Comparison of estimation methods for the parameters of the weighted Lindley distribution J. Mazucheli a , F. Louzada b , M.E. Ghitany c,⇑ a Universidade Estadual de Maringá, DEs, PR, Brazil b Universidade de São Paulo, ICMC, SP, Brazil c Department of Statistics & O.R., Faculty of Science, Kuwait University, Kuwait article info Keywords: Weighted Lindley distribution Maximum likelihood Method of moments Ordinary least-squares Weighted least-squares abstract The aim of this paper is to compare through Monte Carlo simulations the finite sample properties of the estimates of the parameters of the weighted Lindley distribution obtained by four estimation methods: maximum likelihood, method of moments, ordinary least- squares, and weighted least-squares. The bias and mean-squared error are used as the cri- terion for comparison. The study reveals that the ordinary and weighted least-squares esti- mation methods are highly competitive with the maximum likelihood method in small and large samples. Statistical analysis of two real data sets are presented to demonstrate the conclusion of the simulation results. Ó 2013 Elsevier Inc. All rights reserved. 1. Introduction The Lindley distribution was introduced by Lindley [7], see also [8], in the context of fiducial distributions and Bayes’ the- orem. Its probability density function (p.d.f.) is given by f 1 ðxjaÞ¼ a 2 a þ 1 ð1 þ xÞ e ax ; x > 0; a > 0: ð1Þ The corresponding cumulative distribution function (c.d.f.) and hazard rate function (h.r.f.), respectively, are given by F 1 ðxjaÞ¼ 1  1 þ ax a þ 1   e ax ; x > 0; a > 0; ð2Þ and h 1 ðxjaÞ¼ a 2 ð1 þ xÞ að1 þ xÞþ 1 ; x > 0; a > 0: ð3Þ Note that h 1 ðxjaÞ is an increasing function in x, for all a > 0. Ghitany et al. [5] studied many statistical properties of the Lindley distribution from the reliability/survival analysis point of view. They also showed, using a real data set, that the Lindley distribution provides a better fit than the exponential distribution. Application of the Lindley distribution in the competing risks analysis and in stress-strength reliability studies are con- sidered by Mazucheli and Achcar [9] and Al-Mutairi et al. [1], respectively. 0096-3003/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.amc.2013.05.082 ⇑ Corresponding author. E-mail address: meghitany@yahoo.com (M.E. Ghitany). Applied Mathematics and Computation 220 (2013) 463–471 Contents lists available at SciVerse ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc