power2 {VaRES}

Power function II distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the power function II distribution given by

\begin{array}{ll} &\displaystyle f (x) = b (1 - x)^{b - 1}, \\ &\displaystyle F (x) = 1 - (1 - x)^b, \\ &\displaystyle {\rm VaR}_p (X) = 1 - (1 - p)^{1 / b}, \\ &\displaystyle {\rm ES}_p (X) = 1 + \frac {b \left[ (1 - p)^{1 / b + 1} - 1 \right]}{p (b + 1)} \end{array}

for 0 < x < 1, 0 < p < 1, and b > 0, the shape parameter.

Usage

dpower2(x, b=1, log=FALSE)
ppower2(x, b=1, log.p=FALSE, lower.tail=TRUE)
varpower2(p, b=1, log.p=FALSE, lower.tail=TRUE)
espower2(p, 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

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.

Author(s)

Saralees Nadarajah

References

Stephen Chan, Saralees Nadarajah & Emmanuel Afuecheta (2016). An R Package for Value at Risk and Expected Shortfall, Communications in Statistics - Simulation and Computation, 45:9, 3416-3434, doi:10.1080/03610918.2014.944658

Examples

x=runif(10,min=0,max=1)
dpower2(x)
ppower2(x)
varpower2(x)
espower2(x)