Hlogis function

Hosking logistic distribution

Computes the pdf, cdf, value at risk and expected shortfall for the Hosking logistic distribution due to Hosking (1989, 1990) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = \frac {(1 - k x)^{1 / k - 1}}{\left[ 1 + (1 - k x)^{1 / k} \right]^2},\\&\displaystyleF (x) = \frac {1}{1 + (1 - k x)^{1 / k}},\\&\displaystyle{\rm VaR}_p (X) = \frac {1}{k} \left[ 1 - \left( \frac {1 - p}{p} \right)^k \right],\\&\displaystyle{\rm ES}_p (X) = \frac {1}{k} - \frac {1}{kp} B_p (1 - k, 1 + k)\end{array} [REMOVE_ME_2]$

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.

Description

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

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.

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

Returns

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

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, tools:::Rd_expr_doi("10.1080/03610918.2014.944658")

Author(s)

Saralees Nadarajah

Examples

x=runif(10,min=0,max=1)
dHlogis(x)
pHlogis(x)
varHlogis(x)
esHlogis(x)