Inference on the overlap coefficient: The binormal approach and alternatives

Alba María Franco-Pereira, Christos T. Nakas, Benjamin Reiser, María Carmen Pardo

Research output: Contribution to journalArticlepeer-review


The overlap coefficient ((Formula presented.)) measures the similarity between two distributions through the overlapping area of their distribution functions. Given its intuitive description and ease of visual representation by the straightforward depiction of the amount of overlap between the two corresponding histograms based on samples of measurements from each one of the two distributions, the development of accurate methods for confidence interval construction can be useful for applied researchers. The overlap coefficient has received scant attention in the literature since it lacks readily available software for its implementation, while inferential procedures that can cover the whole range of distributional scenarios for the two underlying distributions are missing. Such methods, both parametric and non-parametric are developed in this article, while R-code is provided for their implementation. Parametric approaches based on the binormal model show better performance and are appropriate for use in a wide range of distributional scenarios. Methods are assessed through a large simulation study and are illustrated using a dataset from a study on human immunodeficiency virus-related cognitive function assessment.

Original languageEnglish
Pages (from-to)2672-2684
Number of pages13
JournalStatistical Methods in Medical Research
Issue number12
StatePublished - Dec 2021

Bibliographical note

Funding Information:
The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partially supported by grant PID2019-104681RB-I00 and GR15-17-962004-2021 of the Spanish Ministry of Science and Innovation.

Publisher Copyright:
© The Author(s) 2021.


  • Bootstrap
  • Box-Cox transformation
  • ROC curve analysis
  • delta method
  • kernel methods

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability
  • Health Information Management


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