The College of Education for Pure Sciences, Department of Mathematics, organized a scientific lecture on "Finding the Best Estimate of the Parameters of the New Compound Distribution." The lecture, delivered by lecturer Iman Qais Abdulrahman, included finding a compound probability distribution (Pareto-Truncated Exponential) in the interval (θ,∞). The proposed distribution was derived, along with its properties and parameters, using estimation methods (maximum likelihood, moments, and partial estimations). The best estimation method was identified for application to real data. To achieve the thesis objective, the results were discussed experimentally and applied. The R programming language (version 4.0.5) was used in the simulation program to estimate the parameters and find the best estimation method among the methods used. This was achieved by using different default values ​​for the parameters and three different sample sizes (100, 50, and 25). The experiment was repeated 1,000 times. Using the MSE criterion to compare estimation results, the maximum likelihood method was found to be the best. In the practical aspect, data on machine failure times were used to estimate the parameters for the new distribution. The maximum likelihood method was used for estimation in the practical aspect because it was the best method in the experimental aspect