VaRES (version 1.0.1)

arcsine: 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.

References

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

Examples

# NOT RUN {
x=runif(10,min=0,max=1)
darcsine(x)
parcsine(x)
vararcsine(x)
esarcsine(x)
# }