uniform {VaRES}

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.

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)
duniform(x)
puniform(x)
varuniform(x)
esuniform(x)