logbeta {VaRES}

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}}{x B (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 {\rm VaR}_p (X) = c \left( \frac {d}{c} \right)^{I_p^{-1} (a, b)}, \\ &\displaystyle {\rm ES}_p (X) = \frac {c}{p} \int_0^p \left( \frac {d}{c} \right)^{I_v^{-1} (a, b)} dv \end{array}

for 0 < c \leq x \leq 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)

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

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)
dlogbeta(x)
plogbeta(x)
varlogbeta(x)
eslogbeta(x)