Rad, Najmeh NakhaeiSalehi, MahdiMehrali, YaserChen, Ding-Geng (Din)2025-02-052025-02-052024-11Nakhaei Rad, N.; Salehi, M.; Mehrali, Y.; Chen, D.-G. SkewSymmetric Generalized Normal and Generalized t Distributions. Axioms 2024, 13, 782. https://doi.org/10.3390/axioms13110782.2075-1680 (online)10.3390/axioms13110782http://hdl.handle.net/2263/100549DATA AVAILABITY STATEMENT: Data are contained within the article.This article forms part of a special Issue titled 'Methods and Applications of Advanced Statistical Analysis, 2nd Edition'.In this paper, we introduce the skew-symmetric generalized normal and the skewsymmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively. We derive key distributional properties for these new distributions, including a recurrence relation and an explicit form for the cumulative distribution function (cdf) of the skew-symmetric generalized t distribution. Numerical examples including a simulation study and a real data analysis are presented to illustrate the practical applicability of these distributions.en© 2024 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 (https:// creativecommons.org/licenses/by/ 4.0/).Skew-normal distributionSkew-t distributionGeneralized skew-normal distributionGeneralized skew-t distributionSkew-symmetric distributionsRecurrence relationsSDG-04: Quality educationSDG-09: Industry, innovation and infrastructureArticle