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

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 kurtosi...

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Veröffentlicht in:Symmetry (Basel) Jg. 11; H. 9; S. 1150
Hauptverfasser: Olmos, Neveka M., Venegas, Osvaldo, Gómez, Yolanda M., Iriarte, Yuri A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.09.2019
Schlagworte:
Algorithms
Asymmetry
Electric power distribution
Independent variables
Kurtosis
Maximization
Maximum likelihood estimators
Normal distribution
Optimization
Probability distribution functions
Quotients
Random variables
Skewed distributions
ISSN:2073-8994, 2073-8994
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Abstract 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.
AbstractList 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.
Author Gómez, Yolanda M.
Olmos, Neveka M.
Venegas, Osvaldo
Iriarte, Yuri A.
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  surname: Venegas
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  givenname: Yolanda M.
  surname: Gómez
  fullname: Gómez, Yolanda M.
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  givenname: Yuri A.
  surname: Iriarte
  fullname: Iriarte, Yuri A.
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Cites_doi 10.1007/s11766-016-3366-3
10.1016/S0167-9473(02)00303-1
10.2991/jsta.2015.14.4.4
10.1007/b98855
10.1214/aos/1176344136
10.1080/02331888.2012.694441
10.1109/TAC.1974.1100705
10.1111/j.2517-6161.1977.tb01600.x
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10.1080/03610920701826088
10.1111/j.1467-9574.1972.tb00191.x
10.1007/s00362-011-0391-4
ContentType Journal Article
Copyright 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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SubjectTerms Algorithms
Asymmetry
Electric power distribution
Independent variables
Kurtosis
Maximization
Maximum likelihood estimators
Normal distribution
Optimization
Probability distribution functions
Quotients
Random variables
Skewed distributions
Title An Asymmetric Distribution with Heavy Tails and Its Expectation–Maximization (EM) Algorithm Implementation
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