A Three-Parameter Generalized Topp-Leone ArcTan Exponential Distribution: Inference and Applications to Lifetime Data

This paper introduces a new transformation technique based on the cumulative distribution function and inverse trigonometric function, aimed to propose a new generalized family of lifetime distribution which is parsimonious in parameter and flexibility in baseline distribution that can produce four different classes of distributions as an special case. The proposed transformation technique is applied using the exponential distribution as a baseline, and its various statistical properties are thoroughly examined. Further, the analytical, graphical, and numerical approaches are employed to study the characteristics of the resulting distribution, which is found to be positively skewed with a heavy tailed while the hazard function displays increasing, decreasing, and constant patterns. The maximum likelihood method of estimation is used to estimate the model parameters, and their performance is evaluated through a detailed Monte Carlo simulation study. The flexibility and practical utility of the proposed Generalized Topp-Leone Arctan Exponential (GTLATE) distribution is thoroughly demonstrated through the analysis of two real-world data sets. By comparing its performance against a range of existing lifetime distribution models, the study evaluates the effectiveness of the GTLATE model using various goodness-of-fit measures. These comparisons reveal that the GTLATE model consistently performs better in compare to the several competing models that exhibit similar hazard rate patterns, particularly in handling data sets with increasing, decreasing, or constant hazard rate patterns. This superior performance highlights the GTLATE model enhanced flexibility in fitting diverse types of real-world data, making it a valuable tool for practical applications in fields such as reliability analysis, survival studies. AMS Classification: 62E05, 62B10, 62F15.