VaRES (version 1.0)

genbeta2: Generalized beta II distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the generalized beta II distribution given by $$\begin{array}{ll} &\displaystyle f (x) = \frac {c x^{ac - 1} \left( 1 - x^c \right)^{b - 1}}{B (a, b)}, \\ &\displaystyle F (x) = I_{x^c} (a, b), \\ &\displaystyle {\rm VaR}_p (X) = \left[ I_p^{-1} (a, b) \right]^{1 / c}, \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{p} \int_0^p \left[ I_v^{-1} (a, b) \right]^{1 / c} dv \end{array}$$ for \(0 < x < 1\), \(0 < p < 1\), \(a > 0\), the first shape parameter, \(b > 0\), the second shape parameter, and \(c > 0\), the third shape parameter.

Usage

dgenbeta2(x, a=1, b=1, c=1, log=FALSE)
pgenbeta2(x, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE)
vargenbeta2(p, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE)
esgenbeta2(p, a=1, b=1, c=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

c

the value of the third 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)
dgenbeta2(x)
pgenbeta2(x)
vargenbeta2(x)
esgenbeta2(x)
# }