تقدير دالة البقاء لتوزيع رايلي باريتو المحول باستعمال الصيغة الاسية المحولة مع تطبيق عملي.

Rp-Estimating the Survival function of The Transmuted Rayleigh-Pareto Distribution using the converted exponential formula with a practical ..pdf

Abstract
The study sought to use the theory of quadratic transformed distributions in constructing a proposed new probability distribution known as the Transmuted Rayleigh Pareto Distribution with three parameters (α, γ, θ), as some of its properties were studied, its parameters were estimated, and survival function estimators were calculated using three estimation methods (method The greatest possibility (MLE), the Kramer von Mises method (CVM) and the partial estimators method (PER), and we chose the best methods for estimating the parameters and the survival function by employing the Monte Carlo simulation method using the Mathematica program to conduct many iterations of experiments with sample sizes Different, small (20), medium (75-50) and large (100-150) and by means of the statistical mean square error (MSE) the results showed the preference of the Cramer von Masse (CVM) method in calculating survival function estimators for the proposed distribution at small sample sizes ( 20) and the preference of the method of greatest possibility at the sizes of medium and large samples (50, 75, 100, 150), and the distribution was applied using the method whose preference appeared on the experimental side on real data by (105) observations representing survival times in weeks for people with cirrhosis until death, and through tests of good conformity The preference of the proposed distribution (TRP) in representing and describing this data has been demonstrated compared to the (Rayleigh Pareto Distribution), as well as the survival function for real data has been estimated using the method of greatest possibility, whose preference appeared in the experimental side. The method of greatest possibility has taken the first place in preference when calculating the estimations of the survival function for the distribution of the Rayleigh-Pareto distribution with three parameters at the sizes of large samples, and this means that it is suitable for the sizes of large samples. Cramer von Mises (CVM) estimated the survival function as it had the least mean squares error. While the method of the greatest possibility (MLE) ranked second, and the method of fractional estimators (PER) ranked third, depending on the arrangement of the mean squares of error. At sample sizes (150-100-75-50), the method of greatest possibility (MLE) ranked first in preference for the survival function, followed by the Cramer von Mises (CVM) method in the second place, and the method of fractional estimators (PER) ranked third, depending on the values of The mean squares of the errors are ordered from lowest to highest. Hence, we conclude that the method of greatest possibility is the best in estimating the parameters and survival function of any converted distribution at large samples.