استعمال قاعدة Transmuted LOWER Record Type مع تطبيق عملي

Rp-Use Transmuted Lower Record Type With Practical application.pdf

This thesis seeks to study a new formula for the (generalized Inverse Weibull) distribution, by adding an additional parameter to its distribution function, noting that we have not found the new distribution in any other research work through the transformation map (Transmuted Lower Record), so it becomes the (Transmuted Lower Record generalized Inverse Weibull) distribution. The four-parameter transformer is distinguished by its flexibility and accuracy over other distributions. The statistical and structural properties of the distribution were studied and extracted, and the distribution was applied to three traditional estimation methods. Among these methods are both (Maximum Likelihood Method) and Least Square Method. And the Method of Cramer-Von Mises Minimum. For the purpose of comparing methods for estimating parameters and the survival function, the Monte Carlo simulation method was employed using a program in the language (Wolfram Mathematica 12.2) to conduct several experiments with eight models with different sample sizes. (Small (30), medium (and 100.50) and large (150)) and through the statistical criterion Mean Squared Error (MSE) the results showed the superiority of the maximum likelihood method in calculating the estimates of the fuzzy reliability function for the new distribution (Transmuted Lower Record generalized Inverse Weibull) when Sample sizes are large and medium, and the preference of the Cramer-von Mises method is for small and medium sample sizes. The distribution was applied to real data with (150) observations representing survival times for people with stroke, and through goodness-of-fit tests, it was proven to be better in representing and describing these data compared to the (generalized Inverse Weibull Distribution). The reliability function for real data was also estimated using The maximum potential method has proven its superiority in the experimental aspect over the rest of the methods used. We have found that the average operating time until failure for the devices is (5.1458049) weeks, and that the value of the estimated average survival function is (0.519332), meaning that the device can be relied upon by 52% within three months. Almost half.