E-Bayesian and Hierarchical Bayesian Estimations for the Inverse Weibull Distribution

Basheer, Abdulkareem M.; Okasha, Hassan M.; El-Baz, A. H.; Tarabia, A. M. K.

doi:10.1007/s40745-020-00320-x

Cited by 7 publications

(3 citation statements)

References 21 publications

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“…The expected-Bayesian (E-Bayesian) estimation was firstly proposed by Han [39], and has attracted wide attention and been discussed by many authors. See, for example, some recent works of Basheer et al [40], Okasha and Wang [41], among others.…”

Section: E-bayesian Estimationmentioning

confidence: 99%

Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations

2022

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In this paper, a competing risks model with dependent causes of failure is considered under left-truncated and right-censoring scenario. When the dependent failure causes follow a Marshall–Olkin bivariate exponential distribution, estimation of model parameters and reliability indices are proposed from classic and Bayesian approaches, respectively. Maximum likelihood estimators and approximate confidence intervals are constructed, and conventional Bayesian point and interval estimations are discussed as well. In addition, E-Bayesian estimators are proposed and their asymptotic behaviors have been investigated. Further, another objective-Bayesian analysis is also proposed when a noninformative probability matching prior is used. Finally, extensive simulation studies are carried out to investigate the performance of different methods. Two real data examples are presented to illustrate the applicability.

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Section: E-bayesian Estimationmentioning

confidence: 99%

Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations

2022

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“…Athirakrishnan and Abdul-Sathar [11] computed E-B and HB estimations to estimate the parameter of inverse Rayleigh distribution. Basheer et al [12] derived E-B and HB estimates of inverse Weibull distribution. Reyad et al [13] analyzed E-B and HB methods to estimate the parameter of inverse Weibull distribution on the basis of dual generalized order statistics.…”

Section: Introductionmentioning

confidence: 99%

E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces

et al. 2023

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In this study, we use the idea of the hierarchical model (HM) to estimate an unknown parameter of the hierarchical Poisson-Gamma model using the E-Bayesian (E-B) theory. We propose the idea of hierarchical probability function instead of the traditional hierarchical prior density function. We aim to infer E-B estimates with respect to the conjugate Gamma prior distribution along with the E-posterior risks on the basis of different symmetric and asymmetric loss functions (LFs) under restricted and unrestricted parameter spaces using uniform hyperprior. Whereas, E-B estimators are compared with maximum likelihood estimators (MLEs) using mean squared error (MSE). Monte Carlo simulations are prosecuted to study the efficiency of E-B estimators empirically. It is shown that the LFs under a restricted parameter space dominate to estimate the parameter of the hierarchical Poisson-Gamma model. It is also found that the E-B estimators are more precise than MLEs, and Stein’s LF has the least E-PR. Moreover, the application of outcomes to a real-life example has been made for analysis, comparison, and motivation.

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“…Iqbal and Yousuf Shad [12] used the E-Bayesian technique to estimate the parameters of the inverse gamma distribution. Basheer et al [13] presented hierarchical and E-Bayesian estimations for the inverse Weibull model and concluded that the E-Bayesian was better than the other compared methods. Nassar et al [14] used the E-Bayesian and Bayesian estimation approaches to estimate the generalized inverted exponential distribution parameters under type-II censored data.…”

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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E-Bayesian and Hierarchical Bayesian Estimations for the Inverse Weibull Distribution

Cited by 7 publications

References 21 publications

Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations

Reliability Estimation for Dependent Left-Truncated and Right-Censored Competing Risks Data with Illustrations

E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces

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

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