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An Asymptotic Test for Bimodality Using The Kullback–Leibler Divergence

Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4030000, Chile
Symmetry 2020, 12(6), 1013; https://doi.org/10.3390/sym12061013
Received: 16 May 2020 / Revised: 1 June 2020 / Accepted: 9 June 2020 / Published: 16 June 2020
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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. View Full-Text
Keywords: bimodality; bimodal skew-symmetric normal distribution; Kullback–Leibler divergence; Shannon entropy; sea surface temperature bimodality; bimodal skew-symmetric normal distribution; Kullback–Leibler divergence; Shannon entropy; sea surface temperature
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Contreras-Reyes, J.E. An Asymptotic Test for Bimodality Using The Kullback–Leibler Divergence. Symmetry 2020, 12, 1013.

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