genbeta2 {VaRES} | R Documentation |
Generalized beta II distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the generalized beta II distribution given by
\begin{array}{ll}
&\displaystyle
f (x) = \frac {c x^{ac - 1} \left( 1 - x^c \right)^{b - 1}}{B (a, b)},
\\
&\displaystyle
F (x) = I_{x^c} (a, b),
\\
&\displaystyle
{\rm VaR}_p (X) = \left[ I_p^{-1} (a, b) \right]^{1 / c},
\\
&\displaystyle
{\rm ES}_p (X) = \frac {1}{p} \int_0^p \left[ I_v^{-1} (a, b) \right]^{1 / c} dv
\end{array}
for 0 < x < 1
, 0 < p < 1
, a > 0
, the first shape parameter, b > 0
, the second shape parameter, and c > 0
, the third shape parameter.
Usage
dgenbeta2(x, a=1, b=1, c=1, log=FALSE)
pgenbeta2(x, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE)
vargenbeta2(p, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE)
esgenbeta2(p, a=1, b=1, c=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 shape parameter, must be positive, the default is 1 |
b |
the value of the second shape parameter, must be positive, the default is 1 |
c |
the value of the third 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)
dgenbeta2(x)
pgenbeta2(x)
vargenbeta2(x)
esgenbeta2(x)