Noninformative priors for Pareto distribution

Abstract

Abstract In this paper, we develop noninformative priors for two parameter Pareto distri-bution. Specially, we derive Je reys’ prior, probability matching prior and referenceprior for the parameter of interest. In our case, the probability matching prior is onlya rst order matching prior and there does not exist a second order matching prior. Some simulation reveals that the matching prior performs better to achieve the coverageprobability. A real example is also considered.Keywords: Je reys’ prior, Pareto distribution, probability matching prior, referenceprior. 1. Introduction The Pareto distribution has found applications in modeling problems involving distribu-tions of income when incomes exceed a certain limit.Many socio-economic and other naturally occurring quantities are distributed accordingto certain statistical distributions with very long right tails. Examples of some of theseempirical phenomena are distributions of city population sizes, occurrence of natural re-sources, stock price uctuations, size of rms, personal incomes, and error clustering incommunication circuits.Many distributions have been developed in an attempt to model such real life data. ThePareto and lognormal distributions have played a major part in these investigations. It hasbeen observed that while the t of the Pareto curve may be rather good at the extremities ofthe income range, the t over the whole range is often rather poor. On the other hand, thelognormal distribution ts well over a larger part of the income range but diverges markedlyat the extremities.For economists concerned with upper tails of distributions, the Pareto distribution isprobably more useful than the lognormal which generally gives poor t in the tails.