Bayesian  Estimation for Two Parameters of Gamma Distribution Under Precautionary Loss Function

Naji, Loaiy F.; Rasheed, Huda A.

doi:10.30526/32.1.1914

Cited by 9 publications

(8 citation statements)

References 3 publications

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“…The results in this study were similar to those of Srivastava [7] in that the Bayesian point estimation method under the squared-error loss function provided estimates nearer to the true value of the Poisson parameter. Besides, the Bayesian estimators under different loss functions performed better than the classical estimator (MLE) in the case of small and different values of the hyperparameters, which is similar to the findings of Hassan and Baizid [12] and Naji and Rasheed who found that Bayesian estimate parameters under precautionary [15], generalized weighted [14] or entropy [16] loss functions were the better than the classical approaches of MLE and the method of moments.…”

Section: -Discussionsupporting

confidence: 85%

Bayesian Approaches for Poisson Distribution Parameter Estimation

Supharakonsakun

2021

Emerg Sci J

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The Bayesian approach, a non-classical estimation technique, is very widely used in statistical inference for real world situations. The parameter is considered to be a random variable, and knowledge of the prior distribution is used to update the parameter estimation. Herein, two Bayesian approaches for Poisson parameter estimation by deriving the posterior distribution under the squared error loss or quadratic loss functions are proposed. Their performances were compared with frequentist (maximum likelihood estimator) and Empirical Bayes approaches through Monte Carlo simulations. The mean square error was used as the test criterion for comparing the methods for point estimation; the smallest value indicates the best performing method with the estimated parameter value closest to the true parameter value. Coverage Probabilities (CPs) and average lengths (ALs) were obtained to evaluate the performances of the methods for constructing confidence intervals. The results reveal that the Bayesian approaches were excellent for point estimation when the true parameter value was small (0.5, 1 and 2). In the credible interval comparison, these methods obtained CP values close to the nominal 0.95 confidence level and the smallest ALs for large sample sizes (50 and 100), when the true parameter value was small (0.5, 1 and 2). Doi: 10.28991/esj-2021-01310 Full Text: PDF

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Section: -Discussionsupporting

confidence: 85%

Bayesian Approaches for Poisson Distribution Parameter Estimation

Supharakonsakun

2021

Emerg Sci J

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“…In general, α, β can be estimated by the maximum likelihood function, which can refer to Ref. [117]. The Gamma process is a monotone and stable process, so it is very suitable to establish the degradation process.…”

Section: Gammamentioning

confidence: 99%

Digital Twin-Driven Remaining Useful Life Prediction for Gear Performance Degradation: A Review

Liu

Dong

2021

Journal of Computing and Information Science in Engineering

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As a transmission component, the gear has been obtained widespread attention. The remaining useful life (RUL) prediction of gear is critical to the prognostics health management (PHM) of gear transmission systems. The digital twin (DT) provides support for gear RUL prediction with the advantages of rich health information data and accurate health indicators (HI). This paper reviews digital twin-driven RUL prediction methods for gear performance degradation, from the view of digital twin-driven physical model-based and virtual model-based prediction method. From the view of physical model-based one, it includes prediction model based on gear crack, gear fatigue, gear surface scratch, gear tooth breakage, and gear permanent deformation. From the view of digital twin-driven virtual model-based one, it includes non-deep learning methods, and deep learning methods. Non-deep learning methods include wiener process, gamma process, hidden Markov model (HMM), regression-based model, proportional hazard model. Deep learning methods include deep neural networks (DNN), deep belief networks (DBN), convolutional neural networks (CNN), and recurrent neural networks (RNN), etc. It mainly summarizes the performance degradation and life test of various models in gear, and evaluates the advantages and disadvantages of various methods. In addition, it encourages future works.

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“…where u µ, σ 2 is any function for µ and σ 2 [18]. We can use Lindley's approximation procedure to estimate the parameters.…”

Section: The Eb Estimator Of µ and σ 2 With Respect To The Sel Funmentioning

confidence: 99%

Empirical Bayes Based on Squared Error Loss and Precautionary Loss Functions in Sequential Sampling Plan

et al. 2020

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An acceptance sampling plans are statistical tools in quality control which often used for lot inspection in several areas such as industry, engineering and business. It can be applied for preserving the quality of products in industry process and preserving the producer's risk and consumer's risk in the production process of manufactures. The objective of this study is to utilize the Empirical Bayes approach based on squared error loss and precautionary loss functions for parameter estimation in sequential sampling plans. The parameters are estimated using Lindley's approximation technique, and hyper-parameters can be obtained via Gibbs sampling technique. Data are normally distributed under an unknown mean and variance. The proposed plans are compared with traditional approaches including a single sampling plan and sequential sampling plan. The probability of acceptance (P a) and average sample number (ASN) are used as criterion for comparison. Results show that the proposed plans yielded the smaller ASN and higher P a than both classical methods.

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Bayesian Estimation for Two Parameters of Gamma Distribution Under Precautionary Loss Function

Cited by 9 publications

References 3 publications

Bayesian Approaches for Poisson Distribution Parameter Estimation

Bayesian Approaches for Poisson Distribution Parameter Estimation

Digital Twin-Driven Remaining Useful Life Prediction for Gear Performance Degradation: A Review

Empirical Bayes Based on Squared Error Loss and Precautionary Loss Functions in Sequential Sampling Plan

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