Abstract
Section 3.3 of “Contreras-Reyes, J.E.; Cortés, D.D. Bounds on Rényi and Shannon Entropies for Finite Mixtures of Multivariate Skew-Normal Distributions: Application to Swordfish (Xiphias gladius Linnaeus). Entropy 2016, 18, 382” contains errors. Therefore, this section is retracted. However, these changes do not influence the conclusions and the other results of the paper.
Highlights
The authors were not aware of one error made in the proofreading phase; we wish to make the following correction to this paper [1]: On Equation (14), the multinomial (MN) theorem is considered [2] to obtain p(y; θ, π)αdy =
MN theorem can not be considered for the approximation of the Rényi entropy for any finite mixture, with αth-order satisfying 0 < α < ∞ and α = 1
On pages 6–8, Section 3.3 must not be considered by the readers that need an approximation of Rényi entropy for a finite mixture of skew-normals or other densities
Summary
The authors were not aware of one error made in the proofreading phase; we wish to make the following correction to this paper [1]: On Equation (14), the multinomial (MN) theorem is considered [2] to obtain p(y; θ , π)αdy = [πi i=1 f (y; θi )]ki dy under the condition with A = {ki ∈ N : ki > 0, ∑im=1 ki = α; i = 1, . Given that integral in (1) is based on the αth-order Rényi entropy on variable y: Rα[Y; θ , π]
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