| halflogis {VaRES} | R Documentation |
Half logistic distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the half logistic distribution given by
\begin{array}{ll}
&\displaystyle
f (x) = \frac {2 \lambda \exp \left( -\lambda x \right)}
{\left[ 1 + \exp \left( -\lambda x \right) \right]^2},
\\
&\displaystyle
F (x) = \frac {1 - \exp \left( -\lambda x \right)}{1 + \exp \left( -\lambda x \right)},
\\
&\displaystyle
{\rm VaR}_p (X) = -\frac {1}{\lambda} \log \frac {1 - p}{1 + p},
\\
&\displaystyle
{\rm ES}_p (X) = -\frac {1}{\lambda} \log \frac {1 - p}{1 + p} + \frac {1}{\lambda p} \log \left( 1 - p^2 \right)
\end{array}
for x > 0, 0 < p < 1, and \lambda > 0, the scale parameter.
Usage
dhalflogis(x, lambda=1, log=FALSE)
phalflogis(x, lambda=1, log.p=FALSE, lower.tail=TRUE)
varhalflogis(p, lambda=1, log.p=FALSE, lower.tail=TRUE)
eshalflogis(p, 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 |
lambda |
the value of the 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)
dhalflogis(x)
phalflogis(x)
varhalflogis(x)
eshalflogis(x)