Study on New Sine Family of Distributions with Properties and Applications in Reliability and Survival Analysis

Statistical modeling is essential for interpreting lifespan data in many scientific fields, including engineering, medicine, and economics. Accurately describing the amount of time until a particular event such as the failure of a mechanical component or the death of a biological subject occurs is the main goal of survival and reliability analysis. By combining the robust heavy-tailed properties of the exponentiated Pareto distribution with the Sine-G generator, the Sine exponentiated Pareto generalized family of distributions is presented. This study explores the mathematical properties of this new family and assesses how well it performs in reliability and survival analysis scenarios. The adaptability and robustness of this new family are studied by analyzing two sub-models the exponential and inverse exponential distributions. In the simulation study, the maximum likelihood estimate approach is used and the effectiveness of the estimate is assessed on the basis of the results of the simulation study. A Bayesian information criterion and Akaike information criteria are employed to illustrate the use of the model in four real-world datasets. It is concluded that the Sine exponentiated Pareto exponential distribution is a robust and effective model in survival analysis and reliability engineering, since the proposed model is found to be better than the selected comparator models.