# compbeta: Complementary beta 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 complementary beta distribution due to Jones (2002) given by

\begin{array}{ll} &\displaystyle f (x) = B (a, b) ≤ft\{ I_x^{-1} (a, b) \right\}^{1 - a} ≤ft\{ 1 - I_x^{-1} (a, b) \right\}^{1 - b}, \\ &\displaystyle F (x) = I_x^{-1} (a, b), \\ &\displaystyle {\rm VaR}_p (X) = I_p (a, b), \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{p} \int_0^p I_v (a, b) dv \end{array}

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

## Usage

 1 2 3 4 dcompbeta(x, a=1, b=1, log=FALSE) pcompbeta(x, a=1, b=1, log.p=FALSE, lower.tail=TRUE) varcompbeta(p, a=1, b=1, log.p=FALSE, lower.tail=TRUE) escompbeta(p, a=1, b=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 a the value of the first shape parameter, must be positive, the default is 1 b 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.

## Author(s)

 1 2 3 4 5 x=runif(10,min=0,max=1) dcompbeta(x) pcompbeta(x) varcompbeta(x) escompbeta(x)