LUCINI Maria magdalena
Asymptotic Distribution of Certain Types of Entropy under the Multinomial Law
REY, ANDREA; FRERY, ALEJANDRO CESAR; LUCINI, MARÍA MAGDALENA; GAMBINI, JULIANA
MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI
Lugar: Basel; Año: 2023 vol. 25
We obtain expressions for the asymptotic distributions of the Rényi and Tsallis of order q entropies and Fisher information when computed on the maximum likelihood estimator of probabilities from multinomial random samples. We verify that these asymptotic models, two of which (Tsallis and Fisher) are normal, describe well a variety of simulated data. In addition, we obtain test statistics for comparing (possibly different types of) entropies from two samples without requiring the same number of categories. Finally, we apply these tests to social survey data and verify that the results are consistent but more general than those obtained with a x2 test.