expgeo function

Exponential geometric distribution

Computes the pdf, cdf, value at risk and expected shortfall for the exponential geometric distribution due to Adamidis and Loukas (1998) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef(x) = \frac {\lambda \theta \exp (-\lambda x)}{\left[ 1 - (1 - \theta) \exp (-\lambda x) \right]^2},\\&\displaystyleF (x) = \frac {\theta \exp (-\lambda x)}{1 - (1 - \theta) \exp (-\lambda x)},\\&\displaystyle{\rm VaR}_p (X) = -\frac {1}{\lambda} \log \frac {p}{\theta + (1 - \theta) p},\\&\displaystyle{\rm ES}_p (X) = -\frac {\log p}{\lambda} - \frac {\theta \log \theta}{\lambda p (1 - \theta)} +\frac {\theta + (1 - \theta) p}{\lambda p (1 - \theta)} \log \left[ \theta + (1 - \theta) p \right]\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, $0 < \theta < 1$, the first scale parameter, and $\lambda > 0$, the second scale parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the exponential geometric distribution due to Adamidis and Loukas (1998) given by

for $x > 0$, $0 < p < 1$, $0 < \theta < 1$, the first scale parameter, and $\lambda > 0$, the second scale parameter.

dexpgeo(x, theta=0.5, lambda=1, log=FALSE)
pexpgeo(x, theta=0.5, lambda=1, log.p=FALSE, lower.tail=TRUE)
varexpgeo(p, theta=0.5, lambda=1, log.p=FALSE, lower.tail=TRUE)
esexpgeo(p, theta=0.5, lambda=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
• theta: the value of the first scale parameter, must be in the unit interval, the default is 0.5
• lambda: 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)
dexpgeo(x)
pexpgeo(x)
varexpgeo(x)
esexpgeo(x)