# R/CompoundIndicators.R In GB2: Generalized Beta Distribution of the Second Kind: Properties, Likelihood, Estimation

```# At-risk-of-poverty threshold
arpt.cgb2 <- function(prop, shape1, scale, shape2, shape3, pl0, pl, decomp="r"){
median <- qcgb2(0.5, shape1, scale, shape2, shape3, pl0, pl, decomp)   # scaled median
return(prop*median)
}

# At-risk-of-poverty rate
arpr.cgb2 <- function(prop, shape1, shape2, shape3, pl0, pl, decomp="r"){
return(pcgb2(arpt.cgb2(prop, shape1, 1, shape2, shape3, pl0, pl, decomp),shape1, 1, shape2, shape3, pl0, pl, decomp))
}

# Relative median poverty gap
rmpg.cgb2 <- function(arpr, shape1, shape2, shape3, pl0, pl, decomp="r"){
return(1-qcgb2(arpr/2, shape1, 1, shape2, shape3, pl0, pl, decomp)/qcgb2(arpr, shape1, 1, shape2, shape3, pl0, pl, decomp))
}

# Quintile share ratio
qsr.cgb2 <- function(shape1, shape2, shape3, pl0, pl, decomp="r") {
q20 <- qcgb2(0.2, shape1, 1, shape2, shape3, pl0, pl, decomp)
q80 <- qcgb2(0.8, shape1, 1, shape2, shape3, pl0, pl, decomp)
return((1-incompl.cgb2(q80, 1, shape1, 1, shape2, shape3, pl0, pl, decomp))/incompl.cgb2(q20, 1, shape1, 1, shape2, shape3, pl0, pl, decomp))
}

# The four indicators and the median
main.cgb2 <- function(prop, shape1, scale, shape2, shape3,pl0,pl,decomp="r"){
arpr <-arpr.cgb2(prop, shape1,shape2, shape3, pl0, pl,decomp=decomp)
main <- c(qcgb2(0.5, shape1, scale, shape2, shape3,pl0, pl,decomp=decomp),
moment.cgb2(1,shape1, scale, shape2, shape3, pl0, pl,decomp=decomp),
arpr ,
rmpg.cgb2(arpr,shape1,shape2, shape3, pl0, pl,decomp=decomp),
qsr.cgb2(shape1,shape2, shape3, pl0, pl,decomp=decomp))
names(main) <- c("median","mean","arpr","rmpg","qsr")
return(main)
}
```

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GB2 documentation built on May 2, 2019, 5:53 a.m.