The Lindley-Lindley Distribution: Characterizations, Copula, Properties, Bayesian and Non-Bayesian Estimation

International Journal of Mathematical Modelling & Computations

مقاله 3، دوره 11، 1 (WINTER) - شماره پیاپی 41، خرداد 2021، صفحه 29-47   

نوع مقاله: Full Length Article

شناسه دیجیتال (DOI): 10.30495/ijm2c.2021.681361

نویسندگان

Christophe Chesneau^{* 1}؛ Haitham M. Yousof²؛ G. G. Hamedani³؛ Mohamed Ibrahim⁴

¹Department of Mathematics, LMNO, University of Caen, France

²Department of Statistics,Mathematics and Insurance, Benha University, Benha, Egypt

³Department of Mathematics, Statistics and Computer Science, Marquette University, USA

⁴Department of Applied Statistics and Insurance, Faculty of Commerce, Damietta University, Damietta, Egypt

چکیده

‎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 a‎
‎function 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 parameter‎
‎values 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.

کلیدواژه‌ها

Different methods of estimations؛ Markov chain Monte Carlo simulations؛ Bayesian estimation؛ Cramer-Von-Mises؛ Lindley distribution؛ Copula؛ Characterizations