loggamma function

Log gamma distribution

Computes the pdf, cdf, value at risk and expected shortfall for the log gamma distribution due to Consul and Jain (1971) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = \frac {a^r x^{a - 1} (-\log x)^{r - 1}}{\Gamma (r)},\\&\displaystyleF (x) = Q (r, -a \log x),\\&\displaystyle{\rm VaR}_p (X) = \exp \left[ -\frac {1}{a} Q^{-1} (r, p) \right],\\&\displaystyle{\rm ES}_p (X) = \frac {1}{p} \int_0^p \exp\left[ -\frac {1}{a} Q^{-1} (r, v) \right] dv\end{array} [REMOVE_ME_2]$

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

Description

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

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

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

Returns

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

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, tools:::Rd_expr_doi("10.1080/03610918.2014.944658")

Author(s)

Saralees Nadarajah

Examples

x=runif(10,min=0,max=1)
dloggamma(x)
ploggamma(x)
varloggamma(x)
esloggamma(x)