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Open AccessArticle

Multivariate Skew-Power-Normal Distributions: Properties and Associated Inference

1
Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería 230002, Colombia
2
Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078970, RN, Brazil
3
Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(12), 1509; https://doi.org/10.3390/sym11121509
Received: 8 November 2019 / Revised: 4 December 2019 / Accepted: 7 December 2019 / Published: 12 December 2019
The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution, we extend the univariate power-normal distribution to the multivariate setup. Structural properties of the new multivariate distributions are established. We consider the maximum likelihood method to estimate the unknown parameters, and the observed and expected Fisher information matrices are also derived. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes. View Full-Text
Keywords: distribution theory; maximum likelihood estimation; multivariate models; parametric inference; skewed distributions distribution theory; maximum likelihood estimation; multivariate models; parametric inference; skewed distributions
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Martínez-Flórez, G.; Lemonte, A.J.; Salinas, H.S. Multivariate Skew-Power-Normal Distributions: Properties and Associated Inference. Symmetry 2019, 11, 1509.

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