Bayesian estimation of the parameters of the spherical distribution using the squared loss function

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 research, a Bayesian estimation of the parameters of the spherical distribution was used, where the default values of the three-dimensional spherical Dirichlet distribution were obtained experimentally from conducting several experiments and selecting the values at which the Bayes estimates stabilized and gave the best results in the default parameters  where the results showed that the quadratic loss function achieved an advantage at sample size (500) achieved an advantage over the rest of the sample sizes in estimating the parameters of the spherical distribution followed by the sample size (400) because

At the default parameters   the Bayes method under the loss function (quadrature) at a sample size (500) achieved an advantage over the rest of the sample sizes in estimating the parameters of the spherical distribution, followed by the sample size (400) because it recorded the lowest average error squares.