1. This thesis aims, propose a new two-parameter probability distribution, called A Flexible Lomax–Rayleigh Distribution: Properties and Applications, by combining the cumulative distribution functions of the Lomax and Rayleigh distributions, each of which is characterized by a single parameter. The proposed distribution provides greater flexibility in modeling real-life data, particularly data containing extreme values.
   Several mathematical and statistical properties of the proposed distribution were derived. The parameters of the new distribution were estimated using three classical estimation methods: the Maximum Likelihood Estimation (MLE) method, the Ordinary Least Squares Estimation (OLSE) method, and the Rank Set Sampling Estimation (RSSE) method. In addition, a Monte Carlo simulation technique was employed to estimate the parameters and the survival function under different sample sizes and various initial parameter values using MATLAB. 

A comparative study of the three estimation methods was conducted based on the Mean Squared Error (MSE) and Mean Absolute Error (MAE) criteria to determine the most efficient method for estimating the parameters and the survival function. Finally, the proposed distribution was applied to real data collected from the Iraqi Ministry of Health, Medical City Department, Oncology Teaching Hospital, to estimate the probability density function, cumulative distribution function, survival function, and hazard function.