uniform function

Uniform distribution

Computes the pdf, cdf, value at risk and expected shortfall for the uniform distribution given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = \frac {1}{b - a},\\&\displaystyleF (x) = \frac {x - a}{b - a},\\&\displaystyle{\rm VaR}_p (X) = a + p (b - a),\\&\displaystyle{\rm ES}_p (X) = a + \frac {p}{2} (b - a)\end{array} [REMOVE_ME_2]$

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

Description

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

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

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

Returns

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

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, tools:::Rd_expr_doi("10.1080/03610918.2014.944658")

Author(s)

Saralees Nadarajah

Examples

x=runif(10,min=0,max=1)
duniform(x)
puniform(x)
varuniform(x)
esuniform(x)