fgt: The Foster Greer Thorbecke poverty index

In mjantti/incdist: A collection of functions for income distribution analysis

The Foster Greer Thorbecke poverty index

Description

This function estimates the Foster Greer Thorbecke poverty index for a resource variable x and optional weights w.

Usage

fgt(
  x,
  w = rep(1, length(x)),
  alpha = 0,
  mean = FALSE,
  fraction = 0.5,
  z = ifelse(mean, fraction * weighted_mean(x, w), fraction * weighted_median(x, w)),
  data = NULL,
  ranked = NULL,
  na.rm = TRUE
)

Arguments

x	the resource variable
w	the sampling weights
alpha	the FGT parameter
mean	a logical indicating whether the default poverty line relate to the mean rather than the median (which is the default)
fraction	the fraction of the mean or median to use as the poverty line (default is 0.5)
z	the poverty line (defaults to the product of median and fraction))
data	a data frame holding the data that contain x and w
na.rm	a logical indicating whether NA's should removed

Details

This function estimates the Foster-Greer-Thorbecke poverty index for a poverty line z. The poverty line z is taken by default to be 1/2 of the weighted median, but can be any fraction of the median or mean or a value given as an argument. For \alpha=0, FGT is the proportion of units with income below z \Pr(x < z). For \alpha=1, FGT equals \Pr(x < z)(1 - \bar x/z ) and for \alpha = 2 FGT equals \Pr(x < z)(1 - \bar x/z )CV^2, where CV^2 is the squared coefficient of variation.

The poverty line can be set explicitly or can be taken to be a fraction of either the median (default) or the mean.

Value

A list with elements

fgt	the index value
n	sample size
z	poverty line
sumq	sum of weights

Author(s)

Markus Jantti [e-mail]

References

\insertRef

fostergreerandthorbecke1984incdist

See Also

poverty

Examples

fgt(runif(100))
n <- 100
income <- exp(10 + rnorm(n)*sqrt(2))
weight <- rpois(n,7)
fgt(income, weight)
sapply(seq(.3, .6, by = .1), function(x) fgt(income, weight, fraction = x)$fgt)

mjantti/incdist documentation built on Aug. 23, 2023, 5:33 p.m.