FR function

Freimer distribution

Computes the pdf, cdf, value at risk and expected shortfall for the Freimer distribution due to Freimer et al. (1988) given by [REMOVE_ME]$\begin{array}{ll}&\displaystyle{\rm VaR}_p (X) = \frac {1}{a} \left[ \frac {p^b - 1}{b} -\frac {(1 - p)^c - 1}{c} \right],\\&\displaystyle{\rm ES}_p (X) = \frac {1}{a} \left( \frac {1}{c} - \frac {1}{b} \right) +\frac {p^b}{a b (b + 1)} + \frac {(1 - p)^{c + 1} - 1}{p a c (c + 1)}\end{array} [REMOVE_ME_2]$

for $0 < p < 1$, $a > 0$, the scale parameter, $b > 0$, the first shape parameter, and $c > 0$, the second shape parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Freimer distribution due to Freimer et al. (1988) given by

for $0 < p < 1$, $a > 0$, the scale parameter, $b > 0$, the first shape parameter, and $c > 0$, the second shape parameter.

varFR(p, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE)
esFR(p, a=1, b=1, c=1)

Arguments

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

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)
varFR(x)
esFR(x)