VaRES (version 1.0.1)

geninvbeta: Generalized inverse beta distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the generalized inverse beta distribution given by $$\begin{array}{ll} &\displaystyle f (x) = \frac {a x^{ac - 1}}{B (c, d) \left( 1 + x^a \right)^{c + d}}, \\ &\displaystyle F (x) = I_{\frac {x^a}{1 + x^a}} (c, d), \\ &\displaystyle {\rm VaR}_p (X) = \left[ \frac {I_p^{-1} (c, d)}{1 - I_p^{-1} (c, d)} \right]^{1/a}, \\ &\displaystyle {\rm ES}_p (X) = \frac {1}{p} \int_0^p \left[ \frac {I_v^{-1} (c, d)}{1 - I_v^{-1} (c, d)} \right]^{1/a} dv \end{array}$$ for \(x > 0\), \(0 < p < 1\), \(a > 0\), the first shape parameter, \(c > 0\), the second shape parameter, and \(d > 0\), the third shape parameter.

Usage

dgeninvbeta(x, a=1, c=1, d=1, log=FALSE)
pgeninvbeta(x, a=1, c=1, d=1, log.p=FALSE, lower.tail=TRUE)
vargeninvbeta(p, a=1, c=1, d=1, log.p=FALSE, lower.tail=TRUE)
esgeninvbeta(p, a=1, c=1, 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

a

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

c

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

d

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)
dgeninvbeta(x)
pgeninvbeta(x)
vargeninvbeta(x)
esgeninvbeta(x)
# }