paf: The PaF income polarization index

In DER: Income Polarization Index

The PaF income polarization index

Description

The PaF income polarization index

Usage

paf(y, a, ncores = 1)
pafF(y, a, ncores = 1)

Arguments

y	A numeric vector with income data.
a	The value of \alpha. This can either be a number or a vector with many values. In any case, the \alpha may take values between 0.25 and 1.
ncores	The number of cores to use. If greater than 1, parallel computing will take place. It is advisable to use it if you have many observations and or many variables, otherwise it will slow down the process. The default is 1, meaning that code is executed serially.

Details

The functions compute the PaF index of Duclos, Esteban and Ray (2004) for either a specific value, or for a range of values, of \alpha. The pafF() estimates the index using Eq. (8) and (9) in the paper, whereas paf() is faster as it uses Eq. (3) of the paper.

Value

The paf() function, for a single value of \alpha, returns a vector with the PaF index, the alienation (twice the Gini index) and identification components and 1 + the normalized covariance. If a range of values of \alpha are given, it will return a matrix with the same components, where each row corresponds to a specific value of \alpha.

The pafF() function returns only the PaF index for either one or more values of \alpha.

Author(s)

Michail Tsagris and Christos Adam.

R implementation and documentation: Michail Tsagris [e-mail] and Christos Adam [e-mail].

References

Duclos J. Y., Esteban, J. and Ray D. (2006). Polarization: concepts, measurement, estimation. In The Social Economics of Poverty (pp. 54–102). Routledge.

Duclos J. Y., Esteban, J. and Ray D. (2004). Polarization: concepts, measurement, estimation. Econometrica, 72(6): 1737–1772.

See Also

paf.boot

Examples

y <- rgamma(100, 10, 0.01)
paf(y, 0.25)
paf( y, c(0.25, 0.5, 0.75, 1) )

DER documentation built on Nov. 13, 2025, 1:07 a.m.