GB2 (version 2.1.1)

CompoundMoments: Moments of the Compound Distribution based on the GB2

Description

These functions calculate the moment of order k and incomplete moment of order k of a GB2 compound random variable \(X\) as well as the moment of order k for each component density.

Usage

mkl.cgb2(k, shape1, scale, shape2, shape3, pl0, decomp="r")
moment.cgb2(k, shape1, scale, shape2 ,shape3, pl0, pl, decomp="r")
incompl.cgb2(x, k, shape1, scale, shape2, shape3, pl0, pl, decomp="r")

Arguments

x

numeric; vector of quantiles.

k

numeric; order of the moment.

shape1,scale,shape2,shape3

numeric; positive parameters of the GB2 distribution.

pl0

numeric; a vector of initial proportions defining the number of components and the weight of each component density in the decomposition. Sums to one.

pl

numeric; a vector of mixture probabilities. Sums to one. If \(pl=pl0\) we obtain the GB2 distribution.

decomp

string; specifying if the decomposition of the GB2 is done with respect to the right tail ("r") or the left tail ("l") of the distribution. By default, decomp = "r" - right tail decomposition.

Value

mkl.cgb2 returns a vector of the moments of the component densities, moment.cgb2 returns the moment of order k and incompl.cgb2 - the incomplete moment of order k.

References

Graf, M., Nedyalkova, D., Muennich, R., Seger, J. and Zins, S. (2011) AMELI Deliverable 2.1: Parametric Estimation of Income Distributions and Indicators of Poverty and Social Exclusion. Technical report, AMELI-Project.

Examples

# NOT RUN {
#\dontrun{

#\library{cubature}

# GB2 parameters
af <- 5
bf <- 20000
pf <- 0.45 
qf <- 0.75

p0 <- rep(1/3,3)
p1 <- c(0.37,0.43,0.2)

# moments for the component densities
mkl.cgb2(1,af,bf,pf,qf,p0)
mkl.cgb2(-1,af,bf,pf,qf,p0,"l")

#Moment of order k
moment.cgb2(0.5,af,bf,pf,qf,p0,p1)
moment.cgb2(0.5,af,bf,pf,qf,p0,p1,"l")

#Incomplete moment of order k
incompl.cgb2(20000,1,af,bf,pf,qf,p0,p1)
incompl.cgb2(20000,1,af,bf,pf,qf,p0,p1,"l")
#}
# }