loggamma {VaRES}

Log gamma distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the log gamma distribution due to Consul and Jain (1971) given by

\begin{array}{ll} &\displaystyle f (x) = \frac {a^r x^{a - 1} (-\log x)^{r - 1}}{\Gamma (r)}, \\ &\displaystyle F (x) = Q (r, -a \log x), \\ &\displaystyle {\rm VaR}_p (X) = \exp \left[ -\frac {1}{a} Q^{-1} (r, p) \right], \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{p} \int_0^p \exp \left[ -\frac {1}{a} Q^{-1} (r, v) \right] dv \end{array}

for x > 0, 0 < p < 1, a > 0, the first shape parameter, and r > 0, the second shape parameter.

Usage

dloggamma(x, a=1, r=1, log=FALSE)
ploggamma(x, a=1, r=1, log.p=FALSE, lower.tail=TRUE)
varloggamma(p, a=1, r=1, log.p=FALSE, lower.tail=TRUE)
esloggamma(p, a=1, r=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 scale parameter, must be positive, the default is 1

r

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)
dloggamma(x)
ploggamma(x)
varloggamma(x)
esloggamma(x)