exppois function

Exponential Poisson distribution

Computes the pdf, cdf, value at risk and expected shortfall for the exponential Poisson distribution due to Kus (2007) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef(x) = \frac {b \lambda \exp \left[ -b x - \lambda + \lambda \exp (-b x) \right]}{1 - \exp (-\lambda)},\\&\displaystyleF (x) = \frac {1 - \exp \left[ -\lambda + \lambda \exp (-b x) \right]}{1 - \exp (-\lambda)},\\&\displaystyle{\rm VaR}_p (X) = -\frac {1}{b} \log \left\{ \frac {1}{\lambda} \log \left[ 1 - p + p \exp (-\lambda) \right] + 1 \right\},\\&\displaystyle{\rm ES}_p (X) = -\frac {1}{b p} \int_0^p \log \left\{ \frac {1}{\lambda} \log\left[ 1 - v + v \exp (-\lambda) \right] + 1 \right\} dv\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, $b > 0$, 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 Poisson distribution due to Kus (2007) given by

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

dexppois(x, b=1, lambda=1, log=FALSE)
pexppois(x, b=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
varexppois(p, b=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
esexppois(p, b=1, 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
• b: the value of the first scale parameter, must be positive, the default is 1
• 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)
dexppois(x)
pexppois(x)
varexppois(x)
esexppois(x)