Using the Bx-G Family Rule with the Two-Parameter Lindley Distribution with a Practical Application

Abstract

The expansion of probability distributions from commercial operations has been greatly improved over thousands of years, to the fact that the distributions of comprehensive data are not widely and accurately represented, and the publication of the distribution distribution using different families and categories is one of the newly exclusive methods in the expansion of distributions. In this thesis, the Burr X-G Family Distribution was used and applied to the Lindley two-parameter distribution (two-parameter Lindley Distribution) on new probability models (Burr X-LindleyTwoParameter Distribution), which is more distributed than the basic distributions under study. Some of its statistical properties were studied, such as the probability function, the cumulative function, the survival function, the risk function, and the survival function. The parameters and survival function of the probability model (LindleyTwoParameter Distribution) were estimated using the method (the maximum determination method, the Cray von Mises method). In order to obtain the best method for estimating the parameters and the survival condition, a brief simulation study was conducted using the Monte-Carlo method, which was used, and several cupping experiments were conducted. Small, medium, and large samples (150, 100, 75, and 50) were used, with five models using different values ​​for the unknown parameters. The mean square error (MSE) was used to compare the four estimation methods for parameter estimates, and the best method was found to provide the maximum likelihood of estimating the unknown parameters and the survival function for all light sources. However, in a side application, the new probabilistic model (BurrX-Lindley Two-Parameter Distribution) was applied to real data of (150) observations from the Karbala Health Department, Al-Hussein Teaching Hospital, representing the survival times of patients with the disease until death. The performance of the proposed distribution was compared with the basic Lindley distributions under study. The new model provided a reading of flexibility and efficiency in interpreting the data, proving its superiority in interpreting the data.