Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function

Kamaljit Kaur,Kalpana K Mahajan,Sangeeta Arora

doi:10.1155/2015/964824

Kamaljit Kaur, Kalpana K Mahajan + Show 1 more

Open Access

https://doi.org/10.1155/2015/964824

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Journal: Advances in Statistics	Publication Date: Jan 29, 2015
Citations: 18	License type: CC BY 3.0

Affiliation: Panjab University

Abstract

Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

Highlights

The Pareto distribution is a skewed, heavy-tailed distribution that is used to model the distribution of incomes and other financial variables
Linear Exponential (LINEX) loss function is used for estimating the shape parameter, Gini index, Mean income, and a Poverty measure in the context of Pareto distribution using noninformative priors (Uniform prior and Jeffreys’ prior) and one conjugate prior (Truncated Erlang distribution) along with some assumptions regarding the sampled population
In order to assess the statistical performance of these estimators of shape parameter, Gini index, Mean income, and Poverty measure using LINEX loss function, a simulation study is conduced

Summary

Introduction

The Pareto distribution is a skewed, heavy-tailed distribution that is used to model the distribution of incomes and other financial variables. LINEX loss function is used for estimating the shape parameter, Gini index, Mean income, and a Poverty measure in the context of Pareto distribution using noninformative priors (Uniform prior and Jeffreys’ prior) and one conjugate prior (Truncated Erlang distribution) along with some assumptions regarding the sampled population. Bayesian estimator αof α using uniform prior (17) and posterior density (18), under the assumption of the LINEX loss function In case of Jeffreys’ prior (19) and using posterior density (20), the Bayesian estimators of α, G, M, and P0 under the assumption of the LINEX loss function are obtained as follows: αj

Simulation Study

Conclusion