schabe function

Schabe distribution

Computes the pdf, cdf, value at risk and expected shortfall for the Schabe distribution due to Schabe (1994) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef(x) = \frac {\displaystyle 2 \gamma + (1 - \gamma) x / \theta}{\displaystyle \theta (\gamma + x/\theta)^2},\\&\displaystyleF(x) = \frac {\displaystyle (1 + \gamma) x}{\displaystyle x + \gamma \theta},\\&\displaystyle{\rm VaR}_p (X) = \frac {p \gamma \theta}{1 + \gamma - p},\\&\displaystyle{\rm ES}_p (X) = -\theta \gamma - \frac {\theta \gamma (1 + \gamma)}{p}\log \frac {1 + \gamma - p}{1 + \gamma}\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, $0 < \gamma < 1$, the first scale parameter, and $\theta > 0$, the second scale parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Schabe distribution due to Schabe (1994) given by

for $x > 0$, $0 < p < 1$, $0 < \gamma < 1$, the first scale parameter, and $\theta > 0$, the second scale parameter.

dschabe(x, gamma=0.5, theta=1, log=FALSE)
pschabe(x, gamma=0.5, theta=1, log.p=FALSE, lower.tail=TRUE)
varschabe(p, gamma=0.5, theta=1, log.p=FALSE, lower.tail=TRUE)
esschabe(p, gamma=0.5, 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
• gamma: the value of the first scale parameter, must be in the unit interval, the default is 0.5
• theta: 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

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)
dschabe(x)
pschabe(x)
varschabe(x)
esschabe(x)