Develop a Nonlinear Model for the Conditional Expectation of the Bayesian Probability Distribution (Gamma – Gamma)

In this paper a method has been suggested to describe the conditional expectation of Bayesian probability distribution (Gamma-Gamma) by nonlinear regression model and using power transformation for the observations of the predictor variables in the observable distribution to get the best possible fitting to the model of the posterior conditional expectation. The parameters of the described model have been estimated by depending on experimental data which has been generated using different values for the parameters of conditional probability distribution. The best estimation of the power parameter of the described model was found by using Draper & Smith method which gave best fitting of the suggested model and best estimate for the conditional expectation of the Bayesian Probability Distribution (Gamma–Gamma).