Inference on Overlap for Two Inverse Gaussian Populations: Equal Means Case

Abstract

The inverse Gaussian distribution is often suited for modeling positive and/or positively skewed data (see Chhikara and Folks, 1989) and presents an interesting alternative to the Gaussian model in such cases. We note here that overlap coefficients and their variants are widely studied in the literature for Gaussian populations (see Mishra, 1994, 2000, and references therein for further details). This article studies the properties and addresses point estimation for large samples of commonly used measures of overlap when the populations are described by inverse Gaussian distributions. The bias and mean square error properties of the estimators are studied through a simulation study.

Numerical Integral Approximation to Estimate Matusita Overlapping Coefficient for Normal Distributions

“…The problem of estimating the OVL coefficients for other densities have been addressed in the literature. For example, see [7,8,9,10,11,12,13].…”

Inference on the overlap coefficient: The binormal approach and alternatives

“…23 , a major reason why OVL has not been widely used in practice is partially due to the lack of methods for confidence interval (CI) estimation. In most of the existing literature, parametric methods 12,[25][26][27]14,[28][29][30] have not yet been applied to general Gaussian (i.e. without equal mean or equal variance assumptions) or mixture Gaussian distributions, while non-parametric methods only focused on the point estimator for the cases with large sample sizes 7,31,14,32 .…”