Asymptotic Distribution of Certain Types of Entropy under the Multinomial Law

Author:

Rey Andrea A.1ORCID,Frery Alejandro C.2ORCID,Lucini Magdalena3ORCID,Gambini Juliana4ORCID,Chagas Eduarda T. C.5ORCID,Ramos Heitor S.5ORCID

Affiliation:

1. Signal and Image Processing Center, Universidad Tecnológica Nacional, Ciudad Autónoma de Buenos Aires C1179AAQ, Argentina

2. School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand

3. Department of Mathematics, FaCENA, Universidad Nacional del Nordeste and CONICET, Corrientes W3400AYY, Argentina

4. CIDIA, Universidad Nacional de Hurlingham, Pcia. de Buenos Aires Argentina—CPSI Universidad Tecnológica Nacional, Buenos Aires C1041AAJ, Argentina

5. Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, Belo Horizonte 31270-901, Brazil

Abstract

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 χ2 test.

Funder

Victoria University of Wellington

Fundação de Amparo à Pesquisa do Estado de São Paulo

Fundação de Amparo à Pesquisa do Estado de Minas Gerais

Publisher

MDPI AG

Subject

General Physics and Astronomy

Reference24 articles.

1. Johnson, N.L., Kotz, S., and Balakrishnan, N. (1997). Discrete Multivariate Distributions, Wiley-Interscience.

2. Links between entropy, complexity, and the technological singularity;Modis;Technol. Forecast. Soc. Chang.,2022

3. A test for comparing diversities based on the Shannon formula;Hutcheson;J. Theor. Biol.,1970

4. Some moments of an estimate of Shannon’s measure of information;Hutcheson;Commun. Stat. Theory Methods,1974

5. Entropy computations via analytic depoissonization;Jacquet;IEEE Trans. Inf. Theory,1999

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