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

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 $\alpha$ . Combined with an existing generalized pivotal quantity for $\beta$ , these pivot quantities support fiducial-based construction of statistical intervals for functions of the shape parameters $\alpha$ and $\beta$ , 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.