VaRES (version 1.0.2)

logbeta: Log beta distribution

Description

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

Usage

dlogbeta(x, a=1, b=1, c=1, d=2, log=FALSE)
plogbeta(x, a=1, b=1, c=1, d=2, log.p=FALSE, lower.tail=TRUE)
varlogbeta(p, a=1, b=1, c=1, d=2, log.p=FALSE, lower.tail=TRUE)
eslogbeta(p, a=1, b=1, c=1, d=2)

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.

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, must be positive, the default is 1

d

the value of the second location parameter, must be positive and greater than c, the default is 2

a

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

b

the value of the second scale 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

Author

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

Examples

x=runif(10,min=0,max=1)
dlogbeta(x)
plogbeta(x)
varlogbeta(x)
eslogbeta(x)