Fiducial‐Based Statistical Intervals for Bounded Bioanalytical Data Using the Kumaraswamy Distribution

ABSTRACT Biological measurements such as percent monomer from size exclusion chromatography (SEC) or cell‐based percentages from flow cytometry are continuous quantities bounded between 0 and 1. These continuous bounded data are frequently skewed and therefore construction of normal‐based confidence, prediction, and tolerance intervals may not be appropriate. Transformation based approaches (e.g., logit or arcsine‐square‐root) are often recommended to analyze bounded data; however, for highly skewed data with sample size, they may yield intervals that are too wide for practical applications. Although the beta distribution is a natural model for continuous bounded data, routine interval procedures remain limited in Chemical, Manufacturing, and Controls (CMC) practice. The Kumaraswamy distribution is a flexible and mathematically tractable alternative. In this manuscript, we develop two new pivotal quantities for the Kumaraswamy shape parameter . Combined with an existing generalized pivotal quantity for , these pivot quantities support fiducial‐based construction of statistical intervals for functions of the shape parameters and , such as confidence intervals for the mean and fiducial‐type tolerance and prediction intervals. We investigate finite‐sample performance of these intervals through a simulation study and compare the proposed methods with a published pivotal approach and commonly used transformations. We also illustrate the methods with a simulated percent monomer data representative of CMC bioanalytical practice. Practical recommendations for routine use are provided.