Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

The most essential process in statistical image and signal processing is the parameter estimation of probability density functions (PDFs). The estimation of the probability density functions is a contentious issue in the domains of artificial intelligence and machine learning. The study examines challenges related to estimating density functions from random variables. Based on minimal predictions regarding densities, the study discusses a framework for evaluating probability density functions. During the Bayesian approach, which is to generate correct samplings that reflect the probability aspect of the variables, sampling is widely used to estimate as well as define the probabilistic model of unknown variables. Because of its effectiveness and extensive application, the generalized likelihood uncertainty estimation (GLUE) method has earned the most popularity among the various methodologies. The Bayesian technique allows parameters of the model to be estimated using prior expertise in the parameter results and experimental observations. The study uses a number of engineering issues that were lately looked into to illustrate the effectiveness of the upgraded GLUE. As the focus is on the examination of sampling effectiveness in view of engineering components, only a brief summary is provided to describe every challenge. The suggested GLUE method’s outcomes are contrasted with those obtained using MCMC. Nevertheless, using the GLUE approach, the model’s mean squared error of prediction is substantially higher than that of the previous algorithms. The methods’ results are affected by the assumptions being made on parameter values in advance. The concepts of prediction accuracy, as well as the utility of geometric testing, are presented. Such notions are valuable in demonstrating that the GLUE approach defines an inconsistent and incoherent statistical inference process.

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“…Bayesian Technique. Bayesian theorem, the following equation provides the posterior parameter distribution [23]:…”

Section: Proposed Methodology With Gluementioning

confidence: 99%

Estimation of Parameters on Probability Density Function Using Enhanced GLUE Approach

Al-Duais

Sayed-Ahmed

2022

Computational Intelligence and Neuroscience

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“…A linear exponential loss function (LINEX) is developed to estimate the scale parameter and reliability function of the inverse Weibull distribution (IWD) based on lower record values [ 6 ]. The Bayesian technique is also necessary for this study, in addition to employing Maximum Likelihood to estimate the parameters.…”

Section: Introductionmentioning

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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Estimation of the Kumaraswamy distribution parameters using the E-Bayesian method

Al-Duais

Yassen

Almazah

et al. 2022

Alexandria Engineering Journal

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Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

Cited by 6 publications

References 19 publications

Estimation of Parameters on Probability Density Function Using Enhanced GLUE Approach

Estimation of Parameters on Probability Density Function Using Enhanced GLUE Approach

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

Estimation of the Kumaraswamy distribution parameters using the E-Bayesian method

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