Hlogis: Hosking logistic distribution

Description Usage Arguments Value Author(s) References Examples

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}}{≤ft[ 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} ≤ft[ 1 - ≤ft( \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, -∞ < x < ∞ if k = 0, and -∞ < k < ∞, the shape parameter.

Usage

1
2
3
4
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

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

Examples

1
2
3
4
5
x=runif(10,min=0,max=1)
dHlogis(x)
pHlogis(x)
varHlogis(x)
esHlogis(x)

VaRES documentation built on May 29, 2017, 8:27 p.m.

Search within the VaRES package
Search all R packages, documentation and source code