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Mathematical Problems in Engineering
Volume 2016, Article ID 7946828, 13 pages
http://dx.doi.org/10.1155/2016/7946828
Research Article

Parameter Estimation and Joint Confidence Regions for the Parameters of the Generalized Lindley Distribution

Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

Received 23 October 2015; Accepted 28 December 2015

Academic Editor: Vladimir Turetsky

Copyright © 2016 Wenhao Gui and Man Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We deal with the problem of estimating the parameters of the generalized Lindley distribution. Besides the classical estimator, inverse moment and modified inverse estimators are proposed and their properties are investigated. A condition for the existence and uniqueness of the inverse moment and modified inverse estimators of the parameters is established. Monte Carlo simulations are conducted to compare the estimators’ performances. Two methods for constructing joint confidence regions for the two parameters are also proposed and their performances are discussed. A real example is presented to illustrate the proposed methods.