A new family of generalized distributions based on logistic-x transformation: sub-model, properties and useful applications

This study introduces the NGLXT-E, a novel probability distribution derived from the Logistic-X family, designed to enhance flexibility and robustness in modeling datasets with extreme skewness and heavy tails. The distribution excels in survival analysis, reliability engineering, and financial risk management, outperforming established models. Objectives include defining the new family, deriving properties, analyzing a special sub-model, and developing parameter estimation methods under an uncensored sample. Applications involve diverse datasets, such as HIV/AIDS death rates in Germany (2000–2020), infection times for kidney dialysis patients, failure times of repairable items, and Bitcoin trading volumes (2014–2024). The NGLXT-E distribution demonstrates a superior fit over existing models like the generalized inverted exponential and Weibull distributions, assessed via statistical criteria such as the Kolmogorov-Smirnov test, Akaike information criterion (AIC), and Bayesian information criterion (BIC). Additionally, Bitcoin’s volatility was modeled using an exponential GARCH (eGARCH) framework, validating the NGLXT-E distribution’s applicability to financial data. This research significantly contributes to statistical literature by proposing a flexible new family of distributions, advancing parameter inference techniques, and demonstrating practical superiority across real-world datasets.