Using the Bayesian method to estimate and comparison the regression of the exponential and gamma survival (Simulation)

     Parametric regression models It is one of the oldest and most common regression models and can be defined as one of the statistical methods that is used to describe and estimate the relationship between a dependent random variable and explanatory random variables. These models have types, including quantitative models, of their linear and non-linear types, and qualitative models that The dependent variable is a binary response variable. These models are characterized by the fact that all cases that are studied are assumed to be normally distributed and measurable, and that the regression function determines the parameters that cannot be changed except by changing the number of variables included in the study, relying on probability distributions, which are the exponential distribution and the Gamma, we will obtain parametric regression models, which are the exponential regression model, and the gamma regression model, relying on the Cox regression model to be used in forming these models, which are models that require the presence of information and hypotheses about the distribution of the population used in the test that is appropriate for the units or data, as well as the variables that enter. The test or experiment on which the survival function is based, in this thesis, it was proposed to estimate the parameters of these models using the Bayesian method. The simulation method was used to generate data that follows parametric survival regression models according to various factors. The simulation results showed that the third model of the exponential probability distribution of the survival function shows the lowest value according to the MSE criterion. This indicates that Increasing the sample size typically reduces the standard mean error (MSE), which is used as an indicator of the differences between expected and actual values in statistical estimates. Simply put, the larger the sample size, the more accurate the statistical predictions are and the lower the standard deviation from the actual values, indicating that larger samples often contribute to improving the accuracy of statistical estimates.