Bayes estimation of Lorenz curve and Gini-index for power function distribution

E. I. Abdul-Sathar; K. R. Renjini; G. Rajesh; E. S. Jeevanand

E. I. Abdul-Sathar Department of Statistics, University of Kerala, Thiruvananthapuram - 695 581, India
K. R. Renjini Department of Statistics, University of Kerala, Thiruvananthapuram - 695 581, India
G. Rajesh Department of Statistics, DB College, Parumala - 689 626, India
E. S. Jeevanand Department of Mathematics and Statistics, Union Christian College, Aluva - 683 102, India

Keywords: Bayes estimators, Squared error loss function, Weighted squared error loss function, Lorenz curve, Gini-index, Bias-corrected MLE

Abstract

In this article, we estimate the shape parameter, Lorenz curve and Gini-index for 3power function distributions using a Bayesian method. Bayes estimators have been developed under squared error loss function as well as under weighted squared error loss function. We demonstrate the use of the proposed estimation procedure with the U. S. average income data for the period 1913-2010. Our proposed Bayesian estimators are compared using a Monte Carlo simulation study with the ML estimators proposed by Belzunce, Candel and Ruiz (1998).

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