Comparison of estimates using censored samples from  Gompertz model: Bayesian, E-Bayesian, hierarchical  Bayesian and empirical Bayesian schemes

Reyad, Hesham; Younis, Adil Mousa; Alkhedir, Amal Alsir

doi:10.14419/ijasp.v4i1.5914

Cited by 4 publications

(3 citation statements)

References 21 publications

(83 reference statements)

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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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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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“…Prakash (2016) discussed about the Bayes prediction bound length under different censoring plans and statistical inference based on a random scheme under progressive Type-II censored data for Gompertz model. Reyad et al (2016) introduced a comparative study for the E-Bayesian criteria with three various Bayesian approaches; Bayesian, hierarchical Bayesian and empirical Bayesian.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Approximation Techniques for Gompertz Distribution

Sultan¹

2019

Bayesian Analysis and Reliability Estimation of Generalized Probability Distributions

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We presented approximate to Bayesian integrals of Gompertz distribution depending upon numerical integration and simulation study and showed how to study posterior distribution by means of simulation study. From the findings of above tables (1, 2, 3, 4) it has been found that the large sample distribution could be improved when prior is taken into account. In all cases (simulated data as well as real life data) normal approximation, T-K approximation, Bayesian estimates under informative priors are better than those under non-informative priors especially the Inverse levy distribution proves to be efficient with minimum posterior standard deviation. Further we accomplish that the posterior standard deviation based on different priors tends to decrease with the increase in sample size. It indicates that the estimators attained are consistent. It can also be detected that the performance of Bayes estimates under informative priors (inverse levy) is better than non-informative prior.

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“…Reyad and Othman [24] constructed the Bayes and E-Bayes approaches for estimating the unknown shape parameter of the Kumaraswamy distribution based on type-ii censored data and by considering squared error, LINEX, Degroot, quadratic. Reyad et al [25] obtained the Bayes, E-bayes, hierarchical Bayes and empirical Bayes estimates of the unknown shape parameter and hazard function of the Gompertz distribution based on type-II censoring and by considering squared error loss, quadratic loss entropy loss and LINEX functions. The main object of this study is to suggested a new modification for the E-Bayes method of estimation to yield a new technique namely quasi-E-Bayes method (or briefly QE-Bayes).…”

Section: Introductionmentioning

confidence: 99%

Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution

Reyad

Younis

Alkhedir

2016

IJASP

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This paper proposes a new modification for the E-Bayesian method of estimation to introduce a new technique namely Quasi E-Bayesian method (or briefly QE-Bayesian). The suggested criteria built in replacing the likelihood function by the quasi likelihood function in the E-Bayesian technique. This study is devoted to evaluate the performance of the new method versus the quasi-Bayesian, quasihierarchical Bayesian and quasi-empirical Bayesian approaches in estimating the scale parameter of the Erlang distribution.

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Comparison of estimates using censored samples from Gompertz model: Bayesian, E-Bayesian, hierarchical Bayesian and empirical Bayesian schemes

Cited by 4 publications

References 21 publications

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

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

Bayesian Approximation Techniques for Gompertz Distribution

Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution

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