The Bayesian and Bayesian shrinkage estimators under square error and Al-Bayyati loss functions with right censoring scheme

Hosseini, Seyed Rasuol; Deiri, Einolah; Jamkhaneh, Ezzatallah Baloui

doi:10.1080/03610918.2022.2100906

Cited by 5 publications

(1 citation statement)

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“…In past years, Hosseini et al [19] estimated the scale parameter of a two-parameter exponential distribution using Bayesian and Bayesian shrinkage estimations under the SELF and Al-Bayyati LFs based on right-censored data. Amirzadi et al [20] used maximum likelihood and Bayesian estimations to evaluate the shape parameter of the inverse generalized Weibull distribution and reliability function based on several LFs such as the general entropy, squared log error, weight squared error, and a new loss function (LF).…”

Section: Introductionmentioning

confidence: 99%

Bayesian and E-Bayesian Estimation for the Generalized Rayleigh Distribution under Different Forms of Loss Functions with Real Data Application

Eldemery,

Abd-Elfattah,

Mahfouz

et al. 2023

Journal of Mathematics

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This paper investigates the estimation of an unknown shape parameter of the generalized Rayleigh distribution using Bayesian and expected Bayesian estimation techniques based on type-II censoring data. Subsequently, these estimators are obtained using four different loss functions: the linear exponential loss function, the weighted linear exponential loss function, the compound linear exponential loss function, and the weighted compound linear exponential loss function. The weighted compound linear exponential loss function is a novel suggested loss function generated by combining weights with the compound linear exponential loss function. We use the gamma distribution as a prior distribution. In addition, the expected Bayesian estimator is obtained through three different prior distributions of the hyperparameters. Moreover, depending on the four distinct forms of loss functions, Bayesian and expected Bayesian estimation techniques are performed using Monte Carlo simulations to verify the effectiveness of the suggested loss function and to compare Bayesian and expected Bayesian estimation methods. Furthermore, the simulation results indicate that, depending on the minimum mean squared error, the Bayesian and expected Bayesian estimations corresponding to the weighted compound linear exponential loss function suggested in this paper have significantly better performance compared to other loss functions, and the expected Bayesian estimator also performs better than the Bayesian estimator. Finally, the proposed techniques are demonstrated using a set of real data from the medical field to clarify the applicability of the suggested estimators to real phenomena and to show that the discussed weighted compound linear exponential loss function is efficient and can be applied in a real-life scenario.

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Section: Introductionmentioning

confidence: 99%