Novel Logistic Extreme Value Distribution: Properties, Applications, and Parameter Estimation Using Classical and Machine Learning Methods

The life testing and analysis are important in many disciplines, such as medicine, engineering, and finance.Indeed, probability distributions are one of the critical components of accurate modelling as they govern the effectiveness and robustness of statistical evaluations.This study introduces the Novel Logistic Extreme Value Distribution (NLEVD), a flexible three-parameter probability distribution that generalizes the Logistic Extreme Value Distribution.The mathematical properties of NLEVD, including its probability density function, cumulative distribution function, moment-generating function, entropy, and order statistics, are derived.Parameter estimation was conducted via Maximum Likelihood Estimation (MLE) and Support Vector Machine (SVM) techniques, which demonstrated improved accuracy.The proposed model is validated using two real-world datasets, on which it outperforms established lifetime distributions, such as the New Extension Exponential, Gamma-Lindley, Zeghdoudi, X Lindley, and X gamma distributions.The results highlight NLEVD's superior ability to model diverse failure rate behaviors, making it a powerful tool for survival analysis, reliability engineering, and applied statistics.This study provides a robust alternative for modelling lifetime data, offering greater flexibility and precision in statistical modelling.