explog {VaRES}

Exponential logarithmic distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the exponential logarithmic distribution due to Tahmasbi and Rezaei (2008) given by

\begin{array}{ll} &\displaystyle f(x) = -\frac {b (1 - a) \exp (-b x)}{\log a \left[ 1 - (1 - a) \exp (-b x) \right]}, \\ &\displaystyle F (x) = 1 - \frac {\log \left[ 1 - (1 - a) \exp (-b x) \right]}{\log a}, \\ &\displaystyle {\rm VaR}_p (X) = -\frac {1}{b} \log \left[ \frac {1 - a^{1 - p}}{1 - a} \right], \\ &\displaystyle {\rm ES}_p (X) = -\frac {1}{b p} \int_0^p \log \left[ \frac {1 - a^{1 - v}}{1 - a} \right] dv \end{array}

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

Usage

dexplog(x, a=0.5, b=1, log=FALSE)
pexplog(x, a=0.5, b=1, log.p=FALSE, lower.tail=TRUE)
varexplog(p, a=0.5, b=1, log.p=FALSE, lower.tail=TRUE)
esexplog(p, a=0.5, b=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

a

the value of the first scale parameter, must be in the unit interval, the default is 0.5

b

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

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.

Author(s)

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, doi:10.1080/03610918.2014.944658

Examples

x=runif(10,min=0,max=1)
dexplog(x)
pexplog(x)
varexplog(x)
esexplog(x)