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Journal of Applied Mathematics, Statistics and Informatics

The Journal of University of Saint Cyril and Metodius

Editor-in-Chief: Kvasnicka, Vladimír

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Sequences of Inequalities Among Differences of Gini Means and Divergence Measures

Inder J. Taneja
  • Departamento de Matemática Universidade Federal de Santa Catarina 88.040-900 Florianópolis, SC, Brazil, http://www.mtm.ufsc.br/~taneja
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Published Online: 2013-04-13 | DOI: https://doi.org/10.2478/v10294-012-0014-2


In 1938, Gini [3] studied a mean having two parameters. Later, many authors studied properties of this mean. In particular, it contains the famous means as harmonic, geometric, arithmetic, etc. Here we considered a sequence of inequalities arising due to particular values of each parameter of Gini’s mean. This sequence generates many nonnegative differences. Not all of them are convex. We have established new sequences of inequalities of these differences. Some refinement inequalities are also presented. Considering in terms of probability distributions these differences, we have made connections with some well known divergence measures.

Additional Key Words and Phrases: Arithmetic mean; Geometric Mean; Harmonic Mean; Gini Mean; Power Mean; Differences of Means; Divergence measures

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About the article

Published Online: 2013-04-13

Published in Print: 2012-12-01

Citation Information: Journal of Applied Mathematics, Statistics and Informatics, Volume 8, Issue 2, Pages 49–65, ISSN (Print) 1336-9180, DOI: https://doi.org/10.2478/v10294-012-0014-2.

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