Article

Statistical Papers

, Volume 40, Issue 3, pp 247-262

Bayesian estimation for the Pareto income distribution

  • Samir K. BhattacharyaAffiliated withDepartment of Mathematics and Statistics, University of Allahabad
  • , Anoop ChaturvediAffiliated withDepartment of Mathematics and Statistics, University of Allahabad
  • , Nand Kishore SinghAffiliated withDepartment of Mathematics and Statistics, University of Allahabad

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Abstract

The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function. This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized for the doubly truncated gamma prior distribution.

Key words

Bayes estimator Bayesian posterior density (BPD) Doubly Truncated Gamma prior distribution Gini Index (GI) Hyperparameter assessment Likelihood function (LF) Pareto income distribution (PID) Poverty Line (PL) Squared error loss function (SELF)