VaRES (version 1.0.1)

uniform: Uniform distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the uniform distribution given by $$\begin{array}{ll} &\displaystyle f (x) = \frac {1}{b - a}, \\ &\displaystyle F (x) = \frac {x - a}{b - a}, \\ &\displaystyle {\rm VaR}_p (X) = a + p (b - a), \\ &\displaystyle {\rm ES}_p (X) = a + \frac {p}{2} (b - a) \end{array}$$ for \(a < x < b\), \(0 < p < 1\), \(-\infty < a < \infty\) , the first location parameter, and \(-\infty < a < b < \infty\) , the second location parameter.

Usage

duniform(x, a=0, b=1, log=FALSE)
puniform(x, a=0, b=1, log.p=FALSE, lower.tail=TRUE)
varuniform(p, a=0, b=1, log.p=FALSE, lower.tail=TRUE)
esuniform(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)
duniform(x)
puniform(x)
varuniform(x)
esuniform(x)
# }