Inference on the overlap coefficient: The binormal approach and alternatives

The overlap coefficient ($$) 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.