An Asymptotic Test for Bimodality Using The Kullback–Leibler Divergence

Abstract

Detecting bimodality of a frequency distribution is of considerable interest in several fields. Classical inferential methods for detecting bimodality focused in third and fourth moments through the kurtosis measure. Nonparametric approach-based asymptotic tests (DIPtest) for comparing the empirical distribution function with a unimodal one are also available. The latter point drives this paper, by considering a parametric approach using the bimodal skew-symmetric normal distribution. This general class captures bimodality, asymmetry and excess of kurtosis in data sets. The Kullback–Leibler divergence is considered to obtain the statistic’s test. Some comparisons with DIPtest, simulations, and the study of sea surface temperature data illustrate the usefulness of proposed methodology.