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This paper introduces a novel logarithmic beta generated family of distributions, designed specifically for the nuanced analysis of medical data. Through meticulous development, we have establish a comprehensive suite of distributional properties, including quantiles, moments, and hazard rate functions. Central to our contributions is the exploration of the power function distribution, a pivotal sub-model within this innovative family, demonstrating unparalleled flexibility across a broad spectrum of data types. Our investigation delves into seven prominent parameter estimation techniques, rigorously assessing their efficacy through both simulation studies and real-life medical datasets. This comparative analysis highlights the superior performance of the proposed model against existing standards, particularly through improved goodness-of-fit measures across four distinct medical science lifetime datasets. The findings highlight the new model's dominance in capturing complex data patterns, attributable to its adaptable density and hazard rate functions. These attributes significantly enhance modeling capabilities, paving the way for more precise and reliable medical research outcomes. The study concludes by emphasizing the model's potential in advancing statistical methodologies for medical science, backed by theoretical and empirical validations of its superior performance and versatility. [ABSTRACT FROM AUTHOR]

This paper introduces a novel logarithmic beta generated family of distributions, designed specifically for the nuanced analysis of medical data. Through meticulous development, we have establish a comprehensive suite of distributional properties, including quantiles, moments, and hazard rate functions. Central to our contributions is the exploration of the power function distribution, a pivotal sub-model within this innovative family, demonstrating unparalleled flexibility across a broad spectrum of data types. Our investigation delves into seven prominent parameter estimation techniques, rigorously assessing their efficacy through both simulation studies and real-life medical datasets. This comparative analysis highlights the superior performance of the proposed model against existing standards, particularly through improved goodness-of-fit measures across four distinct medical science lifetime datasets. The findings highlight the new model's dominance in capturing complex data patterns, attributable to its adaptable density and hazard rate functions. These attributes significantly enhance modeling capabilities, paving the way for more precise and reliable medical research outcomes. The study concludes by emphasizing the model's potential in advancing statistical methodologies for medical science, backed by theoretical and empirical validations of its superior performance and versatility.