# genbeta: Generalized 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 generalized beta distribution given by

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

for c ≤q x ≤q d, 0 < p < 1, a > 0, the first shape parameter, b > 0, the second shape parameter, -∞ < c < ∞, the first location parameter, and -∞ < c < d < ∞, the second location parameter.

## Usage

 1 2 3 4 dgenbeta(x, a=1, b=1, c=0, d=1, log=FALSE) pgenbeta(x, a=1, b=1, c=0, d=1, log.p=FALSE, lower.tail=TRUE) vargenbeta(p, a=1, b=1, c=0, d=1, log.p=FALSE, lower.tail=TRUE) esgenbeta(p, a=1, b=1, c=0, d=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 c the value of the first location parameter, can take any real value, the default is zero d the value of the second location parameter, can take any real value but must be greater than c, the default is 1 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) dgenbeta(x) pgenbeta(x) vargenbeta(x) esgenbeta(x)