| TL {VaRES} | R Documentation |
Tukey-Lambda distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the Tukey-Lambda distribution due to Tukey (1962) given by
\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}
for 0 < p < 1, and \lambda > 0, the shape parameter.
Usage
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 |
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
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, doi:10.1080/03610918.2014.944658
Examples
x=runif(10,min=0,max=1)
varTL(x)
esTL(x)