Statistical Methods

Statistical Methods and Applications

, Volume 10, Issue 1, pp 41-48

Bayesian estimation of the Bonferroni index from a Pareto-type I population

  • G. M. GiorgiAffiliated withDipartimento di Statistica, Probabilità e Statistiche Applicate, Università “La Sapienza”
  • , M. CrescenziAffiliated withDipartimento di Statistica, Probabilità e Statistiche Applicate, Università “La Sapienza”

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Summary

The Bonferroni index (B) is a measure of income and wealth inequality, and it is particularly suitable for poverty studies. Since most income surveys are of a sample nature, we propose Bayes estimators ofB from a Pareto/I population. The Bayesian estimators are obtained assuming a squared error loss function and, as prior distributions, the truncated Erlang density and the translated exponential one. Two different procedures are developed for a censored sample and for income data grouped in classes.

Key words

Bonferroni inequality index Bayes estimator Pareto/I distribution truncated Erlang distribution translated exponential distribution squared error loss function