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

1
Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
2
Department of Statistics, College of Sciences, Shiraz University, Shiraz 71946 85115, Iran
3
Departamento de Evaluación de Pesquerías, Instituto de Fomento Pesquero, Valparaíso 2361827, Chile
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 403; https://doi.org/10.3390/math7050403
Received: 19 March 2019 / Revised: 25 April 2019 / Accepted: 2 May 2019 / Published: 6 May 2019
(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics)
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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. View Full-Text
Keywords: Skew-Reflected-Gompertz distribution; Gompertz distribution; entropy; Kullback–Leibler divergence; sea surface temperature Skew-Reflected-Gompertz distribution; Gompertz distribution; entropy; Kullback–Leibler divergence; sea surface temperature
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Contreras-Reyes, J.E.; Maleki, M.; Devia Cortés, D. Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records. Mathematics 2019, 7, 403.

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