Saeid Tahmasebi

In the complex and varied landscape of modern industry, statistical data analysis and optimal inference play a critical role in decision-making processes. Probability distributions serve as fundamental tools for understanding data behaviors and making precise predictions. Among these, Weibull distributions are renowned for their adaptability to reliability data in various industries. However, with advances in data collection and analysis, the development of more innovative and accurate models has become imperative. This thesis introduces a novel two-parameter distribution known as the ”flexible Weibullweighted distribution,” which is designed with practical applications in industry in mind. Our investigation combines theoretical and empirical approaches to explore the statistical properties of this new distribution family, utilizing maximum likelihood estimation and other estimation methods. Employing two carefully selected real-world data sets, the model is extracted and compared with established distributions such as FW,GFW, EW, Burll, and gamma distributions. The numerical results convincingly demonstrate that this new distribution achieves a superior fit for the data sets under consideration. Therefore, this thesis not only introduces a new statistical tool but also verifies its applicability amidst the complexities of industrial data, ultimately leading us toward new standards in probabilistic analysis and modeling. key words: gamma distribution, flxible weibull distribution, weighted flexible wiebull distribution, hazard function, maximum likelihood estimation, order statistic.