The Lindley-Lindley Distribution: Characterizations, Copula, Properties, Bayesian and Non-Bayesian Estimation
Subject Areas : International Journal of Mathematical Modelling & ComputationsChristophe Chesneau 1 , Haitham Yousof 2 , G. Hamedani 3 , Mohamed Ibrahim 4
1 - Department of Mathematics, LMNO, University of Caen, France
2 - Department of Statistics,Mathematics and Insurance,
Benha University, Benha, Egypt
3 - Department of Mathematics, Statistics and
Computer Science, Marquette University, USA
4 - Department of Applied Statistics and Insurance,
Faculty of Commerce, Damietta University, Damietta, Egypt
Keywords: COPULA, Bayesian Estimation, Different Methods of Estimations, Markov chain Monte Carlo Simulations, Cramer-Von-Mises, Lindley Distribution, characterizations,
Abstract :
A new continuous distribution called Lindley-Lindley distribution is defined and studied. Relevant mathematical properties are derived. We present three characterizations of the new distribution based on the truncated moments of certain functions of the random variable; the hazard function and in terms of the conditional expectation of afunction of the random variable. Some new bivariate type distributions using Farlie Gumbel Morgenstern copula, modified Farlie Gumbel Morgenstern copula and Clayton copula are introduced. The main justification of this paper is to show how different frequentist estimators of the new model perform for different sample sizes and different parametervalues and to provide a guideline for choosing the best estimation method for the parameters of the proposed model. The unknown parameters of the new distribution are estimated using the maximum likelihood, ordinary least squares, Cramer-Von-Mises, weighted least squares and Bayesian methods. The obtained estimators are compared using Markov Chain Monte Carlo simulations and observed that Bayesian estimators are generally more efficient than the other estimators.