Journal
ENTROPY
Volume 18, Issue 11, Pages -Publisher
MDPI
DOI: 10.3390/e18110382
Keywords
skew-normal; frinite mixtures; Shannon entropy; Renyi entropy; swordfish
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Funding
- Comision Nacional de Investigacion Cientifico y Tecnologico (CONICYT, Santiago, Chile) [21160618, 4128/2016]
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Mixture models are in high demand for machine-learning analysis due to their computational tractability, and because they serve as a good approximation for continuous densities. Predominantly, entropy applications have been developed in the context of a mixture of normal densities. In this paper, we consider a novel class of skew-normal mixture models, whose components capture skewness due to their flexibility. We find upper and lower bounds for Shannon and Renyi entropies for this model. Using such a pair of bounds, a confidence interval for the approximate entropy value can be calculated. In addition, an asymptotic expression for Renyi entropy by Stirling's approximation is given, and upper and lower bounds are reported using multinomial coefficients and some properties and inequalities of L-p metric spaces. Simulation studies are then applied to a swordfish (Xiphias gladius Linnaeus) length dataset.
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