Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm

In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominato...

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Autores principales:	Héctor J. Gómez, Diego I. Gallardo, Karol I. Santoro
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	slash distribution half-normal distribution EM algorithm tpn package Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0f1d1fcf9c404f96a9cd3dbfc4274750
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spelling	oai:doaj.org-article:0f1d1fcf9c404f96a9cd3dbfc42747502021-11-25T19:07:15ZSlash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm10.3390/sym131121642073-8994https://doaj.org/article/0f1d1fcf9c404f96a9cd3dbfc42747502021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2164https://doaj.org/toc/2073-8994In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.Héctor J. GómezDiego I. GallardoKarol I. SantoroMDPI AGarticleslash distributionhalf-normal distributionEM algorithmtpn packageMathematicsQA1-939ENSymmetry, Vol 13, Iss 2164, p 2164 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	slash distribution half-normal distribution EM algorithm tpn package Mathematics QA1-939
spellingShingle	slash distribution half-normal distribution EM algorithm tpn package Mathematics QA1-939 Héctor J. Gómez Diego I. Gallardo Karol I. Santoro Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm
description	In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.
format	article
author	Héctor J. Gómez Diego I. Gallardo Karol I. Santoro
author_facet	Héctor J. Gómez Diego I. Gallardo Karol I. Santoro
author_sort	Héctor J. Gómez
title	Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm
title_short	Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm
title_full	Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm
title_fullStr	Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm
title_full_unstemmed	Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm
title_sort	slash truncation positive normal distribution and its estimation based on the em algorithm
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/0f1d1fcf9c404f96a9cd3dbfc4274750
work_keys_str_mv	AT hectorjgomez slashtruncationpositivenormaldistributionanditsestimationbasedontheemalgorithm AT diegoigallardo slashtruncationpositivenormaldistributionanditsestimationbasedontheemalgorithm AT karolisantoro slashtruncationpositivenormaldistributionanditsestimationbasedontheemalgorithm
_version_	1718410260269498368

Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm

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