exponential function

Exponential distribution

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

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

Description

Computes the pdf, cdf, value at risk and expected shortfall for the exponential distribution given by

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

dexponential(x, lambda=1, log=FALSE)
pexponential(x, lambda=1, log.p=FALSE, lower.tail=TRUE)
varexponential(p, lambda=1, log.p=FALSE, lower.tail=TRUE)
esexponential(p, 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
• lambda: the value of the 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)
dexponential(x)
pexponential(x)
varexponential(x)
esexponential(x)