A comparison between of Maximum Likelihood Method and Cramer von Misses method for Estimating Survival Function Odd Chen Fréchet Distribution with Applications

Abstract

This research presented the compound distribution (Odd Chen Fréchet Distribution) obtained by using the rule (The Odd Chen Generator (Family). This rule was discovered for the first time by the scientist (El-Morshedy and all) in the year (2020), as a basis for proposing distributions Probability, which is characterized as distributions with flexibility and high accuracy in representing statistical data, as it is characterized by the largest number of parameters compared to the existing probability distributions in order to obtain a new probability distribution characterized by accuracy, comprehensiveness, modernity and flexibility in representing the data of the studied phenomenon, as some mathematical properties of the proposed distribution were derived. Where the survival function estimates were derived using the Maximum Likelihood Method, and the Cramer von Mises method in the experimental aspect. Monte Carlo simulations were employed to generate random data for a sample of five sample sizes (30,50,75,100,150) following the proposed model (Odd Chen Fréchet Distribution) in order to give a complete idea of ​​the statistical measures used and using the statistical indicator Mean Square Error (MSE) to compare the preference of the used estimation methods, as it showed the preference of the Cramer von Mises (cvm) method in estimating the survival function for the sizes of medium and large samples As for the applied (real) side, the researcher used the Cramer von Mises method. To estimate the survival function on the study sample (kidney failure patients in the holy governorate of Karbala) for the period between 5/8/2020 until 17/7/2020, as the number of observations was (110), and the results shown in the experimental and applied aspects confirmed the use of Cramer von Mises method to estimate the survival function at the sizes of medium and large samples, as well as the recommendation to adopt the results of the research at the Holy Karbala Health Department