genbeta {VaRES}

Generalized beta distribution

Description

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

\begin{array}{ll} &\displaystyle f (x) = \frac {(x - c)^{a - 1} (d - x)^{b - 1}}{B (a, b) (d - c)^{a + b - 1}}, \\ &\displaystyle F (x) = I_{\frac {x - c}{d - c}} (a, b), \\ &\displaystyle {\rm VaR}_p (X) = c + (d - c) I_p^{-1} (a, b), \\ &\displaystyle {\rm ES}_p (X) = c + \frac {d - c}{p} \int_0^p I_v^{-1} (a, b) dv \end{array}

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

Usage

dgenbeta(x, a=1, b=1, c=0, d=1, log=FALSE)
pgenbeta(x, a=1, b=1, c=0, d=1, log.p=FALSE, lower.tail=TRUE)
vargenbeta(p, a=1, b=1, c=0, d=1, log.p=FALSE, lower.tail=TRUE)
esgenbeta(p, a=1, b=1, c=0, d=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

c

the value of the first location parameter, can take any real value, the default is zero

d

the value of the second location parameter, can take any real value but must be greater than c, the default is 1

a

the value of the first shape parameter, must be positive, the default is 1

b

the value of the second shape parameter, must be positive, 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)
dgenbeta(x)
pgenbeta(x)
vargenbeta(x)
esgenbeta(x)