# FR: Freimer 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 Freimer distribution due to Freimer et al. (1988) given by

\begin{array}{ll} &\displaystyle {\rm VaR}_p (X) = \frac {1}{a} ≤ft[ \frac {p^b - 1}{b} - \frac {(1 - p)^c - 1}{c} \right], \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{a} ≤ft( \frac {1}{c} - \frac {1}{b} \right) + \frac {p^b}{a b (b + 1)} + \frac {(1 - p)^{c + 1} - 1}{p a c (c + 1)} \end{array}

for 0 < p < 1, a > 0, the scale parameter, b > 0, the first shape parameter, and c > 0, the second shape parameter.

## Usage

 1 2 varFR(p, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE) esFR(p, a=1, b=1, c=1) 

## Arguments

 p scaler or vector of values at which the value at risk or expected shortfall needs to be computed a the value of the scale parameter, must be positive, the default is 1 b the value of the first shape parameter, must be positive, the default is 1 c the value of the second shape 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.

## References

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

## Examples

 1 2 3 x=runif(10,min=0,max=1) varFR(x) esFR(x) 

VaRES documentation built on May 29, 2017, 8:27 p.m.