genlogis4 {VaRES} | R Documentation |
Generalized logistic IV distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the generalized logistic IV distribution given by
\begin{array}{ll}
&\displaystyle
f (x) = \frac {1}{\sigma B (\alpha, a)}
\exp \left( -\alpha \frac {x - \mu}{\sigma} \right) \left\{ 1 + \exp \left( -\frac {x - \mu}{\sigma} \right) \right\}^{-\alpha - a},
\\
&\displaystyle
F (x) = I_{\frac {1}{1 + \exp \left( -\frac {x - \mu}{\sigma} \right)}} (\alpha, a),
\\
&\displaystyle
{\rm VaR}_p (X) = \mu - \sigma \log \frac {1 - I_p^{-1} (\alpha, a)}{I_p^{-1} (\alpha, a)},
\\
&\displaystyle
{\rm ES}_p (X) = \mu - \frac {\sigma}{p} \int_0^p \log \frac {1 - I_v^{-1} (\alpha, a)}{I_v^{-1} (\alpha, a)} dv
\end{array}
for -\infty < x < \infty
, 0 < p < 1
, -\infty < \mu < \infty
, the location parameter, \sigma > 0
, the scale parameter,
\alpha > 0
, the first shape parameter, and a > 0
, the second shape parameter.
Usage
dgenlogis4(x, a=1, alpha=1, mu=0, sigma=1, log=FALSE)
pgenlogis4(x, a=1, alpha=1, mu=0, sigma=1, log.p=FALSE, lower.tail=TRUE)
vargenlogis4(p, a=1, alpha=1, mu=0, sigma=1, log.p=FALSE, lower.tail=TRUE)
esgenlogis4(p, a=1, alpha=1, mu=0, sigma=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 |
mu |
the value of the location parameter, can take any real value, the default is zero |
sigma |
the value of the scale parameter, must be positive, the default is 1 |
alpha |
the value of the first shape parameter, must be positive, the default is 1 |
a |
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 |
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)
dgenlogis4(x)
pgenlogis4(x)
vargenlogis4(x)
esgenlogis4(x)