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Rényi entropy and complexity measure for skew-gaussian distributions and related families

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  • Contreras-Reyes, Javier E.

Abstract

In this paper, we provide the Rényi entropy and complexity measure for a novel, flexible class of skew-gaussian distributions and their related families, as a characteristic form of the skew-gaussian Shannon entropy. We give closed expressions considering a more general class of closed skew-gaussian distributions and the weighted moments estimation method. In addition, closed expressions of Rényi entropy are presented for extended skew-gaussian and truncated skew-gaussian distributions. Finally, additional inequalities for skew-gaussian and extended skew-gaussian Rényi and Shannon entropies are reported.

Suggested Citation

  • Contreras-Reyes, Javier E., 2015. "Rényi entropy and complexity measure for skew-gaussian distributions and related families," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 84-91.
    • Handle: RePEc:eee:phsmap:v:433:y:2015:i:c:p:84-91
    DOI: 10.1016/j.physa.2015.03.083
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    5. Contreras-Reyes, Javier E., 2014. "Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 200-208.
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    8. Cedric Flecher & Denis Allard & Philippe Naveau, 2010. "Truncated skew-normal distributions: moments, estimation by weighted moments and application to climatic data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 331-345.
    9. Flecher, C. & Naveau, P. & Allard, D., 2009. "Estimating the closed skew-normal distribution parameters using weighted moments," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1977-1984, October.
    10. Liu, Tong & Zhang, Ping & Dai, Wu-Sheng & Xie, Mi, 2012. "An intermediate distribution between Gaussian and Cauchy distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5411-5421.
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    Cited by:

    1. Javier E. Contreras-Reyes & Mohsen Maleki & Daniel Devia Cortés, 2019. "Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records," Mathematics, MDPI, vol. 7(5), pages 1-14, May.
    2. Contreras-Reyes, Javier E., 2021. "Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Rajaram, R. & Castellani, B., 2016. "An entropy based measure for comparing distributions of complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 35-43.
    4. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    5. W. V. Félix de Lima & A. D. C. Nascimento & G. J. A. Amaral, 2021. "Entropy-based pivotal statistics for multi-sample problems in planar shape," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 153-178, March.
    6. Salah H. Abid & Uday J. Quaez & Javier E. Contreras-Reyes, 2021. "An Information-Theoretic Approach for Multivariate Skew- t Distributions and Applications," Mathematics, MDPI, vol. 9(2), pages 1-13, January.

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