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Asymptotic distribution of the statistical complexity under the multinomial law

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  • Rey, Andrea
  • Frery, Alejandro C.
  • Gambini, Juliana

Abstract

The Statistical Complexity is a feature computed from a probability function that aims to quantify the structure of the system that produced the observations. It is the product between the normalized Shannon Entropy and the normalized Jensen–Shannon distance between the probability function and the uniform law. We obtain the Statistical Complexity asymptotic distribution under the Multinomial model, and we validate this result with numerical experiments. We present examples where this asymptotic result provides a good approximation, even in scenarios where the Multinomial model is not strictly valid, such as in applications to Bandt and Pompe ordinal patterns. We provide the R code that implements these functions.

Suggested Citation

  • Rey, Andrea & Frery, Alejandro C. & Gambini, Juliana, 2025. "Asymptotic distribution of the statistical complexity under the multinomial law," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925000980
    DOI: 10.1016/j.chaos.2025.116085
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    References listed on IDEAS

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    1. Rey, Andrea & Frery, Alejandro C. & Gambini, Juliana & Lucini, Magdalena, 2024. "Asymptotic distribution of entropies and Fisher information measure of ordinal patterns with applications," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    2. Eduarda T. C. Chagas & Marcelo Queiroz‐Oliveira & Osvaldo A. Rosso & Heitor S. Ramos & Cristopher G. S. Freitas & Alejandro C. Frery, 2022. "White Noise Test from Ordinal Patterns in the Entropy–Complexity Plane," International Statistical Review, International Statistical Institute, vol. 90(2), pages 374-396, August.
    3. Helmut Elsinger, 2010. "Independence Tests based on Symbolic Dynamics," Working Papers 165, Oesterreichische Nationalbank (Austrian Central Bank).
    4. Lamberti, P.W & Martin, M.T & Plastino, A & Rosso, O.A, 2004. "Intensive entropic non-triviality measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 119-131.
    5. Martin, M.T. & Plastino, A. & Rosso, O.A., 2006. "Generalized statistical complexity measures: Geometrical and analytical properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 439-462.
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    1. Usatenko, Oleg V. & Pritula, Galyna M., 2026. "Information temperature as a measure of complexity of random symbolic sequences," Chaos, Solitons & Fractals, Elsevier, vol. 202(P1).

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