E-Bayesian Estimation for Burr-X Distribution Based on Generalized Type-I Hybrid Censoring Scheme

Rabie, Abdalla; Li, Junping

doi:10.1080/01966324.2019.1579123

Cited by 17 publications

(11 citation statements)

References 11 publications

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“…where D stands for the set of possible values of a and b,θ B andR (t) B are the Bayesian estimates of θ and R(t), respectively, under the SEL and the LINEX loss functions. See, for more details, [15][16][17][18].…”

Section: E-bayesian Estimation Methodsmentioning

confidence: 99%

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E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

Rabie

2019

Symmetry

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In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods.Generalized Type-II HCS: Fix r ∈ {1, 2, · · · , n} and T 1 ,The experiment is terminated at T 1 , if r-th failure occurs before T 1 . When the r-th failure occurs between T 1 and T 2 , we terminate at Y r:n . In the third case, if r-th failure is observed after time T 2 , the experiment is terminated at T 2 . This scheme has been studied by many authors, such as [3], who presented details on censoring scheme developments in addition to generalized and unified HCS. Ref. [4] discussed Bayesian analysis and prediction based on generalized Type-II HCS for exponential and Pareto models. Ref.[5] studied maximum likelihood, Bayes and percentile bootstrap methods for unknown parameters, failure rate function, the survival function and the coefficient of variation of the exponential Rayleigh distribution with generalized Type-II HCS.Here, generalized Type-II HCS is considered. We observe one of these types of the censored data. Case 1:In this case, the r-th failure is obtained before T 1 , so the experiment is stopped at T 1 and d 1 number of failures is obtained at time T 1 .Case 2:In this case, the r-th failure occurs after T 1 , so the experiment is terminated at Y r:n , and r number of failures is obtained.Case 3:In this case, the r-th failure occurs after T 2 , so the experiment is ended at T 2 and d 2 number of failures is obtained at time T 2 . where T 1 and T 2 are time points determined by the experimenter according to how the experiment should continue based on the information about the product. Burr-X as a Lifetime ModelBurr-X model is part of Burr distribution family suggested by [6]. This distribution is important in many fields such as operations research and statistics. It is widely used in health, agriculture, and biology. For more details on the applications of this model, one can refer to [7], as they discussed the cumulative distribution function (CDF) of Burr-X distribution with the cumulative damage process and the shock model. Also, they assumed a mathematical model for the expected lifetime of AIDS patients, then fitted the observed data of infected persons for Burr-X distribution. The probability density function (PDF) of one-parameter...

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Section: E-bayesian Estimation Methodsmentioning

confidence: 99%

“…Ref. [12] discussed E-Bayesian method and ML and Bayesian methods for the parameter and the reliability function of the Burr-X model under Type-I HCS.…”

Section: Introductionmentioning

confidence: 99%

E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

Rabie

2019

Symmetry

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“…e generalized Type-I HCS has been used to study a variety of distribution functions. For example, Rabie and Li [1] presented the concept of hybrid censoring and studied the E-Bayesian estimation for Burr-X distribution.…”

Section: Hybrid Censoring Scheme (Hcs)mentioning

confidence: 99%

The E-Bayesian Estimation for Lomax Distribution Based on Generalized Type-I Hybrid Censoring Scheme

Liu

Zhang

2021

Mathematical Problems in Engineering

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This article studies the E-Bayesian estimation of the unknown parameter of Lomax distribution based on generalized Type-I hybrid censoring. Under square error loss and LINEX loss functions, we get the E-Bayesian estimation and compare its effectiveness with Bayesian estimation. To measure the error of E-Bayesian estimation, the expectation of mean square error (E-MSE) is introduced. With Markov chain Monte Carlo technology, E-Bayesian estimations are computed. Metropolis–Hastings algorithm is applied within the process. Similarly, the credible interval for the parameter is calculated. Then, we can compare the MSE and E-MSE to evaluate whose result is more effective. For the purpose of illustration in real datasets, cases of generalized Type-I hybrid censored samples are presented. In order to judge whether the sample data can be directly fitted by the Lomax distribution, we adopt the Kolmogorov–Smirnov tests for evaluation. Finally, we can get the conclusion after comparing the results of E-Bayesian and Bayesian estimation.

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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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E-Bayesian Estimation for Burr-X Distribution Based on Generalized Type-I Hybrid Censoring Scheme

Cited by 17 publications

References 11 publications

E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

The E-Bayesian Estimation for Lomax Distribution Based on Generalized Type-I Hybrid Censoring Scheme

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

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