genpowerweibull {VaRES}

Generalized power Weibull distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the generalized power Weibull distribution due to Nikulin and Haghighi (2006) given by

\begin{array}{ll} &\displaystyle f(x) = a \theta x^{a - 1} \left[ 1 + x^a \right]^{\theta - 1} \exp \left\{ 1 - \left[ 1 + x^a \right]^\theta \right\}, \\ &\displaystyle F (x) = 1 - \exp \left\{ 1 - \left[ 1 + x^a \right]^\theta \right\}, \\ &\displaystyle {\rm VaR}_p (X) = \left\{ \left[ 1 - \log (1 - p) \right]^{1 / \theta} - 1 \right\}^{1 / a}, \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{p} \int_0^p \left\{ \left[ 1 - \log (1 - v) \right]^{1 / \theta} - 1 \right\}^{1 / a} dv \end{array}

for x > 0, 0 < p < 1, a > 0, the first shape parameter, and \theta > 0, the second shape parameter.

Usage

dgenpowerweibull(x, a=1, theta=1, log=FALSE)
pgenpowerweibull(x, a=1, theta=1, log.p=FALSE, lower.tail=TRUE)
vargenpowerweibull(p, a=1, theta=1, log.p=FALSE, lower.tail=TRUE)
esgenpowerweibull(p, a=1, theta=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 first shape parameter, must be positive, the default is 1

theta

the value of the second 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)
dgenpowerweibull(x)
pgenpowerweibull(x)
vargenpowerweibull(x)
esgenpowerweibull(x)