Asymptotic Distribution of Certain Types of Entropy under the Multinomial Law.

Rey, Andrea A; Frery, Alejandro C; Lucini, Magdalena; Gambini, Juliana; Chagas, Eduarda T C; Ramos, Heitor S

Rey, Andrea A; Frery, Alejandro C; Lucini, Magdalena; Gambini, Juliana; Chagas, Eduarda T C; Ramos, Heitor S.

Afiliação

Rey AA; Signal and Image Processing Center, Universidad Tecnológica Nacional, Ciudad Autónoma de Buenos Aires C1179AAQ, Argentina.
Frery AC; School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand.
Lucini M; Department of Mathematics, FaCENA, Universidad Nacional del Nordeste and CONICET, Corrientes W3400AYY, Argentina.
Gambini J; CIDIA, Universidad Nacional de Hurlingham, Pcia. de Buenos Aires Argentina-CPSI Universidad Tecnológica Nacional, Buenos Aires C1041AAJ, Argentina.
Chagas ETC; Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, Belo Horizonte 31270-901, Brazil.
Ramos HS; Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, Belo Horizonte 31270-901, Brazil.

Entropy (Basel) ; 25(5)2023 Apr 28.

Article em En | MEDLINE | ID: mdl-37238489

RESUMO

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.

Palavras-chave

asymptotic distributions; entropy; hypothesis tests; multinomial distribution

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Texto completo: 1 Coleções: 01-internacional Base de dados: MEDLINE Idioma: En Revista: Entropy (Basel) Ano de publicação: 2023 Tipo de documento: Article País de afiliação: Argentina País de publicação: Suíça

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