Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series
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Departamento de Estadística, Pontificia Universidad Católica de Chile, Santiago 7820436, Chile
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Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso 2390123, Chile
3
Departamento de Evaluación de Recursos, División de Investigación Pesquera, Instituto de Fomento Pesquero (IFOP), Valparaíso 2361827, Chile
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Instituto de Estadística, Universidad de Valparaíso, Valparaíso 2360102, Chile
5
Institute of Applied Statistics, Johannes Kepler University Linz, Linz 4040, Austria
6
Linz Institute of Technology, Johannes Kepler University Linz, Linz 4040, Austria
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(10), 528; https://doi.org/10.3390/e19100528
Received: 7 September 2017
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Revised: 28 September 2017
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Accepted: 30 September 2017
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Published: 6 October 2017
(This article belongs to the Special Issue Foundations of Statistics)
The problem of measuring the disparity of a particular probability density function from a normal one has been addressed in several recent studies. The most used technique to deal with the problem has been exact expressions using information measures over particular distributions. In this paper, we consider a class of asymmetric distributions with a normal kernel, called Generalized Skew-Normal (GSN) distributions. We measure the degrees of disparity of these distributions from the normal distribution by using exact expressions for the GSN negentropy in terms of cumulants. Specifically, we focus on skew-normal and modified skew-normal distributions. Then, we establish the Kullback–Leibler divergences between each GSN distribution and the normal one in terms of their negentropies to develop hypothesis testing for normality. Finally, we apply this result to condition factor time series of anchovies off northern Chile.
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Keywords:
Shannon entropy; negentropy; skew-normal; modified skew-normal; Kullback–Leibler divergence; condition factor
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MDPI and ACS Style
Arellano-Valle, R.B.; Contreras-Reyes, J.E.; Stehlík, M. Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series. Entropy 2017, 19, 528. https://doi.org/10.3390/e19100528
AMA Style
Arellano-Valle RB, Contreras-Reyes JE, Stehlík M. Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series. Entropy. 2017; 19(10):528. https://doi.org/10.3390/e19100528
Chicago/Turabian StyleArellano-Valle, Reinaldo B., Javier E. Contreras-Reyes, and Milan Stehlík. 2017. "Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series" Entropy 19, no. 10: 528. https://doi.org/10.3390/e19100528
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