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Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records

Author

Listed:
  • Javier E. Contreras-Reyes

    (Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile)

  • Mohsen Maleki

    (Department of Statistics, College of Sciences, Shiraz University, Shiraz 71946 85115, Iran)

  • Daniel Devia Cortés

    (Departamento de Evaluación de Pesquerías, Instituto de Fomento Pesquero, Valparaíso 2361827, Chile)

Abstract

The Skew-Reflected-Gompertz (SRG) distribution, introduced by Hosseinzadeh et al. (J. Comput. Appl. Math. (2019) 349, 132–141), produces two-piece asymmetric behavior of the Gompertz (GZ) distribution, which extends the positive to a whole dominion by an extra parameter. The SRG distribution also permits a better fit than its well-known classical competitors, namely the skew-normal and epsilon-skew-normal distributions, for data with a high presence of skewness. In this paper, we study information quantifiers such as Shannon and Rényi entropies, and Kullback–Leibler divergence in terms of exact expressions of GZ information measures. We find the asymptotic test useful to compare two SRG-distributed samples. Finally, as a real-world data example, we apply these results to South Pacific sea surface temperature records.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:403-:d:228617
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    References listed on IDEAS

    as
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    2. 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.
    3. Bondon, Pascal, 2009. "Estimation of autoregressive models with epsilon-skew-normal innovations," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1761-1776, September.
    4. Adam Lenart & Trifon I. Missov, 2016. "Goodness-of-fit tests for the Gompertz distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(10), pages 2920-2937, May.
    5. Salicru, M. & Morales, D. & Menendez, M. L. & Pardo, L., 1994. "On the Applications of Divergence Type Measures in Testing Statistical Hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 372-391, November.
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