# betadist: 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 beta distribution given by

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

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

## Usage

 1 2 3 4 dbetadist(x, a=1, b=1, log=FALSE) pbetadist(x, a=1, b=1, log.p=FALSE, lower.tail=TRUE) varbetadist(p, a=1, b=1, log.p=FALSE, lower.tail=TRUE) esbetadist(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 scale parameter, must be positive, the default is 1 b 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.

## References

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

## Examples

 1 2 3 4 5 x=runif(10,min=0,max=1) dbetadist(x) pbetadist(x) varbetadist(x) esbetadist(x) 

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