تقدير معلمات ودالة البقاء لتوزيع بيركس المعمم مع تطبيق عملي

Estimate parameters and Survival function for the exponentiated Perks distribution with practical application

Probability distributions are important topics in statistical theory that have gained distinct importance in recent decades for their extensive applications in various fields (medical, engineering, biology and industrial) and accordingly one of the continuing probability distributions, the three-parameter Perks distribution, was studied on the theoretical side, the properties and function of probability density, the cumulative function and the function of survival were used, and four methods were used to estimate the method of Maximum Likelihood Method, Least Squares Methodand two methods of Bayesian derived from these methods of reaching formulas. A comparison was made between the capabilities using the simulation method that carried out simulation experiments using a set of samples of different sizes (10,25, 50,100,150) and repeated each experiment (2,000) times to achieve the goal and for six different models and the results were compared using one of the most important statistical measures, the Integral Mean Square Error( IMSE) and the best methods were reached for each sample size and for each sample size.The results of the Integral Mean Square Error for the survival function were known for each of the six models and compared those results to all models where the result appeared in preference of the method of the Maximum Likelihood Method compared to the rest of the methods.
On the practical side, a random sample of data of (200) was applied in practice to view the monthly mortality times of breast cancer patients in Basra governorate for the period from (1/1/2015) to (31/12/2019) where the survival period was taken,and this was applied The sample for the Exponentiated Perks distribution, and to better illustrate the work of the data, a number of criteria were used to match the practical distribution of the sample data with the Exponentiated perks distribution, and through the results of the standards (AIC,BIC,CAIC) the result appeared with the method of the Maximum Likelihood that is, the method of the Maximum Likelihood gave more appropriate capabilities for data studied .