, 0 < p < 1, b > 0, the first scale parameter and η > 0, the second scale parameter.

## Usage

 1 2 3 4 dgompertz(x, b=1, eta=1, log=FALSE) pgompertz(x, b=1, eta=1, log.p=FALSE, lower.tail=TRUE) vargompertz(p, b=1, eta=1, log.p=FALSE, lower.tail=TRUE) esgompertz(p, b=1, eta=1) 

## Arguments

 x scaler or vector of values at which the pdf or cdf needs to be computed p scaler or vector of values at which the value at risk or expected shortfall needs to be computed b the value of the first scale parameter, must be positive, the default is 1 eta the value of the second scale parameter, must be positive, the default is 1 log if TRUE then log(pdf) are returned log.p if TRUE then log(cdf) are returned and quantiles are computed for exp(p) lower.tail if FALSE then 1-cdf are returned and quantiles are computed for 1-p

## Value

An object of the same length as x, giving the pdf or cdf values computed at x or an object of the same length as p, giving the values at risk or expected shortfall computed at p.

## Author(s)

 1 2 3 4 5 x=runif(10,min=0,max=1) dgompertz(x) pgompertz(x) vargompertz(x) esgompertz(x)