Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data

El-Din, M. M. Mohie; Nagy, M.; Abu‐Moussa, Mahmoud H.

doi:10.1007/s40745-019-00199-3

Cited by 24 publications

(3 citation statements)

References 17 publications

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“…There are a lot of approximation methods to obtain an approximate value for the integration that depend on the posterior distribution as Monte Carlo methods (Kloek and Van Dijk [31] and Zellner and Rossi [32]) and Lindley method [33], which are computationally intensive. For extra studies where the MCMC and Lindley method are used, see, e.g., [34][35][36][37] and [38]. Tierney and Kadane [39] implemented an easily computable integration approximation method that was based on the posterior distribution as the mean and variance of a non-negative parameter or a smooth parameter function that is non-zero within the space of the parameter.…”

Section: Tk-approximation For Bayesian Estimatesmentioning

confidence: 99%

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

et al. 2020

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In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

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Section: Tk-approximation For Bayesian Estimatesmentioning

confidence: 99%

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

et al. 2020

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“…Many authors discussed the GD, for example, Mohie El-Din and Abu-Moussa 7 introduced statistical inference for the GD based on multiply type-I censored data. Also, Mohie El-Din et al 8 an estimation and prediction for the GD using the Generalized hybrid censored data. Wu et al 9 considered the Gompertz competing risks model under progressive Type-I hybrid censored scheme.…”

Section: Introductionmentioning

confidence: 99%

E‐Bayesian estimation for the parameters and hazard function of Gompertz distribution based on progressively type‐II right censoring with application

El-Din

Sharawy

Abu‐Moussa

2023

Quality & Reliability Eng

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E-Bayesian inference is of incremental significance in the area related to the reliability of industrial products dealing with censored data sets. In this article, based on the progressive Type-II right censored order statistics (PTIIRCOS), the E-Bayesian estimates (E-BE) for the parameters of Gompertz distribution (GD) and its hazard function are obtained and compared with the maximum likelihood (MLE) and Bayesian (BE) estimates. The squared error loss function (SE), linear-exponential loss function (LINEX), and Al-Bayyati loss function (ALB) are considered for the methods of BE and E-BE. Some properties for the E-BE estimates are discussed based on PTIIRCOS. Real data is established to clear the theoretical procedures. Akaike information criterion (AIC) is used to prove that GD is the best to model the data compared to other competitors and could potentially be very adequate in describing and modeling industrial products data.Finally, simulation study has been operated for comparing the E-BEs with the MLEs and BEs.

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“…For example, see the works by Wu et al, 33 Mohie El-Din and Abu-Moussa, 34 Mohie El-Din et al, 35 Lv et al, 36 Lone and Panahi, 37 and Al-Essa et al 38 . Many writers have examined the Gompertz distribution.…”

Section: Introductionmentioning

confidence: 99%

Classical and Bayesian estimation for Gompertz distribution under the unified hybrid censored sampling with application

Abo-Kasem,

Abdelgaffar,

Al Mutairi

et al. 2023

AIP Advances

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This study discusses the Gompertz distribution’s statistical inference using unified hybrid censored data. Under various loss functions, the maximum likelihood and Bayesian approaches are explored for estimating the parameters for the Gompertz distribution. To compare the suggested methodologies, the Monte Carlo simulation is used, which also introduces the simulation research. By examining a genuine dataset, the applicability of the presented inference in practice is finally demonstrated.

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Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data

Cited by 24 publications

References 17 publications

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

E‐Bayesian estimation for the parameters and hazard function of Gompertz distribution based on progressively type‐II right censoring with application

Classical and Bayesian estimation for Gompertz distribution under the unified hybrid censored sampling with application

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