Parameter Estimations of Inverse Weibull Distribution

2011 ◽  
Vol 199-200 ◽  
pp. 564-568
Author(s):  
Wei An Yan ◽  
Bao Wei Song ◽  
Zhao Yong Mao ◽  
Huang Yong Le
Keyword(s):  
Monte Carlo Simulation ◽  
Weibull Distribution ◽  
Empirical Bayes ◽  
Bayes Estimation ◽  
Conjugate Prior ◽  
Monte Carlo Simulation Study ◽  
Empirical Bayes Estimation ◽  
Asymptotically Optimal ◽  
Parameter Estimations ◽  
Inverse Weibull Distribution

under entropy loss function, the E-Bayes estimation and empirical bayes estimation to the parameter of inverse Weibull distribution used conjugate prior are discussed. And we prove the empirical bayes estimation is asymptotically optimal. At last, the MSE of the estimations are compared based on Monte Carlo simulation study. According to these comparisons, it is suggested that the accuracy of E-Bayes estimation is close to the empirical bayes estimation.

scholarly journals Modeling In-Match Sports Dynamics Using the Evolving Probability Method

2021 ◽  
Vol 11 (10) ◽  
pp. 4429
Author(s):  
Ana Šarčević ◽  
Damir Pintar ◽  
Mihaela Vranić ◽  
Ante Gojsalić
Keyword(s):  
Monte Carlo Simulation ◽  
Statistical Models ◽  
Empirical Bayes ◽  
Hybrid Approach ◽  
Real Life ◽  
Bayes Estimation ◽  
Probability Method ◽  
Specific Nature ◽  
Sport Event ◽  
Insight Into

The prediction of sport event results has always drawn attention from a vast variety of different groups of people, such as club managers, coaches, betting companies, and the general population. The specific nature of each sport has an important role in the adaption of various predictive techniques founded on different mathematical and statistical models. In this paper, a common approach of modeling sports with a strongly defined structure and a rigid scoring system that relies on an assumption of independent and identical point distributions is challenged. It is demonstrated that such models can be improved by introducing dynamics into the match models in the form of sport momentums. Formal mathematical models for implementing these momentums based on conditional probability and empirical Bayes estimation are proposed, which are ultimately combined through a unifying hybrid approach based on the Monte Carlo simulation. Finally, the method is applied to real-life volleyball data demonstrating noticeable improvements over the previous approaches when it comes to predicting match outcomes. The method can be implemented into an expert system to obtain insight into the performance of players at different stages of the match or to study field scenarios that may arise under different circumstances.

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