Bonferroni and Gini indices for various parametric families of distributions

Abstract

The Bonferroni index (BI) and Bonferroni curve (BC) have assumed relief not only in economics to study income and poverty, but also in other fields like reliability, demography, insurance and medicine. Besides, the increasingly frequent comparison with the Lorenz curve (LC) and Gini index (GI) both in theoretical and applied studies has driven us to derive explicit expressions for BI, BC, GI and LC for some thirty five continuous distributions. It is expected that these expressions could provide a useful reference and encourage further research within the aforementioned fields

From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective

“…In addition to its role when studying income and poverty, the Bonferroni function B F (p) has also found many uses in other fields such as reliability, demography, insurance, and medicine (e.g., Giorgi and Crescenzi 2001;and references wherein). For detailed historical notes and references with explicit expressions of the Lorenz and Bonferroni functions, as well as of the Gini and Bonferroni indices, for many parametric distributions, we refer to Giorgi and Nadarajah (2010). The role of the Bonferroni function within the framework of L-functions for measuring economic inequality and actuarial risks can be found in Tarsitano (2004), and Greselin et al (2009).…”

Measuring Economic Inequality and Risk: A Unifying Approach Based on Personal Gambles, Societal Preferences and References

“…Giorgi & Crescenzi, 2001; and references wherein). For detailed historical notes and references with explicit expressions for the Lorenz and Bonferroni functions, as well as for the Gini and Bonferroni indices, in the case of a great many parametric distributions, we refer to Giorgi & Nadarajah (2010). The role of the Bonferroni function within the framework of L-functions for measuring economic inequality and actuarial risks can be found in Tarsitano (2004), and Greselin et al (2009).…”

Histogram-Based Interpolation of the Lorenz Curve and Gini Index for Grouped Data

“…In this case, the Lorenz curve would be 0 and jump to 1 at α = 1. If X follows a known parametric distribution, the Lorenz curve and the Gini index can be derived as functions of these parameters (for a review, see Sarabia 2008;Giorgi and Nadarajah 2010). For example,…”

“…A review of expressions of the Lorenz curve and the Gini index for a variety of parametric distributions can be found in Giorgi and Nadarajah (2010). Income distributions, however, seem to have modeling-resistant distributions.…”