VaRES (version 1.0.1)

genbeta: Generalized beta distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the generalized beta distribution given by $$\begin{array}{ll}& {\displaystyle f(x)=\frac{(x-c{)}^{a-1}(d-x{)}^{b-1}}{B(a,b)(d-c{)}^{a+b-1}},}\\ & {\displaystyle F(x)=I_{\frac{x-c}{d-c}}(a,b),}\\ & {\displaystyle {\mathrm{V}\mathrm{a}\mathrm{R}}_p(X)=c+(d-c)I_p^{-1}(a,b),}\\ & {\displaystyle {\mathrm{E}\mathrm{S}}_p(X)=c+\frac{d-c}{p}{\int }_0^p{I}_v^{-1}(a,b)dv}\end{array}$$ for $c\le x\le d$, $0<p<1$, $a>0$, the first shape parameter, $b>0$, the second shape parameter, $-\mathrm{\infty }<c<\mathrm{\infty }$, the first location parameter, and $-\mathrm{\infty }<c<d<\mathrm{\infty }$, 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.

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)
dgenbeta(x)
pgenbeta(x)
vargenbeta(x)
esgenbeta(x)
# }