Cubic Transformation Rayleigh Pareto with Practical Applications
Preface letter to
Council of the College of Administration and Economics / University of Karbala, which is part of the requirements for obtaining a master’s degree in statistics
Submitted by the researcher By
Tamazar Kifah Hassan
Supervised By
Prof. Awad Kadim Shaalan AL-Khalidi Ass. Prof. Dr. Mushtaq Kareem Abd Al-Rahem
Abstract
The Rayleigh Pareto Distribution (Rayleigh Pareto Distribution) with parameters (α, γ, θ) is one of the widespread distributions. This distribution was derived from its true position in the best contracts due to the importance of its use in probabilistic cases. This distribution was applied in the study of reliability and survival, time display, and monitoring. Quality and acceptability (sample acceptance) in cases where normal distributions are an imperfect model.
The study sought to study the distributions of the cubic transformed distributions in constructing the new probability distribution (Rayleigh Pareto Distribution) with three parameters. Some of the structural and statistical gains of the proposed complex distribution (the cubic Rayleigh Pareto transformation) were studied, and its parameters and the estimators of the survival function of the distribution were estimated using third estimation methods, namely Each of the (Maximum Likelihood Method (MLE), Cramer von Mises Method (CVM) and the Optical Estimators Method (PER), and for the purpose of demonstrating the superiority of the estimation methods mentioned, is examined, as it depends on the extrapolation of the Mean Squared Error (MSE) through the use of a simulation method. Monte Carlo (Monte Carlo) to search for many repetitions of different substitutions from different grains (30), medium (50) and large (150-100) with seven models and repeating the experiment (1000) times for the experiment, and showed the best search results for the method of possibility. (MLE) in calculating final survival parameters and estimators for the proposed distribution at large remaining sizes to compare the preference of estimation methods and apply the proposed joint data using the method I chose in the experimental aspect on a real represented (108) observations representing survival times in weeks because it will contribute to establishing the colon until the start. After conducting a goodness-of-match test to show a large portion of the real data with the proposed distribution based on the Chi-Square statistical elasticity, and for the purpose of proving the efficiency of the proposed distribution compared with the Pareto rally distribution in representing the real data based on the statistical criteria (AIC, ACc, BIC), where the distribution was shown to be efficient. It is a good competitor and has the lowest values for the standards used.
