A thesis submitted to the council of the college of Administration &Economics \ University of Karbala as partial fulfillment of the requirements for the degree of Master of Statistics Science

By
Adham mohammed sahib
Supervised by
Dr. Enas Abdel-Hafez Mohamed

This thesis presents the mixed probabilistic model (Exponential – Gamma of the second order) (EG) which was obtained by mixing two single distributions, namely the exponential distribution with a measurement parameter ( ) and the distribution of Gamma of the second order with the shape parameter (n=3) and the scale parameter ( ), by using a parameter known as the parameter mixing between distributions (w) whose value lies between ( ) so that in order to obtain a new probability distribution It is characterized by accuracy, comprehensiveness , modernity and flexibility in representing the studied phenomenon data. The thesis mainly is aimed at estimating the survival function until death for a sample of patients with kidney failure disease who were lying in the Kidney Disease and Transplant Hospital in Baghdad, City of Medicine for the period from (17/1/2015 to 27/12/2017), by using four estimation methods, which are (Maximum likelihood , Moment, Bayesian, and weighted least squares . Where in the experimental side (simulation) random data was generated for a sample of three sizes (30,60,100) following the mixed probabilistic probabilistic (exponential – gamma of the second order), as well as choosing default values for the distribution parameters (β, ), by four models (four models) in order to give a complete idea about the used statistical measures and by using the MSE index to compare between the four methods of estimation, the weighted least squares method (WLS) was preferred in estimating the survival function over the rest of the other methods and for all sample sizes, and on the real (applied) side, the weighted least squares method was used on the study sample (patients with kidney failure) Where the number of views (91) The results presented in the fourth chapter of this thesis confirm the clear correspondence between the experimental and practical (real) aspects . The thesis led to several results, the most important of which is the emphasis on using the weighted least squares method when estimating the survival function for this distribution and for all sample sizes (small, medium and large), as well as recommending the approval of the results of the thesis by the Center for Kidney Diseases and Transplantation in Baghdad Medical City.