VaRES (version 1.0.2)

RS: Ramberg-Schmeiser distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Ramber-Schmeiser distribution due to Ramberg and Schmeiser (1974) given by $$\begin{array}{ll} &\displaystyle {\rm VaR}_p (X) = \frac {p^b - (1 - p)^c}{d}, \\ &\displaystyle {\rm ES}_p (X) = \frac {p^{b}}{d (b + 1)} + \frac {(1 - p)^{c + 1} - 1}{p d (c + 1)} \end{array}$$ for \(0 < p < 1\), \(b > 0\), the first shape parameter, \(c > 0\), the second shape parameter, and \(d > 0\), the scale parameter.

Usage

varRS(p, b=1, c=1, d=1, log.p=FALSE, lower.tail=TRUE)
esRS(p, b=1, c=1, d=1)

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.

Arguments

p

scaler or vector of values at which the value at risk or expected shortfall needs to be computed

d

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

b

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

c

the value of the second 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

Author

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

Examples

x=runif(10,min=0,max=1)
varRS(x)
esRS(x)