On the Generalization and Decomposition of the Bonferroni Index

Elena Barcena-Martin and Jacques Silber

No 51, OPHI Working Papers from Queen Elizabeth House, University of Oxford

Abstract: A simple algorithm is proposed which defines the Bonferroni index as the product of a row vector of individual population shares, a linear mathematical operator called the Bonferroni matrix and a column vector of income shares. This algorithm greatly simplifies the decomposition of the Bonferroni index by income sources or classes and population subgroups. The proposed algorithm also links the Bonferroni index to the concepts of relative deprivation and social welfare and leads to a generalization where the traditional Bonferroni and Gini indices are special cases. The paper ends with an empirical illustration based on EU-SILC data for the year 2008.

Date: 2012-06
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Journal Article: On the generalization and decomposition of the Bonferroni index (2013)
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