tip: The "three I's of poverty" (TIP) or "Cumulated Poverty Gap"...

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

The "three I's of poverty" (TIP) or "Cumulated Poverty Gap" (CGP) curve

Description

This function returns the cumulated poverty gap.

Usage

tip(x, ...)

Arguments

x	the resource variable
w	the sampling weights
q	an integer or logical. If an integer, it is the number of equally spaced points at which the Lorenz curve ordinates are estimated. If FALSE, then the Lorenz curve is estimated at every point in x.
z	the poverty line
data	the data frame where the variables are found.
alpha	the FGT parameter
normalize	a logical. If true, tip returns the normalized gap (i.e., the gap divided by the poverty line).
mean	a logical indicating whether the default poverty line relate to the mean rather than the median
fraction	the fraction of the mean or median to use as the poverty line
na.rm	a logical indicating whether NA's should removed

Details

This function computes the 'TIP'curve, that is, the cumulated poverty gap as a function of the population proportion as

TIP(p) := \sum_{F^{-1}(x_i) < p} I(x_i < z) (z - x_i),

or, if the normalized by the poverty line,

TIP(p) := \sum_{F^{-1}(x_i) < p} I(x_i < z) (1 - x_i/z).

The TIP curve is increasing for values of x below the poverty line z, at which point it becomes horizontal. That point gives the proportion below the poverty line (p) and the cumulative average poverty gap (the value of the TIP curve). If weights are given, the function returns the weighted TIP curve. If q = FALSE, tip() returns an object whose elements p and ordinates are of length(x).

Simple summary, print and plot methods are provided.

Value

A object of class tip with elements

p	the population proportion
ordinates	the TIP curve value at p
hc	the proportion of units with x less than z
relgap	the average poverty gap (across the poor population)
n	sample size
z	the poverty line
sum.weights	the sum of weights

Author(s)

Markus Jantti [e-mail]

References

\insertRef

jenkinsandlambert1997incdist

See Also

lorenz, fgt

Examples

income <- rexp(100)
weight <- rpois(100,5)
tip.ex <- tip(income, weight, q = FALSE)
plot(tip.ex, lwd = 2)

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