VaRES (version 1.0.1)

compbeta: Complementary beta distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the complementary beta distribution due to Jones (2002) given by $$\begin{array}{ll} &\displaystyle f (x) = B (a, b) \left\{ I_x^{-1} (a, b) \right\}^{1 - a} \left\{ 1 - I_x^{-1} (a, b) \right\}^{1 - b}, \\ &\displaystyle F (x) = I_x^{-1} (a, b), \\ &\displaystyle {\rm VaR}_p (X) = I_p (a, b), \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{p} \int_0^p I_v (a, b) dv \end{array}$$ for \(0 < x < 1\), \(0 < p < 1\), \(a > 0\), the first shape parameter, and \(b > 0\), the second shape parameter.

Usage

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.

References

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

Examples

# NOT RUN {
x=runif(10,min=0,max=1)
dcompbeta(x)
pcompbeta(x)
varcompbeta(x)
escompbeta(x)
# }