A Discrete Exponential Generalized-G Family of Distributions: Properties with Bayesian and Non-Bayesian Estimators to Model Medical, Engineering and Agriculture Data

Mohamed S. Eliwa (), Mahmoud El-Morshedy and Haitham M. Yousof
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Mohamed S. Eliwa: Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
Mahmoud El-Morshedy: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Haitham M. Yousof: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt

Mathematics, 2022, vol. 10, issue 18, 1-29

Abstract: This paper introduces a new flexible probability tool for modeling extreme and zero-inflated count data under different shapes of hazard rates. Many relevant mathematical and statistical properties are derived and analyzed. The new tool can be used to discuss several kinds of data, such as “asymmetric and left skewed”, “asymmetric and right skewed”, “symmetric”, “symmetric and bimodal”, “uniformed”, and “right skewed with a heavy tail”, among other useful shapes. The failure rate of the new class can vary and can take the forms of “increasing-constant”, “constant”, “monotonically dropping”, “bathtub”, “monotonically increasing”, or “J-shaped”. Eight classical estimation techniques—including Cramér–von Mises, ordinary least squares, L-moments, maximum likelihood, Kolmogorov, bootstrapping, and weighted least squares—are considered, described, and applied. Additionally, Bayesian estimation under the squared error loss function is also derived and discussed. Comprehensive comparison between approaches is performed for both simulated and real-life data. Finally, four real datasets are analyzed to prove the flexibility, applicability, and notability of the new class.

Keywords: survival discretization; Gibbs sampler; Metropolis–Hastings technique; L-moment structure; bootstrapping approach; Kolmogorov method; Bayesian analysis; Markov chain Monte Carlo; extreme and zero-inflated count data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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