| xie {VaRES} | R Documentation |
Xie distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the Xie distribution due to Xie et al. (2002) given by
\begin{array}{ll}
&\displaystyle
f(x) = \lambda b \left( \frac {x}{a} \right)^{b - 1}
\exp \left[ (x/a)^b \right] \exp \left( \lambda a \right)
\exp \left\{ -\lambda a \exp \left[ (x/a)^b \right] \right\},
\\
&\displaystyle
F (x) =
1 - \exp \left( \lambda a \right)
\exp \left\{ -\lambda a \exp \left[ (x/a)^b \right] \right\},
\\
&\displaystyle
{\rm VaR}_p (X) =
a \left\{ \log \left[ 1 - \frac {\log (1 - p)}{\lambda a} \right] \right\}^{1/b},
\\
&\displaystyle
{\rm ES}_p (X) =
\frac {a}{p} \int_0^p \left\{ \log \left[ 1 - \frac {\log (1 - v)}{\lambda a} \right] \right\}^{1/b} dv
\end{array}
for x > 0, 0 < p < 1, a > 0, the first scale parameter, b > 0, the shape parameter,
and \lambda > 0, the second scale parameter.
Usage
dxie(x, a=1, b=1, lambda=1, log=FALSE)
pxie(x, a=1, b=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
varxie(p, a=1, b=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
esxie(p, a=1, b=1, lambda=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 |
a |
the value of the first scale parameter, must be positive, the default is 1 |
lambda |
the value of the second scale parameter, must be positive, the default is 1 |
b |
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)
dxie(x)
pxie(x)
varxie(x)
esxie(x)