| Type: | Package |
| Title: | Income Polarization Index |
| Version: | 1.3 |
| Date: | 2025-11-12 |
| Maintainer: | Michail Tsagris <mtsagris@uoc.gr> |
| Depends: | R (≥ 4.0) |
| Imports: | Rfast, Rfast2, Rcpp, RcppParallel, stats |
| LinkingTo: | Rcpp, RcppParallel |
| Encoding: | UTF-8 |
| SystemRequirements: | GNU make |
| Description: | Extremely fast and memory efficient computation of the DER (or PaF) income polarization index as proposed by Duclos J. Y., Esteban, J. and Ray D. (2004). "Polarization: concepts, measurement, estimation". Econometrica, 72(6): 1737–1772. <doi:10.1111/j.1468-0262.2004.00552.x>. The index may be computed for a single or for a range of values of the alpha-parameter and bootstrapping is also available. |
| License: | GPL-2 |GPL-3 [expanded from: GPL (≥ 2)] |
| RoxygenNote: | 7.3.3 |
| NeedsCompilation: | yes |
| Packaged: | 2025-11-12 19:06:14 UTC; mtsag |
| Author: | Michail Tsagris [aut, cre], Christos Adam [aut] |
| Repository: | CRAN |
| Date/Publication: | 2025-11-12 20:10:16 UTC |
Income Polarization Index
Description
Description: The PaF income polarization index as proposed by Duclos,Esteban, and Ray. (2004). The index may be computed for asingle or for a range of values of the\alpha-parameter and bootstrappingis also available. In all cases, we first divide the data by\mu^{1-\alpha}, where\mu is the mean (income), as described inDuclos, Esteban and Ray (2004). If you want to make the index comparable to theGini index you should divide the alienation component (and the paf eventually)by 2.
Details
| Package: | DER |
| Type: | Package |
| Version: | 1.2 |
| Date: | 2025-11-12 |
Maintainers
Michail Tsagris <mtsagris@uoc.gr>.
Author(s)
Michail Tsagris and Christos Adam.
References
Duclos J. Y., Esteban, J. and Ray D. (2004). Polarization: concepts,measurement, estimation. Econometrica, 72(6): 1737–1772.
Bootstrapping the PaF income polarization index
Description
Bootstrapping the PaF income polarization index
Usage
paf.boot(y, a, R = 1000, ncores = 1)Arguments
y | A numeric vector with income data. |
a | The value of |
R | The number of bootstrap resamples to perform. |
ncores | The number of cores to use. If greater than 1, parallel computing will takeplace. It is advisable to use it if you have many observations and or manyvariables, otherwise it will slow down the process. The default is 1, meaningthat code is executed serially. |
Details
The function compute the PaF index of Duclos, Esteban and Ray (2004) for aspecific value of\alpha, the alienation and identification components,the 1 + normalized covariance, and also their bootstrap estimates, the estimatedbias, the estimated standard error of each and the percentile bootstrapconfidence interval for the PaF index are returned.
Value
A list including:
boot | A matrix with the bootstrap estimates. |
index | The estimates. |
info | A matrix with: the bootstrap based estimates, the bootstrap estimated bias ofthe estimates, the bootstrap estimated standard errors of the estimates, and the95% percentile bootstrap confidence intervals for each component. |
Author(s)
Michail Tsagris and Christos Adam.
R implementation and documentation: Michail Tsagrismtsagris@uoc.grand Christos Adameconp266@econ.soc.uoc.gr.
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
Examples
y <- rgamma(100, 10, 0.01)paf.boot(y, 0.25)Bootstrapping the decomposed PaF income polarization index
Description
Bootstrapping the decomposed PaF income polarization index
Usage
paf2.boot(y, a, R = 1000, ncores = 1)Arguments
y | A numeric vector with income data. |
a | The value of |
R | The number of bootstrap resamples to perform. |
ncores | The number of cores to use. If greater than 1, parallel computing will takeplace. It is advisable to use it if you have many observations and or manyvariables, otherwise it will slow down the process. The default is 1, meaningthat code is executed serially. |
Details
The function computes the decomposed PaF index of Duclos, Esteban and Ray (2004)for a specific value of\alpha. The decomposition is with respect to thedeprivation and surplus components as suggested by Araar (2008). The PaF index,the deprivation and surplus components, and also their bootstrap estimates, theestimated bias and the estimated standard error of each, and the confidenceintervals are returned.
Value
A list including:
boot | A matrix with the bootstrap estimates. |
index | The estimates. |
info | A matrix with: the bootstrap based estimates, the bootstrap estimated bias ofthe estimates, the bootstrap estimated standard errors of the estimates, and the95% percentile bootstrap confidence intervals for each component. |
Author(s)
Michail Tsagris and Christos Adam.
R implementation and documentation: Michail Tsagrismtsagris@uoc.grand Christos Adameconp266@econ.soc.uoc.gr.
References
Araar A. (2008). On the Decomposition of Polarization Indices: Illustrationswith Chinese and Nigerian Household Surveys. CIRPEE Working Paper No. 08-06.https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1136142
Duclos J. Y., Esteban, J. and Ray D. (2004). Polarization: concepts,measurement, estimation. Econometrica, 72(6): 1737–1772.
See Also
Examples
y <- rgamma(100, 10, 0.01)paf2.boot(y, 0.25)Kernel Density Estimation (KDE)
Description
Kernel density estimation of a univariate sample using a Gaussian kernel.
