dagum function

Dagum distribution

Computes the pdf, cdf, value at risk and expected shortfall for the Dagum distribution due to Dagum (1975, 1977, 1980) given by [REMOVE_ME]$\begin{array}{ll}&\displaystylef (x) = \frac {a c b^a x^{a c - 1}}{\left[ x^a + b^a \right]^{c + 1}},\\&\displaystyleF (x) = \left[ 1 + \left( \frac {b}{x} \right)^a \right]^{-c},\\&\displaystyle{\rm VaR}_p (X) = b \left( 1- p^{-1 / c} \right)^{-1 / a},\\&\displaystyle{\rm ES}_p (X) = \frac {b}{p} \int_0^p \left( 1 - v^{-1 / c} \right)^{-1 / a} dv\end{array} [REMOVE_ME_2]$

for $x > 0$, $0 < p < 1$, $a > 0$, the first shape parameter, $b > 0$, the scale parameter, and $c > 0$, the second shape parameter.

Description

Computes the pdf, cdf, value at risk and expected shortfall for the Dagum distribution due to Dagum (1975, 1977, 1980) given by

for $x > 0$, $0 < p < 1$, $a > 0$, the first shape parameter, $b > 0$, the scale parameter, and $c > 0$, the second shape parameter.

ddagum(x, a=1, b=1, c=1, log=FALSE)
pdagum(x, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE)
vardagum(p, a=1, b=1, c=1, log.p=FALSE, lower.tail=TRUE)
esdagum(p, a=1, b=1, c=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 scale parameter, must be positive, the default is 1
• 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
• 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

Returns

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

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")

Author(s)

Saralees Nadarajah

Examples

x=runif(10,min=0,max=1)
ddagum(x)
pdagum(x)
vardagum(x)
esdagum(x)