Bayesian Estimation of Spherical Distribution Parameters under DeGroot Loss Function
DOI:
https://doi.org/10.62933/pcq5x378Keywords:
Bayesian Estimation , Spherical Distribution, DeGroot Loss FunctionAbstract
There are many statistical methods and approaches to estimating the parameters of statistical models. These estimations are distinguished by important criteria to indicate the preference in the estimation, the most important criteria are the standard mean square error. The main goal of any estimation process is to reach the best or closest estimate of the unknown parameter among all possible estimates.
In this paper, Bayesian estimation of spherical distribution parameters was used. The default values of the three-dimensional spherical Dirichlet distribution were obtained experimentally by conducting many experiments and choosing the values at which Bayes estimates stabilized and gave the best results. Using as an intial values. The results showed that the DeGroot loss function gave the best results when the sample size was greater than 400.
A sample of size 720 patient was selected randomly and used in the applied aspect for myopia variables for real data, and the study concluded that the values of the probability density function estimated by the Bayes method at the DeGroot loss function are consistent with the values of the true probability density function for the three-dimensional spherical Dirichlet distribution.
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Copyright (c) 2025 Awad Kadim al-Khalidy, Mariam mahdi anad, Marwa haider ghazi (Author)
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