🤖 AI Summary
This study addresses the lack of flexible and interpretable probability distribution models suitable for upper-tail quantile analysis in clinical research. The authors propose a novel class of quantile-based effective duration functions, defined as the ratio of the mean to a given quantile, and derive a two-parameter family of non-negative distributions with closed-form expressions by incorporating Möbius transformations and natural boundary conditions. This distributional framework provides a unified characterization of tail behavior in survival data and facilitates quantile-based reliability measures and L-moment analysis. Empirical evaluation on real-world survival datasets demonstrates that the proposed method significantly outperforms existing approaches in both goodness-of-fit and model interpretability.
📝 Abstract
Motivated by upper-tail quantile-domain summaries, we study the quantile-based effectiveness persistence function defined as the ratio between the tail mean and the quantile function. We derive statistical properties of this measure and consider a rational (Möbius) specification of the quantilebased effectiveness persistence function. Under natural boundary conditions, this specification reduces to a canonical form. The resulting canonical family defines a two-parameter class of nonnegative distributions through its quantile function. Various properties, including descriptive measures, L-moments, and quantile-based reliability concepts, are derived for this class. Estimation of the model parameters using maximum likelihood is also developed. The proposed family is illustrated using a real survival dataset.