E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter based on asymmetric loss function

Yousefzadeh, Fatemeh

doi:10.1080/03610926.2014.968736

Cited by 31 publications

(7 citation statements)

References 3 publications

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“…In Bayesian estimation, another of the loss functions is LINEX. As per Zellner, the LINEX loss method's posterior prediction [ 27 ]. One of the Bayesian techniques is the LINEX loss function.…”

Section: Proposed Methodologymentioning

confidence: 99%

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

Mohammed

Alaziz

Sumati

et al. 2022

Computational Intelligence and Neuroscience

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The LINEX loss function, which climbs exponentially with one-half of zero and virtually linearly on either side of zero, is employed to analyze parameter analysis and prediction problems. It can be used to solve both underestimation and overestimation issues. This paper explained the Bayesian estimation of mean, Gamma distribution, and Poisson process. First, an improved estimator for μ 2 is provided (which employs a variation coefficient). Under the LINEX loss function, a better estimator for the square root of the median is also derived, and an enhanced estimation for the average mean in such a negatively exponential function. Second, giving a gamma distribution as a prior and a likelihood function as posterior yields a gamma distribution. The LINEX method can be used to estimate an estimator λ B L ^ using posterior distribution. After obtaining λ B L ^ , the hazard function h B L ^ and D B L ^ the function of survival estimators are used. Third, the challenge of sequentially predicting the intensity variable of a uniform Poisson process with a linear exponentially (LINEX) loss function and a constant cost of production time is investigated using a Bayesian model. The APO rule is offered as an approximation pointwise optimal rule. LINEX is the loss function used. A variety of prior distributions have already been studied, and Bayesian estimation methods have been evaluated against squared error loss function estimation methods. Finally, compare the results of Maximum Likelihood Estimation (MLE) and LINEX estimation to determine which technique is appropriate for such information by identifying the lowest Mean Square Error (MSE). The displaced estimation method under the LINEX loss function was also examined in this research, and an improved estimation was proposed.

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Section: Proposed Methodologymentioning

confidence: 99%

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

Mohammed

Alaziz

Sumati

et al. 2022

Computational Intelligence and Neuroscience

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show abstract

“…The hyper parameters α j and β j should be selected to guarantee that π ( λ j | α j , β j ) is a decreasing function of λ j . The derivative of π ( λ j | α j , β j ) with respect to λ j is

\frac{d π (() λ_{j} | α_{j}, β_{j})}{d λ_{j}} = \frac{{β_{j}}^{α_{j}} {λ_{j}}^{α_{j} - 2} e^{- β_{j} λ_{j}} ((), α_{j} - 1 - β_{j} λ_{j})}{normalΓ ((), α_{j})} < 0 .

…”

Section: Bayesian Estimationmentioning

confidence: 99%

“…The hyper parameters j and j should be selected to guarantee that ( j | j , j ) is a decreasing function of j . [16][17][18] The derivative of ( j | j , j ) with respect to j is…”

Section: Prior Distributionmentioning

confidence: 99%

“…Hierarchical Bayesian estimation, the thought of hierarchical prior distribution, was first introduced by Lindley and Smith, and the hierarchical Bayesian method needs two stages to finish the setting of the prior distribution; hence, it is more robust than the Bayesian method. Although E‐Bayesian and hierarchical Bayesian methods have been widely applied to data analysis, no research has been found for analyzing the masked data in a parallel system.…”

Section: Introductionmentioning

confidence: 99%

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E‐Bayesian and hierarchical Bayesian estimations for parallel system model in the presence of masked data

Cai

Shi

Lin

2019

Concurrency and Computation

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Summary In this paper, we consider the statistical analysis of parallel system with inverse Weibull distributed components. Due to cost and time constraints, the causes of system failures are masked and the type‐II censored observations might occur in the collected data. Under the symmetric and asymmetric loss functions, the expected Bayesian (E‐Bayesian) method and the hierarchical Bayesian method are proposed to estimate the parameters, as well as the reliability function. Numerical simulations using the Monte Carlo (MC) method are given to demonstrate the performances of the estimations under different masking levels and effective sample sizes. Finally, one data set is analyzed for illustrative purpose.

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“…Han (1997) developed styles to construct hierarchical prior distribution, and E-Bayesian and H-Bayesian techniques were introduced. Lately, E-Bayesian and H-Bayesian techniques are employed by Han (2011) to estimate exponential distribution parameter and Bernoulli distribution reliability estimation, by Jaheen and Okasha (2011) to estimate of reliability of the kind 12 distribution supported Type II progressive censoring samples, by Wang et al (2012) and Yousefzadeh (2017) to estimate of Pascal distribution parameters. Also, Han (2017) gives the property of E-Bayesian estimation and H-Bayesian estimation of the system reliability parameter.…”

Section: Introductionmentioning

confidence: 99%

E-Bayesian and Hierarchical Bayesian Estimation of Rayleigh Distribution Parameter with Type-II Censoring from Imprecise Data

Heidari

Deiri

2022

J Indian Soc Probab Stat

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Bayesian estimation methods for Rayleigh distribution parameter affect accurate information. However, in real-world conditions, empirical performance results cannot always be recorded or measured accurately. Thus, we'd like to generalize the estimated methods for real numbers to fuzzy numbers. during this paper, Bayesian, E-Bayesian and Hierarchical Bayesian (H-Bayesian) methods are discussed for Rayleigh distribution parameter on the idea of a Type-II censoring schemes under the squared error loss function. Data is taken into account as imprecise and within the form fuzzy numbers. Then, the efficiency of estimation methods is compared via Monte Carlo simulation. Finally, a true data set for the needs described is analyzed.

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E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter based on asymmetric loss function

Cited by 31 publications

References 3 publications

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

E‐Bayesian and hierarchical Bayesian estimations for parallel system model in the presence of masked data

E-Bayesian and Hierarchical Bayesian Estimation of Rayleigh Distribution Parameter with Type-II Censoring from Imprecise Data

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