VaRES (version 1.0.1)

loggamma: 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.

References

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

Examples

# NOT RUN {
x=runif(10,min=0,max=1)
dloggamma(x)
ploggamma(x)
varloggamma(x)
esloggamma(x)
# }