Skew-Reflected-Gompertz information quantifiers with application to sea surface temperature records

Javier E. Contreras-Reyes; Mohsen Maleki; Daniel Devia Cortés

doi:10.3390/math7050403

Skew-Reflected-Gompertz information quantifiers with application to sea surface temperature records

Javier E. Contreras-Reyes, Mohsen Maleki, Daniel Devia Cortés

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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 datawith 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.

Original language	English
Article number	403
Journal	Mathematics
Volume	7
Issue number	5
DOIs	https://doi.org/10.3390/math7050403
State	Published - May 2019
Externally published	Yes

Keywords

Entropy
Gompertz distribution
Kullback-Leibler divergence
Sea surface temperature
Skew-Reflected-Gompertz distribution

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10.3390/math7050403

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title = "Skew-Reflected-Gompertz information quantifiers with application to sea surface temperature records",

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 datawith a high presence of skewness. In this paper, we study information quantifiers such as Shannon and R{\'e}nyi 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.",

keywords = "Entropy, Gompertz distribution, Kullback-Leibler divergence, Sea surface temperature, Skew-Reflected-Gompertz distribution",

author = "Contreras-Reyes, {Javier E.} and Mohsen Maleki and Cort{\'e}s, {Daniel Devia}",

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journal = "Mathematics",

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AU - Contreras-Reyes, Javier E.

AU - Maleki, Mohsen

AU - Cortés, Daniel Devia

PY - 2019/5

Y1 - 2019/5

N2 - 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 datawith 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.

AB - 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 datawith 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.

KW - Entropy

KW - Gompertz distribution

KW - Kullback-Leibler divergence

KW - Sea surface temperature

KW - Skew-Reflected-Gompertz distribution

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Skew-Reflected-Gompertz information quantifiers with application to sea surface temperature records

Abstract

Keywords

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