arcsine {VaRES}

Arcsine distribution

Description

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

\begin{array}{ll} &\displaystyle f (x) = \frac {1}{\pi \sqrt{(x - a) (b - x)}}, \\ &\displaystyle F (x) = \frac {2}{\pi} \arcsin \left( \sqrt{\frac {x - a}{b - a}} \right), \\ &\displaystyle {\rm VaR}_p (X) = a + (b - a) \sin^2 \left( \frac {\pi p}{2} \right), \\ &\displaystyle {\rm ES}_p (X) = a + \frac {b - a}{p} \int_0^p \sin^2 \left( \frac {\pi v}{2} \right) dv \end{array}

for a \leq x \leq b, 0 < p < 1, -\infty < a < \infty, the first location parameter, and -\infty < a < b < \infty, the second location parameter.

Usage

darcsine(x, a=0, b=1, log=FALSE)
parcsine(x, a=0, b=1, log.p=FALSE, lower.tail=TRUE)
vararcsine(p, a=0, b=1, log.p=FALSE, lower.tail=TRUE)
esarcsine(p, a=0, 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 location parameter, can take any real value, the default is zero

b

the value of the second location parameter, can take any real value but must be greater than a, 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)
darcsine(x)
parcsine(x)
vararcsine(x)
esarcsine(x)