Wagener, MatthiasBekker, Andriette, 1958-Arashi, Mohammad2022-05-242022-05-242021-10-20Wagener, M.; Bekker, A.; Arashi, M. Mastering the Body and Tail Shape of a Distribution. Mathematics 2021, 9, 2648. https://DOI.org/ 10.3390/math9212648.2227-739010.3390/math9212648https://repository.up.ac.za/handle/2263/85643The 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© 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.Body-tailFinite mixtureAutoregressiveNormalGeneralizedKurtosisMaximum likelihoodMaximum product spacingStock returnsWind speedBody-tail generalized normal (BTGN)Article