VaRES (version 1.0.1)

genpareto: Generalized Pareto distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the generalized Pareto distribution due to Pickands (1975) given by $$\begin{array}{ll} &\displaystyle f (x) = \frac {1}{k} \left( 1 - \frac {c x}{k} \right)^{1 / c - 1}, \\ &\displaystyle F (x) = 1 - \left( 1 - \frac {c x}{k} \right)^{1 / c}, \\ &\displaystyle {\rm VaR}_p (X) = \frac {k}{c} \left[ 1 - (1 - p)^c \right], \\ &\displaystyle {\rm ES}_p (X) = \frac {k}{c} + \frac {k (1 - p)^{c + 1}}{p c (c + 1)} - \frac {k}{p c (c + 1)} \end{array}$$ for \(x < k/c\) if \(c > 0\), \(x > k/c\) if \(c < 0\), \(x > 0\) if \(c = 0\), \(0 < p < 1\), \(k > 0\), the scale parameter and \(-\infty < c < \infty\), the shape parameter.

Usage

dgenpareto(x, k=1, c=1, log=FALSE)
pgenpareto(x, k=1, c=1, log.p=FALSE, lower.tail=TRUE)
vargenpareto(p, k=1, c=1, log.p=FALSE, lower.tail=TRUE)
esgenpareto(p, k=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

k

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

c

the value of the shape parameter, can take any real value, 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)
dgenpareto(x)
pgenpareto(x)
vargenpareto(x)
esgenpareto(x)
# }