Kappa-Cover: a novel asymmetric comparison of distributions

A novel approach for comparing distributions is introduced. This approach is inspired by a frequently occurring problem in the development of generic drugs, namely the comparison of a test distribution to a reference distribution in the absence of additional information. A theoretical framework for such comparisons of distributions is presented, which is based on the proposed concept of kappa-cover. Assuming normal distributions, a statistical test termed covering-test is suggested. The covering-test is an extension of an existing approach that compares two quantiles by using a generalized test variable. The extension makes it possible to maintain the desired size when carrying out two such quantile comparisons simultaneously, despite the resulting multiple testing issue. Simulations indicate that this extended test possesses desirable statistical properties. To demonstrate the usefulness of the suggested concept, the proposed test is applied to a data set from the pharmaceutical industry. Since it is often important in pharmaceutical research to include information on tolerances in the comparison of drugs, it is also shown that the concept presented can be adapted to such a situation.