Mastering the Body and Tail Shape of a Distribution

The normal distribution and its perturbation have left an immense mark on the statistical literature. Several generalized forms exist to model different skewness, kurtosis, and body shapes. Although they provide better fitting capabilities, these generalizations do not have parameters and formulae w...

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Autores principales:	Matthias Wagener, Andriette Bekker, Mohammad Arashi
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	body-tail finite mixture autoregressive normal generalized kurtosis Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/865efc2b129541849239253dccb326c9
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id	oai:doaj.org-article:865efc2b129541849239253dccb326c9
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spelling	oai:doaj.org-article:865efc2b129541849239253dccb326c92021-11-11T18:13:40ZMastering the Body and Tail Shape of a Distribution10.3390/math92126482227-7390https://doaj.org/article/865efc2b129541849239253dccb326c92021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2648https://doaj.org/toc/2227-7390The normal distribution and its perturbation have left an immense mark on the statistical literature. Several generalized forms exist to model different skewness, kurtosis, and body shapes. Although they provide better fitting capabilities, these generalizations do not have parameters and formulae with a clear meaning to the practitioner on how the distribution is being modeled. We propose a neat integration approach generalization which intuitively gives direct control of the body and tail shape, the body-tail generalized normal (BTGN). The BTGN provides the basis for a flexible distribution, emphasizing parameter interpretation, estimation properties, and tractability. Basic statistical measures are derived, such as the density function, cumulative density function, moments, moment generating function. Regarding estimation, the equations for maximum likelihood estimation and maximum product spacing estimation are provided. Finally, real-life situations data, such as log-returns, time series, and finite mixture modeling, are modeled using the BTGN. Our results show that it is possible to have more desirable traits in a flexible distribution while still providing a superior fit to industry-standard distributions, such as the generalized hyperbolic, generalized normal, tail-inflated normal, and t distributions.Matthias WagenerAndriette BekkerMohammad ArashiMDPI AGarticlebody-tailfinite mixtureautoregressivenormalgeneralizedkurtosisMathematicsQA1-939ENMathematics, Vol 9, Iss 2648, p 2648 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	body-tail finite mixture autoregressive normal generalized kurtosis Mathematics QA1-939
spellingShingle	body-tail finite mixture autoregressive normal generalized kurtosis Mathematics QA1-939 Matthias Wagener Andriette Bekker Mohammad Arashi Mastering the Body and Tail Shape of a Distribution
description	The normal distribution and its perturbation have left an immense mark on the statistical literature. Several generalized forms exist to model different skewness, kurtosis, and body shapes. Although they provide better fitting capabilities, these generalizations do not have parameters and formulae with a clear meaning to the practitioner on how the distribution is being modeled. We propose a neat integration approach generalization which intuitively gives direct control of the body and tail shape, the body-tail generalized normal (BTGN). The BTGN provides the basis for a flexible distribution, emphasizing parameter interpretation, estimation properties, and tractability. Basic statistical measures are derived, such as the density function, cumulative density function, moments, moment generating function. Regarding estimation, the equations for maximum likelihood estimation and maximum product spacing estimation are provided. Finally, real-life situations data, such as log-returns, time series, and finite mixture modeling, are modeled using the BTGN. Our results show that it is possible to have more desirable traits in a flexible distribution while still providing a superior fit to industry-standard distributions, such as the generalized hyperbolic, generalized normal, tail-inflated normal, and t distributions.
format	article
author	Matthias Wagener Andriette Bekker Mohammad Arashi
author_facet	Matthias Wagener Andriette Bekker Mohammad Arashi
author_sort	Matthias Wagener
title	Mastering the Body and Tail Shape of a Distribution
title_short	Mastering the Body and Tail Shape of a Distribution
title_full	Mastering the Body and Tail Shape of a Distribution
title_fullStr	Mastering the Body and Tail Shape of a Distribution
title_full_unstemmed	Mastering the Body and Tail Shape of a Distribution
title_sort	mastering the body and tail shape of a distribution
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/865efc2b129541849239253dccb326c9
work_keys_str_mv	AT matthiaswagener masteringthebodyandtailshapeofadistribution AT andriettebekker masteringthebodyandtailshapeofadistribution AT mohammadarashi masteringthebodyandtailshapeofadistribution
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Mastering the Body and Tail Shape of a Distribution

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