Hlogis {VaRES}

Hosking logistic distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Hosking logistic distribution due to Hosking (1989, 1990) given by

\begin{array}{ll} &\displaystyle f (x) = \frac {(1 - k x)^{1 / k - 1}}{\left[ 1 + (1 - k x)^{1 / k} \right]^2}, \\ &\displaystyle F (x) = \frac {1}{1 + (1 - k x)^{1 / k}}, \\ &\displaystyle {\rm VaR}_p (X) = \frac {1}{k} \left[ 1 - \left( \frac {1 - p}{p} \right)^k \right], \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{k} - \frac {1}{kp} B_p (1 - k, 1 + k) \end{array}

for x < 1/k if k > 0, x > 1/k if k < 0, -\infty < x < \infty if k = 0, and -\infty < k < \infty, the shape parameter.

Usage

dHlogis(x, k=1, log=FALSE)
pHlogis(x, k=1, log.p=FALSE, lower.tail=TRUE)
varHlogis(p, k=1, log.p=FALSE, lower.tail=TRUE)
esHlogis(p, 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

k

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)
dHlogis(x)
pHlogis(x)
varHlogis(x)
esHlogis(x)