CompoundIndicators: Indicators of Poverty and Social Exclusion under the Compound...

In GB2: Generalized Beta Distribution of the Second Kind: Properties, Likelihood, Estimation

Indicators of Poverty and Social Exclusion under the Compound Distribution based on the GB2

Description

Functions to calculate four primary social welfare indicators under the compound GB2 distribution, i.e. the at-risk-of-poverty threshold, the at-risk-of-poverty rate, the relative median at-risk-of-poverty gap, and the income quintile share ratio.

Usage

arpt.cgb2(prop, shape1, scale, shape2, shape3, pl0, pl, decomp="r")
arpr.cgb2(prop, shape1, shape2, shape3, pl0, pl, decomp="r")
rmpg.cgb2(arpr, shape1, shape2, shape3, pl0, pl, decomp="r")
qsr.cgb2(shape1, shape2, shape3, pl0, pl, decomp="r")
main.cgb2(prop, shape1, scale, shape2, shape3, pl0, pl, decomp="r")

Arguments

prop	numeric; proportion (in general is set to 0.6).
arpr	numeric; the value of the at-risk-of-poverty rate.
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.

Details

The four indicators are described in details in the case of the GB2. The difference here is that we need to give an initial vector of proportions, fitted proportions and define for which decomposition (left or right) the indicators should be calculated.

Value

arpt.cgb2 gives the ARPT, arpr.cgb2 the ARPR, rmpg.cgb2 the RMPG, qsr.cgb2 gives the QSR and main.cgb2 calculates the median, the mean, the ARPR, the RMPG and the QSR under the compound GB2.

Author(s)

Monique Graf

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.

See Also

arpr.gb2 for details on the welfare indicators under the GB2.

Examples

# GB2 parameters
a <- 3.9
b <- 18873
p <- 0.97
q <- 1.03

# Proportions defining the component densities
p0 <- rep(1/3,3)

# Mixture probabilities
pl <- c(0.39,0.26,0.35)

# for the right discretization
arpt <- arpt.cgb2(0.6, a, b, p, q, p0, pl)
arpr <- arpr.cgb2(0.6, a, p, q, p0, pl)
rmpg <- rmpg.cgb2(arpr, a, p, q, p0, pl)
qsr <- qsr.cgb2(a, p, q, p0, pl)

# for the left discretization
arptleft <- arpt.cgb2(0.6, a, b, p, q, p0, pl, "l")

GB2 documentation built on June 22, 2022, 9:07 a.m.