Development of sine Topp-Leone exponentiated inverse exponential distribution: Properties and applications

Abstract

The exponential distribution remains a cornerstone of probability theory, particularly valued in reliability engineering, survival analysis, and risk management for its computational efficiency and distinctive memoryless property. While mathematically elegant, this distribution's constrained single-parameter framework presents significant limitations when modeling complex empirical phenomena, especially those displaying non-monotonic failure patterns. Academic literature documents numerous extensions to address these constraints, including the inverse exponential distribution and its exponentiated variants, which achieve greater modeling flexibility by introducing additional shape parameters. Building upon these developments, the current study presents an enhanced probability model through the innovative synthesis of the Inverse Exponential distribution with the Sine Topp-Leone Exponentiated-G (STLEG) family, yielding the novel Sine Topp-Leone Exponentiated Inverse Exponential (STLEIE) Distribution. Our investigation encompasses a rigorous analysis of the model's fundamental statistical properties, including its survival characteristics, hazard function behavior, moment structure, quantile properties, and order statistics. For parameter estimation, we implement and compare two established methodologies: the widely-used Maximum Likelihood Estimation (MLE) approach and the Maximum Product of Spacing (MPS) technique, both renowned for their statistical efficiency. Comprehensive Monte Carlo simulations demonstrate the consistent performance of these estimators, with both bias and Root Mean Squared Error (RMSE) metrics showing progressive improvement as sample sizes increase. Empirical validation through application to two real-world datasets reveals the STLEIE distribution's superior modeling capabilities compared to existing alternatives, as evidenced by multiple goodness-of-fit criteria. The concluding comparative analysis substantiates the practical utility of the proposed model, confirming its enhanced flexibility and improved performance across diverse data scenarios, thereby offering researchers and practitioners a more robust analytical tool for complex statistical modeling applications.