Distributional Flexibility under Box-Cox Normality: A Theoretical and Empirical Evaluation of the Power-Normal Distribution
Abstract
Methods based on Box-Cox models have recently been developed for inference on clinically interpretable treatment effects in clinical trials. These methods model marginal outcome distributions using the power-normal distribution (PND), but the range of real-world data distributions that it can adequately approximate remains unclear. We evaluated PND approximations using two parameterizations of the four-parameter generalized F/generalized beta of the second kind family and 165 laboratory variables from the National Health and Nutrition Examination Survey. Overall distributional agreement was assessed using the overlap coefficient and Jensen-Shannon divergence, and location and spread on the original scale were evaluated using relative biases in the median and interquartile range. The PND closely approximated a broad range of smooth unimodal positive distributions in both the theoretical and empirical evaluations. Reduced agreement was associated with pronounced lower-bound accumulation, heaping or discretization, and multicomponent or peak-tail features. These features may be recognizable before fitting and provide practical guidance for assessing the suitability of the PND. We also developed the R package powerNormal for distributional calculations, parameter estimation, reparameterization, and random-number generation for the PND.
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BibTeX
@misc{maruo2026distributional,
title = {{Distributional Flexibility under Box-Cox Normality: A Theoretical and Empirical Evaluation of the Power-Normal Distribution}},
author = {Kazushi Maruo and Yusuke Yamaguchi and Ryota Ishii and Toshio Shimokawwa and Masahiko Gosho},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38454},
eprint = {2610.38454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38454},
}
RIS
TY - UNPB
TI - Distributional Flexibility under Box-Cox Normality: A Theoretical and Empirical Evaluation of the Power-Normal Distribution
AU - Kazushi Maruo
AU - Yusuke Yamaguchi
AU - Ryota Ishii
AU - Toshio Shimokawwa
AU - Masahiko Gosho
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38454
UR - https://arxiv.org/abs/2610.38454
AB - Methods based on Box-Cox models have recently been developed for inference on clinically interpretable treatment effects in clinical trials. These methods model marginal outcome distributions using the power-normal distribution (PND), but the range of real-world data distributions that it can adequately approximate remains unclear. We evaluated PND approximations using two parameterizations of the four-parameter generalized F/generalized beta of the second kind family and 165 laboratory variables from the National Health and Nutrition Examination Survey. Overall distributional agreement was assessed using the overlap coefficient and Jensen-Shannon divergence, and location and spread on the original scale were evaluated using relative biases in the median and interquartile range. The PND closely approximated a broad range of smooth unimodal positive distributions in both the theoretical and empirical evaluations. Reduced agreement was associated with pronounced lower-bound accumulation, heaping or discretization, and multicomponent or peak-tail features. These features may be recognizable before fitting and provide practical guidance for assessing the suitability of the PND. We also developed the R package powerNormal for distributional calculations, parameter estimation, reparameterization, and random-number generation for the PND.
ER -