A New One-Parameter Distribution for Right Censored Bayesian and Non-Bayesian Distributional Validation under Various Estimation Methods

Walid Emam, Yusra Tashkandy, Hafida Goual, Talhi Hamida, Aiachi Hiba, M. Masoom Ali, Haitham M. Yousof () and Mohamed Ibrahim
Additional contact information
Walid Emam: Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Yusra Tashkandy: Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Hafida Goual: Department of Mathematics, Laboratory of Probability and Statistics LaPS, Badji Mokhtar Annaba University, Annaba 23000, Algeria
Talhi Hamida: Department of Mathematics, Laboratory of Probability and Statistics LaPS, Badji Mokhtar Annaba University, Annaba 23000, Algeria
Aiachi Hiba: Department of Mathematics, Laboratory of Probability and Statistics LaPS, Badji Mokhtar Annaba University, Annaba 23000, Algeria
M. Masoom Ali: Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA
Haitham M. Yousof: Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Benha University, Benha 13518, Egypt
Mohamed Ibrahim: Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta 34517, Egypt

Mathematics, 2023, vol. 11, issue 4, 1-21

Abstract: We propose a new extension of the exponential distribution for right censored Bayesian and non-Bayesian distributional validation. The parameter of the new distribution is estimated using several conventional methods, including the Bayesian method. The likelihood estimates and the Bayesian estimates are compared using Pitman’s closeness criteria. The Bayesian estimators are derived using three loss functions: the extended quadratic, the Linex, and the entropy functions. Through simulated experiments, all the estimating approaches offered have been assessed. The censored maximum likelihood method and the Bayesian approach are compared using the BB algorithm. The development of the Nikulin–Rao–Robson statistic for the new model in the uncensored situation is thoroughly discussed with the aid of two applications and a simulation exercise. For the novel model under the censored condition, two applications and the derivation of the Bagdonavičius and Nikulin statistic are also described.

Keywords: Bagdonavičius and Nikulin statistic; Bayesian estimation; BB method; censored applications; lomax model; Nikulin–Rao–Robson; Pitman’s proximity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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