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Open AccessArticle

An Asymmetric Distribution with Heavy Tails and Its Expectation–Maximization (EM) Algorithm Implementation

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Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
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Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
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Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
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Author to whom correspondence should be addressed.
Symmetry 2019, 11(9), 1150; https://doi.org/10.3390/sym11091150
Received: 8 August 2019 / Revised: 31 August 2019 / Accepted: 2 September 2019 / Published: 10 September 2019
In this paper we introduce a new distribution constructed on the basis of the quotient of two independent random variables whose distributions are the half-normal distribution and a power of the exponential distribution with parameter 2 respectively. The result is a distribution with greater kurtosis than the well known half-normal and slashed half-normal distributions. We studied the general density function of this distribution, with some of its properties, moments, and its coefficients of asymmetry and kurtosis. We developed the expectation–maximization algorithm and present a simulation study. We calculated the moment and maximum likelihood estimators and present three illustrations in real data sets to show the flexibility of the new model. View Full-Text
Keywords: slashed half-normal distribution; kurtosis; likelihood; EM algorithm slashed half-normal distribution; kurtosis; likelihood; EM algorithm
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Olmos, N.M.; Venegas, O.; Gómez, Y.M.; Iriarte, Y.A. An Asymmetric Distribution with Heavy Tails and Its Expectation–Maximization (EM) Algorithm Implementation. Symmetry 2019, 11, 1150.

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