Reliability Properties of the NDL Family of Discrete Distributions with Its Inference

Mohammed Mohammed Ahmed Almazah, Badr Alnssyan, Abdul Hadi N. Ahmed and Ahmed Z. Afify
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Mohammed Mohammed Ahmed Almazah: Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
Badr Alnssyan: Department of Administrative Sciences and Humanities, Community College, Qassim University, Buraydah 52325, Saudi Arabia
Abdul Hadi N. Ahmed: Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12631, Egypt
Ahmed Z. Afify: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Mathematics, 2021, vol. 9, issue 10, 1-17

Abstract: The natural discrete Lindley (NDL) distribution is an intuitive idea that uses discrete analogs to well-known continuous distributions rather than using any of the published discretization techniques. The NDL is a flexible extension of both the geometric and the negative binomial distributions. In the present article, we further investigate new results of value in the areas of both theoretical and applied reliability. To be specific, several closure properties of the NDL are proved. Among the results, sufficient conditions that maintain the preservation properties under useful partial orderings, convolution, and random sum of random variables are introduced. Eight different methods of estimation, including the maximum likelihood, least squares, weighted least squares, Cramér–von Mises, the maximum product of spacing, Anderson–Darling, right-tail Anderson–Darling, and percentiles, have been used to estimate the parameter of interest. The performance of these estimators has been evaluated through extensive simulation. We have also demonstrated two applications of NDL in modeling real-life problems, including count data. It is worth noting that almost all the methods have resulted in very satisfactory estimates on both simulated and real-world data.

Keywords: discrete Lindley analog; percentiles; estimation; closure reliability properties; partial orders; total positivity; hazard rates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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