Comparisons of Methods of Estimation for a New Pareto-type Distribution

Abstract

Bourguignon et al. (2016) introduced a new Pareto-type distribution to model income and reliability data. The aim of this paper is to estimate the parameters of this distribution from both frequentist and Bayesian view points. The maximum likelihood estimates, method of moment estimates, percentile estimates, least square and weighted least square estimates and maximum product of spacing estimates are considered as frequentist estimates. We have also considered the Bayes estimates of the unknown parameters and the associated credible intervals. The Bayes estimates are computed using an importance sampling method. To evaluate the performance of the different estimates, a Monte Carlo simulation study is carried out. Some real life data sets have been analyzed for illustrative purposes.

Keywords

• bayesian estimates
• least squares estimates
• maximum likelihood estimates
• method of moment estimates
• monte carlo simulation
• percentiles estimates
• weighted least squares estimates