chen function

Chen distribution

Computes the pdf, cdf, value at risk and expected shortfall for the Chen distribution due to Chen (2000) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef(x) = \lambda b x^{b - 1} \exp \left( x^b \right) \exp \left[ \lambda - \lambda \exp \left( x^b \right) \right],\\&\displaystyleF (x) = 1 - \exp \left[ \lambda - \lambda \exp \left( x^b \right) \right],\\&\displaystyle{\rm VaR}_p (X) = \left\{ \log \left[ 1 - \frac {\log (1 - p)}{\lambda} \right] \right\}^{1 / b},\\&\displaystyle{\rm ES}_p (X) = \frac {1}{p} \int_0^p \left\{ \log \left[ 1 - \frac {\log (1 - v)}{\lambda} \right] \right\}^{1 / b} dv\end{array} [REMOVE_ME_2]$

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

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Chen distribution due to Chen (2000) given by

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

dchen(x, b=1, lambda=1, log=FALSE)
pchen(x, b=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
varchen(p, b=1, lambda=1, log.p=FALSE, lower.tail=TRUE)
eschen(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
• lambda: the value of the scale parameter, must be positive, the default is 1
• b: 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)
dchen(x)
pchen(x)
varchen(x)
eschen(x)