Evaluating the Discrete Generalized Rayleigh Distribution: Statistical Inferences and Applications to Real Data Analysis

Hanan Haj Ahmad (), Dina A. Ramadan and Ehab M. Almetwally ()
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Hanan Haj Ahmad: Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia
Dina A. Ramadan: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt
Ehab M. Almetwally: Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Riyadh, Saudi Arabia

Mathematics, 2024, vol. 12, issue 2, 1-23

Abstract: Various discrete lifetime distributions have been observed in real data analysis. Numerous discrete models have been derived from a continuous distribution using the survival discretization method, owing to its simplicity and appealing formulation. This study focuses on the discrete analog of the newly generalized Rayleigh distribution. Both classical and Bayesian statistical inferences are performed to evaluate the efficacy of the new discrete model, particularly in terms of relative bias, mean square error, and coverage probability. Additionally, the study explores different important submodels and limiting behavior for the new discrete distribution. Various statistical functions have been examined, including moments, stress–strength, mean residual lifetime, mean past time, and order statistics. Finally, two real data examples are employed to evaluate the new discrete model. Simulations and numerical analyses play a pivotal role in facilitating statistical estimation and data modeling. The study concludes that the discrete generalized Rayleigh distribution presents a notably appealing alternative to other competing discrete distributions.

Keywords: generalized Rayleigh; maximum likelihood estimation; Bayes estimation; reliability; simulation analysis; Monte Carlo Markov chain; goodness-of-fit measures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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