E-Bayesian estimation of Burr Type XII model based on adaptive Type-Ⅱ progressive hybrid censored data

Okasha, Hassan M.; Nassar, Mazen; Dobbah, Saeed A.

doi:10.3934/math.2021247

Cited by 12 publications

(10 citation statements)

References 30 publications

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“…where is the domain of c and k such that the prior PDF of ( 9) is decreasing in α and ηBE (c, k) is any Bayesian estimate of η(α). For more details about E-Bayesian, readers may refer to References [15][16][17][18]20,21,28,29].…”

Section: E-bayesian Estimation Of the Reliability Performancesmentioning

confidence: 99%

“…respectively. Using (19), (27) and three priors of (28), the E-Bayesian estimates of R(x) based on SEL can be respectively derived as (34) where F 1:1 (., . ; .)…”

Section: E-bayesian Estimates With Sel Functionmentioning

confidence: 99%

“…Replacing ηBE in ( 27) by ( 21), (22), or (23) and using three priors of (28), the E-Bayesian estimates of α, R(x) and h(x) using LINEX loss are addressed below.…”

Section: E-bayesian Estimates With Linex Loss Functionmentioning

confidence: 99%

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On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme

2021

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Bayesian estimates involve the selection of hyper-parameters in the prior distribution. To deal with this issue, the empirical Bayesian and E-Bayesian estimates may be used to overcome this problem. The first one uses the maximum likelihood estimate (MLE) procedure to decide the hyper-parameters; while the second one uses the expectation of the Bayesian estimate taken over the joint prior distribution of the hyper-parameters. This study focuses on establishing the E-Bayesian estimates for the Lomax distribution shape parameter functions by utilizing the Gamma prior of the unknown shape parameter along with three distinctive joint priors of Gamma hyper-parameters based on the square error as well as two asymmetric loss functions. These two asymmetric loss functions include a general entropy and LINEX loss functions. To investigate the effect of the hyper-parameters’ selections, mathematical propositions have been derived for the E-Bayesian estimates of the three shape functions that comprise the identity, reliability and hazard rate functions. Monte Carlo simulation has been performed to compare nine E-Bayesian, three empirical Bayesian and Bayesian estimates and MLEs for any aforementioned functions. Additionally, one simulated and two real data sets from industry life test and medical study are applied for the illustrative purpose. Concluding notes are provided at the end.

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Section: E-bayesian Estimation Of the Reliability Performancesmentioning

confidence: 99%

“…respectively. Using (19), (27) and three priors of (28), the E-Bayesian estimates of R(x) based on SEL can be respectively derived as (34) where F 1:1 (., . ; .)…”

Section: E-bayesian Estimates With Sel Functionmentioning

confidence: 99%

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On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme

2021

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“…Literature [2] divided the censored measurement into five categories, and focused on the state estimation of the first category. Research on estimation problem of censored system has been widely applied in many fields, such as biological modeling, economics, fault diagnosis, control theory [3][4][5][6][7][8][9][10]. Previous studies on the estimation for censored system mainly focused on the parameter estimation of the measurement equation, such as maximum likelihood estimation approach [1], two-step estimation approach [5], Bayesian estimation approach [6], etc.…”

Section: Introductionmentioning

confidence: 99%

“…Research on estimation problem of censored system has been widely applied in many fields, such as biological modeling, economics, fault diagnosis, control theory [3][4][5][6][7][8][9][10]. Previous studies on the estimation for censored system mainly focused on the parameter estimation of the measurement equation, such as maximum likelihood estimation approach [1], two-step estimation approach [5], Bayesian estimation approach [6], etc. In recent years, in order to solve the state estimation problem for the first-class model, researchers have proposed many methods, such as Tobit Kalman filter approach [7][8][9], strong tracking Tobit Kalman filter approach [10], robust recursive filter approach [11], and so on.…”

Section: Introductionmentioning

confidence: 99%

State estimation for censored system with colored noises: system reconstruction approach

Zhao

Shang

2022

J. Phys.: Conf. Ser.

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A state estimation approach based on system reconstruction for a class of discrete-time linear censored systems with colored noises is proposed. Firstly, the censored system is re-modeled by compensating the censored measurement and adding the weight factor. Then, avoiding the traditional state expansion approach, and according to the random property of adjacent correlation colored noises and projective theory, the innovation variance, prediction gain and prediction error variance with recursive structure are obtained, and the state one-step predictor is given. Finally, a numerical example is applied to verify the feasibility of the proposed method.

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Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models

Elshahhat

Nassar

2023

Stat Papers

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Recently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures.

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E-Bayesian estimation of Burr Type XII model based on adaptive Type-Ⅱ progressive hybrid censored data

Cited by 12 publications

References 30 publications

On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme

On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme

State estimation for censored system with colored noises: system reconstruction approach

Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models

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