E-Bayesian and Hierarchical Bayesian Estimations Based on Dual Generalized Order Statistics from the Inverse Weibull Model

Reyad, Hesham; Younis, Adil Mousa; Othman, Soha

doi:10.9734/jamcs/2017/34540

Cited by 9 publications

(2 citation statements)

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“…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. Yaghoobzadeh Shahrastani [14] computed E-B and HB estimates of Gompertz distribution under the type-II censoring scheme.…”

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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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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“…Han [11] introduced the expected Bayesian (E-Bayesian) estimation method which is very simple and it's a special Bayesian method used in the area related for the life testing of products with high reliability, small sample size or censored data. Many researchers applied the E-Bayesian method to many distributions, such as, Okasha [12], Azimi et al [13], Okasha [14], Reyad and Ahmed [15], Reyad and Ahmed [16], Nasiri and Esfandyarifar [17], Reyad et al [18], EL-Sagheer [19], Shawky and Al-Aboud [20], Reyad et al [21], Reyad and Othman [22], Han [23], Okasha [24], Rabie and Li [25], Algarni et al [26], Han [27], Piriaei et al [28] and Rabie and Li [29].…”

Section: Introductionmentioning

confidence: 99%

Prediction for Modified Topp Leone-Chen Distribution Based on Progressive Type-II Censoring Scheme

AL-Dayian

EL-Helbawy

AL-Sayed

et al. 2021

JAMCS

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Prediction of future events on the basis of the past and present information is a fundamental problem of statistics, arising in many contexts and producing varied solutions. The predictor can be either a point or an interval predictor. This paper focuses on predicting the future observations from the modified Topp-Leone Chen distribution based on progressive Type-II censored scheme. The two-sample prediction is applied to obtain the maximum likelihood, Bayesian and E-Bayesian prediction (point and interval) for future order statistics. The Bayesian and E-Bayesian predictors are considered based on two different loss functions, the balanced squared error loss function; as a symmetric loss function and balanced linear exponential loss function; as an asymmetric loss function. The predictors are obtained based on conjugate gamma prior and uniform hyperprior distributions. A numerical example is provided to illustrate the theoretical results and an application using real data sets are used to demonstrate how the results can be used in practice.

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Properties and estimation approaches of the odd JCA family with applications

Iqbal

Alfaer

Tahir

et al. 2022

Concurrency and Computation

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Summary In this article, we study a new generator of distributions called the odd JCA‐G family. We determine the main mathematical properties of the new family. Some special submodels of the odd JCA‐G family are presented. The special models of the JCA‐G family have tractable densities shapes which possess various kinds of asymmetric, reversed‐J, left‐skewed, right‐skewed, symmetrical shapes. Furthermore, special submodels exhibit flexible hazard rate shapes. Additionally, the parameters of the odd JCA Burr‐XII model are estimated using some classical estimation approaches. The performance and efficiency of these approaches are explored via numerical simulations. The applicability of the odd JCA‐G family is illustrated by fitting two real‐life datasets. The data analysis shows that the odd JCA Burr‐XII model outperforms some well‐known distributions for the selected data.

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E-Bayesian and Hierarchical Bayesian Estimations Based on Dual Generalized Order Statistics from the Inverse Weibull Model

Cited by 9 publications

References 0 publications

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

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

Prediction for Modified Topp Leone-Chen Distribution Based on Progressive Type-II Censoring Scheme

Properties and estimation approaches of the odd JCA family with applications

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