Bayesian Estimation of the Parameters of the Spherical Distribution
Under different Loss Functions
 with  application

A Thesis
Submitted to the council of the College of Administration and Economic- University of Karbala in partial fulfillment of the Requirements for the Degree Doctor of Philosophy of Statistics Science

By
 Marwa Haider Ghazi

Supervision
Prof.  Dr . Awad Kadhum Shalan AlKhalidy

Abstract

There are many statistical methods and methods in estimating the parameters of statistical models, and these estimates distinguish important criteria for indicating preference in the estimation, the most important of which is the error coefficient.

The main goal of any estimation process is to reach the best estimate or the closest estimate of the unknown parameter out of all possible estimates, so the decision maker should choose the best method or formula for estimating the unknown parameter.

In this thesis, the Bayesian estimation of the parameters of the spherical Dirichlet distribution was used under the loss functions selected according to the Bayesian method and the most efficient determination was made by adopting the integral mean error criterion. It is one of the common diseases that need to be studied to diagnose the most important factors that can be subjected to scientific experiments to mitigate the effects of this disease. On the experimental side, the default values of the spherical three-dimensional dericheli distribution were obtained from conducting several experiments and selecting the values at which the Bayes estimates stabilized and gave the best results at the default parameters (α_1=1,α_2=1,α_3=1) as the results showed that the Degroot loss function achieved an advantage at a sample size of (500) achieved an advantage over the rest of the sample sizes in estimating the parameters of the spherical distribution because it recorded the lowest average error squares

We found a very high positive correlation between the likelihood of developing myopia in simulation experiments and the estimated probability of developing the disease after estimating it from real measurements. The factors diagnosed by doctors can explain a very high percentage of the likelihood of children developing myopia, and the chosen model was a good representative of the problem studied

Bayesian Estimation of the Parameters of the Spherical Distribution
Under different Loss Functions

 with  application
A Thesis
Submitted to the council of the College of Administration and Economic- University of Karbala in partial fulfillment of the Requirements for the Degree Doctor of Philosophy of Statistics Science

By
 Marwa Haider Ghazi

Supervision
Prof.  Dr . Awad Kadhum Shalan AlKhalidy

Abstract

There are many statistical methods and methods in estimating the parameters of statistical models, and these estimates distinguish important criteria for indicating preference in the estimation, the most important of which is the error coefficient.

The main goal of any estimation process is to reach the best estimate or the closest estimate of the unknown parameter out of all possible estimates, so the decision maker should choose the best method or formula for estimating the unknown parameter.

In this thesis, the Bayesian estimation of the parameters of the spherical Dirichlet distribution was used under the loss functions selected according to the Bayesian method and the most efficient determination was made by adopting the integral mean error criterion. It is one of the common diseases that need to be studied to diagnose the most important factors that can be subjected to scientific experiments to mitigate the effects of this disease. On the experimental side, the default values of the spherical three-dimensional dericheli distribution were obtained from conducting several experiments and selecting the values at which the Bayes estimates stabilized and gave the best results at the default parameters (α_1=1,α_2=1,α_3=1) as the results showed that the Degroot loss function achieved an advantage at a sample size of (500) achieved an advantage over the rest of the sample sizes in estimating the parameters of the spherical distribution because it recorded the lowest average error squares

We found a very high positive correlation between the likelihood of developing myopia in simulation experiments and the estimated probability of developing the disease after estimating it from real measurements. The factors diagnosed by doctors can explain a very high percentage of the likelihood of children developing myopia, and the chosen model was a good representative of the problem studied