VaRES (version 1.0.1)

gumbel2: Gumbel II distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Gumbel II distribution $$\begin{array}{ll} &\displaystyle f (x) = a b x^{-a - 1} \exp \left( -b x^{-a} \right), \\ &\displaystyle F (x) = 1 - \exp \left( -b x^{-a} \right), \\ &\displaystyle {\rm VaR}_p (X) = b^{1 / a} \left[ -\log (1 - p) \right]^{-1 / a}, \\ &\displaystyle {\rm ES}_p (X) = \frac {b^{1 / a}}{p} \int_0^p \left[ -\log (1 - v) \right]^{-1 / a} dv \end{array}$$ for \(x > 0\), \(0 < p < 1\), \(a > 0\), the shape parameter, and \(b > 0\), the scale parameter.

Usage

dgumbel2(x, a=1, b=1, log=FALSE)
pgumbel2(x, a=1, b=1, log.p=FALSE, lower.tail=TRUE)
vargumbel2(p, a=1, b=1, log.p=FALSE, lower.tail=TRUE)
esgumbel2(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 scale parameter, must be positive, the default is 1

b

the value of the 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)
dgumbel2(x)
pgumbel2(x)
vargumbel2(x)
#esgumbel2(x)
# }