Usage
kde(y, h, ncores = 1)Arguments
y | A numeric vector containing the sample data. |
h | A numeric value for boundwidth. |
ncores | The number of cores to use. If greater than 1, parallel computing will takeplace. It is advisable to use it if you have many observations and or manyvariables, otherwise it will slow down the process. The default is 1, meaningthat code is executed serially. |
Details
The kernel density estimate (KDE) provides a smooth estimate of the probabilitydensity function of the sample data. In this implementation, the KDE isevaluated only at the observed sample points themselves.
Value
A numeric vector of density estimates corresponding to each observation in y.
Author(s)
Michail Tsagris and Christos Adam.
R implementation and documentation: Michail Tsagrismtsagris@uoc.grand Christos Adameconp266@econ.soc.uoc.gr.
Examples
set.seed(123)y <- rnorm(200)dens <- kde(y, h = 1)Many PaF income polarization indices
Description
Many PaF income polarization indices
Usage
colpafs(y, a, ncores = 1)Arguments
y | A numeric matrix with income data. The PaF index will be computed for eachcolumn seperately. |
a | The value of |
ncores | The number of cores to use. If greater than 1, parallel computing will takeplace. It is advisable to use it if you have many observations and or manyvariables, otherwise it will slow down the process. The default is 1, meaningthat code is executed serially. |
Details
The function compute the PaF index of Duclos, Esteban and Ray (2004) for aspecific value of\alpha, for each column of the matrix.
Value
A matrix, where each row contains the PaF index, the alienation (twice the Giniindex) and identification components and 1 + the normalized covariance.
Author(s)
Michail Tsagris and Christos Adam.
R implementation and documentation: Michail Tsagrismtsagris@uoc.grand Christos Adameconp266@econ.soc.uoc.gr.
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
Examples
y <- matrix( rgamma(100 * 10, 10, 0.01), ncol = 10 )colpafs(y, 0.25)Many decomposed PaF income polarization indices
Description
Many decomposed PaF income polarization indices
Usage
colpafs2(y, a, ncores = 1)Arguments
y | A numeric matrix with income data. The PaF index will be computed for eachcolumn seperately. |
a | The value of |
ncores | The number of cores to use. If greater than 1, parallel computing will takeplace. It is advisable to use it if you have many observations and or manyvariables, otherwise it will slow down the process. The default is 1, meaningthat code is executed serially. |
Details
The function compute the decomposed PaF index of Duclos, Esteban and Ray (2004)for a specific value of\alpha, for each column of the matrix. Thedecomposition is with respect to the deprivation and surplus components assuggested by Araar (2008).
Value
A matrix, where each row contains the PaF index, the deprivation and the surpluscomponents.
Author(s)
Michail Tsagris and Christos Adam.
R implementation and documentation: Michail Tsagrismtsagris@uoc.grand Christos Adameconp266@econ.soc.uoc.gr.
References
Araar A. (2008). On the Decomposition of Polarization Indices: Illustrationswith Chinese and Nigerian Household Surveys. CIRPEE Working Paper No. 08-06.https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1136142
Duclos J. Y., Esteban, J. and Ray D. (2004). Polarization: concepts,measurement, estimation. Econometrica, 72(6): 1737–1772.
See Also
Examples
y <- matrix( rgamma(100 * 10, 10, 0.01), ncol = 10 )colpafs2(y, 0.25)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 |
ncores | The number of cores to use. If greater than 1, parallel computing will takeplace. It is advisable to use it if you have many observations and or manyvariables, otherwise it will slow down the process. The default is 1, meaningthat code is executed serially. |
Details
The functions compute the PaF index of Duclos, Esteban and Ray (2004) for eithera 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 fasteras it uses Eq. (3) of the paper.
Value
The paf() function, for a single value of\alpha, returns a vector withthe PaF index, the alienation (twice the Gini index) and identificationcomponents and 1 + the normalized covariance. If a range of values of\alpha are given, it will return a matrix with the same components, whereeach 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 Tsagrismtsagris@uoc.grand Christos Adameconp266@econ.soc.uoc.gr.
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
Examples
y <- rgamma(100, 10, 0.01)paf(y, 0.25)paf( y, c(0.25, 0.5, 0.75, 1) )The decomposed PaF income polarization index
Description
The decomposed PaF income polarization index
Usage
paf2(y, a, ncores = 1)Arguments
y | A numeric vector with income data. |
a | The value of |
ncores | The number of cores to use. If greater than 1, parallel computing will takeplace. It is advisable to use it if you have many observations and or manyvariables, otherwise it will slow down the process. The default is 1, meaningthat code is executed serially. |
Details
The function compute the decomposed PaF index of Duclos, Esteban and Ray (2004)for either a specific value, or for a range of values, of\alpha. Thedecomposition is with respect to the deprivation and surplus components assuggested by Araar (2008).
Value
For a single value of\alpha, the function returns a vector with the PaFindex, the deprivation and the surplus components. If a range of values of\alpha are given, it will return a matrix with the same components, whereeach row corresponds to a specific value of\alpha.
Author(s)
Michail Tsagris and Christos Adam.
R implementation and documentation: Michail Tsagrismtsagris@uoc.grand Christos Adameconp266@econ.soc.uoc.gr.
References
Araar A. (2008). On the Decomposition of Polarization Indices: Illustrationswith Chinese and Nigerian Household Surveys. CIRPEE Working Paper No. 08-06.https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1136142
Duclos J. Y., Esteban, J. and Ray D. (2004). Polarization: concepts,measurement, estimation. Econometrica, 72(6): 1737–1772.
See Also
Examples
y <- rgamma(100, 10, 0.01)paf(y, 0.25)paf2( y, 0.25)