An asymptotic test for bimodality using the Kullback-Leibler divergence

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.