Mastering the body and tail shape of a distribution

dc.contributor.authorWagener, Matthias
dc.contributor.authorBekker, Andriette, 1958-
dc.contributor.authorArashi, Mohammad
dc.contributor.emailandriette.bekker@up.ac.zaen_US
dc.date.accessioned2022-05-24T08:52:12Z
dc.date.available2022-05-24T08:52:12Z
dc.date.issued2021-10-20
dc.description.abstractThe 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.en_US
dc.description.departmentStatisticsen_US
dc.description.librarianam2022en_US
dc.description.sponsorshipThe National Research Foundation (NRF) of South Africa; SARChI Research Chair UID: 71199; the University of Pretoria Visiting Professor Programme; and the Ferdowsi University of Mashhad .en_US
dc.description.urihttps://www.mdpi.com/journal/mathematicsen_US
dc.identifier.citationWagener, M.; Bekker, A.; Arashi, M. Mastering the Body and Tail Shape of a Distribution. Mathematics 2021, 9, 2648. https://DOI.org/ 10.3390/math9212648.en_US
dc.identifier.issn2227-7390
dc.identifier.other10.3390/math9212648
dc.identifier.urihttps://repository.up.ac.za/handle/2263/85643
dc.language.isoenen_US
dc.publisherMDPIen_US
dc.rights© 2021 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.en_US
dc.subjectBody-tailen_US
dc.subjectFinite mixtureen_US
dc.subjectAutoregressiveen_US
dc.subjectNormalen_US
dc.subjectGeneralizeden_US
dc.subjectKurtosisen_US
dc.subjectMaximum likelihooden_US
dc.subjectMaximum product spacingen_US
dc.subjectStock returnsen_US
dc.subjectWind speeden_US
dc.subjectBody-tail generalized normal (BTGN)en_US
dc.titleMastering the body and tail shape of a distributionen_US
dc.typeArticleen_US

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