Mastering the body and tail shape of a distribution

Show simple item record Wagener, Matthias Bekker, Andriette, 1958- Arashi, Mohammad 2022-05-24T08:52:12Z 2022-05-24T08:52:12Z 2021-10-20
dc.description.abstract 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. en_US
dc.description.department Statistics en_US
dc.description.librarian am2022 en_US
dc.description.sponsorship The 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.uri en_US
dc.identifier.citation Wagener, M.; Bekker, A.; Arashi, M. Mastering the Body and Tail Shape of a Distribution. Mathematics 2021, 9, 2648. 10.3390/math9212648. en_US
dc.identifier.issn 2227-7390
dc.identifier.other 10.3390/math9212648
dc.language.iso en en_US
dc.publisher MDPI en_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.subject Body-tail en_US
dc.subject Finite mixture en_US
dc.subject Autoregressive en_US
dc.subject Normal en_US
dc.subject Generalized en_US
dc.subject Kurtosis en_US
dc.subject Maximum likelihood en_US
dc.subject Maximum product spacing en_US
dc.subject Stock returns en_US
dc.subject Wind speed en_US
dc.subject Body-tail generalized normal (BTGN) en_US
dc.title Mastering the body and tail shape of a distribution en_US
dc.type Article en_US

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