VaRES (version 1.0.1)

betagumbel2: Beta Gumbel 2 distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the beta Gumbel II distribution given by $$\begin{array}{ll}& {\displaystyle f(x)=\frac{ab{x}^{-a-1}}{B(c,d)}\exp (-bd{x}^{-a}){[1-\exp (-b{x}^{-a})]}^{c-1},}\\ & {\displaystyle F(x)=I_{1-\exp (-b{x}^{-a})}(c,d),}\\ & {\displaystyle {\mathrm{V}\mathrm{a}\mathrm{R}}_p(X)=b^{1/a}{\{-\log [1-I_p^{-1}(c,d)]\}}^{-1/a},}\\ & {\displaystyle {\mathrm{E}\mathrm{S}}_p(X)=\frac{b^{1/a}}{p}{\int }_0^p{\{-\log [1-I_v^{-1}(c,d)]\}}^{-1/a}dv}\end{array}$$ for $x>0$, $0<p<1$, $a>0$, the first shape parameter, $b>0$, the scale parameter, $c>0$, the second shape parameter, and $d>0$, the third shape parameter.

Usage

dbetagumbel2(x, a=1, b=1, c=1, d=1, log=FALSE)
pbetagumbel2(x, a=1, b=1, c=1, d=1, log.p=FALSE, lower.tail=TRUE)
varbetagumbel2(p, a=1, b=1, c=1, d=1, log.p=FALSE, lower.tail=TRUE)
esbetagumbel2(p, a=1, b=1, c=1, 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

b

the value of the scale parameter, must be positive, the default is 1

a

the value of the first shape parameter, must be positive, the default is 1

c

the value of the second shape parameter, must be positive, the default is 1

d

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)
dbetagumbel2(x)
pbetagumbel2(x)
varbetagumbel2(x)
#esbetagumbel2(x)
# }