A new flexible generalized family for generating continuous models

This research introduces the Marshall–Olkin alpha log-power transformed-G (MOALPTG) family of distributions, a novel generalization designed to enhance the flexibility of statistical models in capturing diverse real-world data patterns. By extending the alpha log-power transformation, this family effectively addresses the limitations of classical distributions, particularly in modeling complex behaviors such as non-monotonic hazard rate functions. Key structural properties of the new family are examined, and parameters are estimated using the maximum likelihood estimation (MLE) method. A comprehensive simulation study across various sample sizes evaluates the performance of the MLE approach. Additionally, the model is applied to both right-skewed and moderately left-skewed datasets, demonstrating superior goodness-of-fit and improved accuracy compared to existing alternatives presented in this research. These findings highlight the versatility and practical applicability of the MOALPTG family, contributing a valuable tool for statistical modeling and data analysis.