Abstract

The Pareto distribution is a commonly used model for heavy tailed data. Pareto distribution is a useful modeling and predicting tool in a wide variety of socioeconomic contexts. In the present study, we model heterogeneous population by using two component mixture model and two parameter Pareto mixture is considered for this purpose. The expressions for Bayes estimators and their posterior risks (using squared error loss function and weighted loss function) are derived. System of non-linear equations that lead to obtain estimate for MLE’s along with component of Fisher information matrix, are also constructed. An extensive simulation at different parameter points using probabilistic mixing is carried out to get censored simulated data. These data are then used to obtain Bayes estimates for parameters of the Pareto mixture and their respective posterior risks. Bayes estimates are obtained by non-informative as well as informative prior. Posterior predictive distribution and predictive intervals are derived using Gamma prior to obtain hyper-parameters. Finally, Pareto mixture is fitted to a real data example which includes estimation and testing of parameters.

Key words: Heavy tailed data, probabilistic mixing, predictive intervals, informative prior, hyper-parameters.