Datasets and free source code (software R) for the manuscript: Exploring and correcting the bias in the estimation of the Gini measure of inequality

Abstract

The aim of this document is to describe how to reproduce the results derived in the article “Exploring and correcting the bias in the estimation of the Gini measure of income inequality”, published in the journal Sociological Methods & Research. First (Section 2), we describe (load) the various R packages required for the computation of the estimators described in this article. In Section 3, we compute the parameters of the probabilistic distributions considered in simulation studies. Section 4 gives examples on how samples can be selected for the various scenarios. For both infinite and finite populations, codes for computing the various estimators of the Gini index are provided in Section 5. Box plots to investigate the effect of the skewness on the bias of the estimation of the Gini index can be seen in Section 6. For the various estimators defined in this document, Section 7 provides codes for computing empirical measures related to such estimators. In particular, functions inf.empirical.measures and fin.empirical.measures gives the: (i) Relative Bias (RB); (ii) Relative Root Mean Square Error (RRMSE); (iii) Bias Ratio (BR); (iv) Expected value based on estimates of the Gini index and; (v) Expected value based on estimates of the coefficient of skewness. Some examples are included, and they indicate how to carry out simulation studies. Finally, various estimators of the Gini index are computed using the data set ES-SILC, with size n=26. The various real data sets can be loaded using the file Datasets.RData.

The aim of this document is to describe how to reproduce the results derived in the article “Exploring and correcting the bias in the estimation of the Gini measure of income inequality”, published in the journal Sociological Methods & Research. First (Section 2), we describe (load) the various R packages required for the computation of the estimators described in this article. In Section 3, we compute the parameters of the probabilistic distributions considered in simulation studies. Section 4 gives examples on how samples can be selected for the various scenarios. For both infinite and finite populations, codes for computing the various estimators of the Gini index are provided in Section 5. Box plots to investigate the effect of the skewness on the bias of the estimation of the Gini index can be seen in Section 6. For the various estimators defined in this document, Section 7 provides codes for computing empirical measures related to such estimators. In particular, functions inf.empirical.measures and fin.empirical.measures gives the: (i) Relative Bias (RB); (ii) Relative Root Mean Square Error (RRMSE); (iii) Bias Ratio (BR); (iv) Expected value based on estimates of the Gini index and; (v) Expected value based on estimates of the coefficient of skewness. Some examples are included, and they indicate how to carry out simulation studies. Finally, various estimators of the Gini index are computed using the data set ES-SILC, with size n=26. The various real data sets can be loaded using the file Datasets.RData.