On E-Bayesian analysis of the hierarchical normal and inverse gamma model using different loss functions and its application

Iqbal, Azeem; Shad, Muhammad Yousaf

doi:10.1080/00949655.2022.2152450

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…In the context of Bayesian estimation, Han [ 30 ] was motivated to suggest the E-Bayesian estimation approach, which treats the hyperparameters as random variables with probabilistic models in response to the challenge of identifying their values. Many studies considered the E-Bayesian methodology; see, for example, Jaheen and Okasha [ 31 ], Okasha [ 32 ], Algarni et al [ 33 ], Han [ 34 ], and Iqbal and Yousuf [ 35 ], among others. It is evident that all studies that took into account the E-Bayesian estimation approach used the LF as the source of observed data to derive the posterior distribution of the parameters vector.…”

Section: Introductionmentioning

confidence: 99%

E‐Bayesian Estimation Using Spacing Function for Inverse Lindley Adaptive Type‐I Progressively Censored Samples: Comparative Study with Applications

Nassar,

Alotaibi,

Elshahhat

2024

Applied Bionics and Biomechanics

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For the first time, this paper offers the Bayesian and E‐Bayesian estimation methods using the spacing function (SF) instead of the classical likelihood function. The inverse Lindley distribution, including its parameter and reliability measures, is discussed in this study through the mentioned methods, along with some other classical approaches. Six‐point and six‐interval estimations based on an adaptive Type‐I progressively censored sample are considered. The likelihood and product of spacing methods are used in classical inferential setups. The approximate confidence intervals are discussed using both classical approaches. For various parameters, the Bayesian methodology is studied by taking both likelihood and SFs as observed data sources to derive the posterior distributions. Moreover, the E‐Bayesian estimation method is considered by using the same data sources in the usual Bayesian approach. The Bayes and E‐Bayes credible intervals using both likelihood and SFs are also taken into consideration. Several Monte Carlo experiments are carried out to assess the performance of the acquired estimators, depending on different accuracy criteria and experimental scenarios. Finally, two data sets from the engineering and physics sectors are analyzed to demonstrate the superiority and practicality of the suggested approaches.

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Section: Introductionmentioning

confidence: 99%

E‐Bayesian Estimation Using Spacing Function for Inverse Lindley Adaptive Type‐I Progressively Censored Samples: Comparative Study with Applications

Nassar,

Alotaibi,

Elshahhat

2024

Applied Bionics and Biomechanics

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“…Han [8] proposed E-B and HB methods to estimate failure rate using exponential distribution. Iqbal and Yousuf Shad [9] derived E-Bayesian estimates of the hierarchical normal and inverse gamma model under diferent LFs. Han [10] evaluated E-B and HB estimates of binomial distribution under three distinct hyperpriors.…”

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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“…Based on diferent loss functions (LFs) such as SELF, ELF, and LINEXLF, Wang et al [11] used E-Bayesian and Bayesian estimation for a simple step-stress model under progressively Type-II censoring. 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.…”

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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On E-Bayesian analysis of the hierarchical normal and inverse gamma model using different loss functions and its application

Cited by 4 publications

References 22 publications

E‐Bayesian Estimation Using Spacing Function for Inverse Lindley Adaptive Type‐I Progressively Censored Samples: Comparative Study with Applications

E‐Bayesian Estimation Using Spacing Function for Inverse Lindley Adaptive Type‐I Progressively Censored Samples: Comparative Study with Applications

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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