invgamma {VaRES} | R Documentation |
Inverse gamma distribution
Description
Computes the pdf, cdf, value at risk and expected shortfall for the inverse gamma distribution given by
\begin{array}{ll}
&\displaystyle
f (x) = \frac {b^a \exp (-b / x)}{x^{a + 1} \Gamma (a)},
\\
&\displaystyle
F (x) = Q (a, b / x),
\\
&\displaystyle
{\rm VaR}_p (X) = b \left[ Q^{-1} (a, p) \right]^{-1},
\\
&\displaystyle
{\rm ES}_p (X) = \frac {b}{p} \int_0^p \left[ Q^{-1} (a, v) \right]^{-1} dv
\end{array}
for x > 0
, 0 < p < 1
, a > 0
, the shape parameter, and b > 0
, the scale parameter.
Usage
dinvgamma(x, a=1, b=1, log=FALSE)
pinvgamma(x, a=1, b=1, log.p=FALSE, lower.tail=TRUE)
varinvgamma(p, a=1, b=1, log.p=FALSE, lower.tail=TRUE)
esinvgamma(p, a=1, b=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 |
b |
the value of the scale parameter, must be positive, the default is 1 |
a |
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)
dinvgamma(x)
pinvgamma(x)
varinvgamma(x)
esinvgamma(x)