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On the Use of Variability Measures to Analyze Source Coding Data Based on the Shannon Entropy

Author

Listed:
  • Helio M. de Oliveira

    (Department of Statistics, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, Brazil)

  • Raydonal Ospina

    (Department of Statistics, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, Brazil
    Department of Statistics, IME, Universidade Federal da Bahia, Salvador 40170-110, Brazil)

  • Carlos Martin-Barreiro

    (Faculty of Natural Sciences and Mathematics, Escuela Superior Politécnica del Litoral (ESPOL), Guayaquil 090902, Ecuador
    Faculty of Engineering, Universidad Espíritu Santo, Samborondón 0901952, Ecuador)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Christophe Chesneau

    (Department of Mathematics, Université de Caen-Normandie, 14 032 Caen, France)

Abstract

Source coding maps elements from an information source to a sequence of alphabetic symbols. Then, the source symbols can be recovered exactly from the binary units. In this paper, we derive an approach that includes information variation in the source coding. The approach is more realistic than its standard version. We employ the Shannon entropy for coding the sequences of a source. Our approach is also helpful for short sequences when the central limit theorem does not apply. We rely on a quantifier of the information variation as a source. This quantifier corresponds to the second central moment of a random variable that measures the information content of a source symbol; that is, considering the standard deviation. An interpretation of typical sequences is also provided through this approach. We show how to use a binary memoryless source as an example. In addition, Monte Carlo simulation studies are conducted to evaluate the performance of our approach. We apply this approach to two real datasets related to purity and wheat prices in Brazil.

Suggested Citation

  • Helio M. de Oliveira & Raydonal Ospina & Carlos Martin-Barreiro & Víctor Leiva & Christophe Chesneau, 2023. "On the Use of Variability Measures to Analyze Source Coding Data Based on the Shannon Entropy," Mathematics, MDPI, vol. 11(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:293-:d:1026782
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    References listed on IDEAS

    as
    1. Camilo Lillo & Víctor Leiva & Orietta Nicolis & Robert G. Aykroyd, 2018. "L-moments of the Birnbaum–Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 187-209, January.
    2. Iuliana Iatan & Mihăiţă Drăgan & Silvia Dedu & Vasile Preda, 2022. "Using Probabilistic Models for Data Compression," Mathematics, MDPI, vol. 10(20), pages 1-29, October.
    3. Marco Riquelme & V�ctor Leiva & Manuel Galea & Antonio Sanhueza, 2011. "Influence diagnostics on the coefficient of variation of elliptically contoured distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 513-532, November.
    Full references (including those not matched with items on IDEAS)

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