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Article

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

1
Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
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Department of Mathematics and Computer, College of Sciences, Ibb University, Ibb 70270, Yemen
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Department of Administrative Sciences and Humanities, Community College, Qassim University, Buraydah 52325, Saudi Arabia
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Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12631, Egypt
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Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
*
Author to whom correspondence should be addressed.
Academic Editor: Vasile Preda
Mathematics 2021, 9(10), 1139; https://doi.org/10.3390/math9101139
Received: 25 March 2021 / Revised: 26 April 2021 / Accepted: 6 May 2021 / Published: 18 May 2021
(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)
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. View Full-Text
Keywords: discrete Lindley analog; percentiles; estimation; closure reliability properties; partial orders; total positivity; hazard rates discrete Lindley analog; percentiles; estimation; closure reliability properties; partial orders; total positivity; hazard rates
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MDPI and ACS Style

Almazah, M.M.A.; Alnssyan, B.; Ahmed, A.H.N.; Afify, A.Z. Reliability Properties of the NDL Family of Discrete Distributions with Its Inference. Mathematics 2021, 9, 1139. https://doi.org/10.3390/math9101139

AMA Style

Almazah MMA, Alnssyan B, Ahmed AHN, Afify AZ. Reliability Properties of the NDL Family of Discrete Distributions with Its Inference. Mathematics. 2021; 9(10):1139. https://doi.org/10.3390/math9101139

Chicago/Turabian Style

Almazah, Mohammed M.A., Badr Alnssyan, Abdul H.N. Ahmed, and Ahmed Z. Afify. 2021. "Reliability Properties of the NDL Family of Discrete Distributions with Its Inference" Mathematics 9, no. 10: 1139. https://doi.org/10.3390/math9101139

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