expext function

Exponential extension distribution

Computes the pdf, cdf, value at risk and expected shortfall for the exponential extension distribution due to Nadarajah and Haghighi (2011) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = a \lambda (1 + \lambda x)^{a - 1} \exp \left[ 1 - (1 + \lambda x)^a \right],\\&\displaystyleF (x) = 1 - \exp \left[ 1 - (1 + \lambda x)^a \right],\\&\displaystyle{\rm VaR}_p (X) = \frac {\left[ 1 - \log (1 - p) \right]^{1 / a} - 1}{\lambda},\\&\displaystyle{\rm ES}_p (X) = -\frac {1}{\lambda} + \frac {1}{\lambda p} \int_0^p \left[ 1 - \log (1 - v) \right]^{1 / a} dv\end{array} [REMOVE_ME_2]$

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

Description

Computes the pdf, cdf, value at risk and expected shortfall for the exponential extension distribution due to Nadarajah and Haghighi (2011) given by

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

dexpext(x, lambda=1, a=1, log=FALSE)
pexpext(x, lambda=1, a=1, log.p=FALSE, lower.tail=TRUE)
varexpext(p, lambda=1, a=1, log.p=FALSE, lower.tail=TRUE)
esexpext(p, lambda=1, a=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
• a: the value of the shape 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)
dexpext(x)
pexpext(x)
varexpext(x)
esexpext(x)