TL function

Tukey-Lambda distribution

Computes the pdf, cdf, value at risk and expected shortfall for the Tukey-Lambda distribution due to Tukey (1962) given by [REMOVE_ME]$\begin{array}{ll}&\displaystyle{\rm VaR}_p (X) = \frac {p^\lambda - (1 - p)^\lambda}{\lambda},\\&\displaystyle{\rm ES}_p (X) = \frac {p^{\lambda + 1} + (1 - p)^{\lambda + 1} - 1}{p \lambda (\lambda + 1)}\end{array} [REMOVE_ME_2]$

for $0 < p < 1$, and $\lambda > 0$, the shape parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Tukey-Lambda distribution due to Tukey (1962) given by

for $0 < p < 1$, and $\lambda > 0$, the shape parameter.

varTL(p, lambda=1, log.p=FALSE, lower.tail=TRUE)
esTL(p, lambda=1)

Arguments

• p: scaler or vector of values at which the value at risk or expected shortfall needs to be computed
• lambda: 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)
varTL(x)
esTL(x)