VaRES (version 1.0.2)

exppois: Exponential Poisson distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the exponential Poisson distribution due to Kus (2007) given by $$\begin{array}{ll} &\displaystyle f(x) = \frac {b \lambda \exp \left[ -b x - \lambda + \lambda \exp (-b x) \right]}{1 - \exp (-\lambda)}, \\ &\displaystyle F (x) = \frac {1 - \exp \left[ -\lambda + \lambda \exp (-b x) \right]}{1 - \exp (-\lambda)}, \\ &\displaystyle {\rm VaR}_p (X) = -\frac {1}{b} \log \left\{ \frac {1}{\lambda} \log \left[ 1 - p + p \exp (-\lambda) \right] + 1 \right\}, \\ &\displaystyle {\rm ES}_p (X) = -\frac {1}{b p} \int_0^p \log \left\{ \frac {1}{\lambda} \log \left[ 1 - v + v \exp (-\lambda) \right] + 1 \right\} dv \end{array}$$ for \(x > 0\), \(0 < p < 1\), \(b > 0\), the first scale parameter, and \(\lambda > 0\), the second scale parameter.

Usage

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)

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.

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

Author

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

Examples

x=runif(10,min=0,max=1)
dexppois(x)
pexppois(x)
varexppois(x)
esexppois(x)