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arXiv · 2606.05317

A Family of Quantile Functions Useful in Clinical Studies

Sankaran P. G.·Prasanth V. P.·Midhu N. N
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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 (M\"obius) 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.

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Sankaran P. G., Prasanth V. P., Midhu N. N. 2026-06-03. A Family of Quantile Functions Useful in Clinical Studies. https://arxiv.org/abs/2606.05317

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