Using some methods of estimating Parameters and Survival function for The Exponentiated Perks distribution with practical application

Abstract

         In this research, some characteristics of the Exponiated Perks distribution and survival function were studied and Two methods of estimation were used, namely the Maximum Likelihood method and the least squares method, and these estimation methods were derived to arrive at formulas of their capabilities. A comparison was made between the capabilities using the simulation method, as the simulation experiments were carried out using a set of samples of different sizes (10, 50,100) and each experiment was repeated (2000) once to achieve the goal and for three different models. The results were compared using one of the most important statistical measures, which is the average of the integrative error squares (IMSE). The best methods were found for each model and for each sample size. The results of the mean of squares of the integral error of the survival function were known, and a comparison was made between those results and all models where the result appeared in the best possible way. As for the applied side, a practical application was made of a random sample of data with a size of (200) Watching times of deaths per month for breast cancer patients in Basra Governorate where they took their survival period, and this sample was applied to distribute Exponiated Perks,Through the results, it became clear that the Maximum Likelihood method gave more appropriate capabilities for the data studied .