VaRES (version 1.0.1)

power1: Power function I distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the power function I distribution given by $$\begin{array}{ll} &\displaystyle f (x) = a x^{a - 1}, \\ &\displaystyle F (x) = x^a, \\ &\displaystyle {\rm VaR}_p (X) = p^{1 / a}, \\ &\displaystyle {\rm ES}_p (X) = \frac {p^{1 / a}}{1 / a + 1} \end{array}$$ for \(0 < x < 1\), \(0 < p < 1\), and \(a > 0\), the shape parameter.

Usage

dpower1(x, a=1, log=FALSE)
ppower1(x, a=1, log.p=FALSE, lower.tail=TRUE)
varpower1(p, a=1, log.p=FALSE, lower.tail=TRUE)
espower1(p, a=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 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)
dpower1(x)
ppower1(x)
varpower1(x)
espower1(x)
# }