expgeo {VaRES} | R Documentation |
Exponential geometric distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the exponential geometric distribution due to Adamidis and Loukas (1998) given by
\begin{array}{ll}
&\displaystyle
f(x) = \frac {\lambda \theta \exp (-\lambda x)}{\left[ 1 - (1 - \theta) \exp (-\lambda x) \right]^2},
\\
&\displaystyle
F (x) = \frac {\theta \exp (-\lambda x)}{1 - (1 - \theta) \exp (-\lambda x)},
\\
&\displaystyle
{\rm VaR}_p (X) = -\frac {1}{\lambda} \log \frac {p}{\theta + (1 - \theta) p},
\\
&\displaystyle
{\rm ES}_p (X) = -\frac {\log p}{\lambda} - \frac {\theta \log \theta}{\lambda p (1 - \theta)} +
\frac {\theta + (1 - \theta) p}{\lambda p (1 - \theta)} \log \left[ \theta + (1 - \theta) p \right]
\end{array}
for x > 0
, 0 < p < 1
, 0 < \theta < 1
, the first scale parameter, and \lambda > 0
, the second scale parameter.
Usage
dexpgeo(x, theta=0.5, lambda=1, log=FALSE)
pexpgeo(x, theta=0.5, lambda=1, log.p=FALSE, lower.tail=TRUE)
varexpgeo(p, theta=0.5, lambda=1, log.p=FALSE, lower.tail=TRUE)
esexpgeo(p, theta=0.5, 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 |
theta |
the value of the first scale parameter, must be in the unit interval, the default is 0.5 |
lambda |
the value of the second scale 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)
dexpgeo(x)
pexpgeo(x)
varexpgeo(x)
esexpgeo(x)