genunif {VaRES}

Generalized uniform distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the generalized uniform distribution given by

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

for a \leq x \leq a + k^{-1/c}, 0 < p < 1, -\infty < a < \infty, the location parameter, c > 0, the first shape parameter, k > 0, the scale parameter, and h > 0, the second shape parameter.

Usage

dgenunif(x, a=0, c=1, h=1, k=1, log=FALSE)
pgenunif(x, a=0, c=1, h=1, k=1, log.p=FALSE, lower.tail=TRUE)
vargenunif(p, a=0, c=1, h=1, k=1, log.p=FALSE, lower.tail=TRUE)
esgenunif(p, a=0, c=1, h=1, k=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 location parameter, can take any real value, the default is zero

k

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

c

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

h

the value of the second scale 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)
dgenunif(x)
pgenunif(x)
vargenunif(x)
esgenunif(x)