VaRES (version 1.0.1)

betagompertz: Beta Gompertz distribution

Description

Computes the pdf, cdf, value at risk and expected shortfall for the beta Gompertz distribution due to Cordeiro et al. (2012b) given by $$\begin{array}{ll}& {\displaystyle f(x)=\frac{b\eta \exp (bx)}{B(c,d)}\exp \left(d\eta \right)\exp [-d\eta \exp (bx)]{\{1-\exp [\eta -\eta \exp (bx)]\}}^{c-1},}\\ & {\displaystyle F(x)=I_{1-\exp [\eta -\eta \exp (bx)]}(c,d),}\\ & {\displaystyle {\mathrm{V}\mathrm{a}\mathrm{R}}_p(X)=\frac{1}{b}\log \{1-\frac{1}{\eta }\log [1-I_p^{-1}(c,d)]\},}\\ & {\displaystyle {\mathrm{E}\mathrm{S}}_p(X)=\frac{1}{pb}{\int }_0^p\log \{1-\frac{1}{\eta }\log [1-I_v^{-1}(c,d)]\}dv}\end{array}$$ for $x>0$, $0<p<1$, $b>0$, the first scale parameter, $\eta >0$, the second scale parameter, $c>0$, the first shape parameter, and $d>0$, the second shape parameter.

Usage

dbetagompertz(x, b=1, c=1, d=1, eta=1, log=FALSE)
pbetagompertz(x, b=1, c=1, d=1, eta=1, log.p=FALSE, lower.tail=TRUE)
varbetagompertz(p, b=1, c=1, d=1, eta=1, log.p=FALSE, lower.tail=TRUE)
esbetagompertz(p, b=1, c=1, d=1, eta=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

b

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

eta

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

c

the value of the first 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)
dbetagompertz(x)
pbetagompertz(x)
varbetagompertz(x)
esbetagompertz(x)
# }