Family of Generalized Symmetric Distributions: Properties and Applications

Generalized distributions are useful for applied statisticians, and some of the populardistributions can be extended in several ways. In this study, we introduce a new familyof generalized symmetric distributions called the generalized symmetricT-R{Y}class.We use the quantile function of a generalized Weibull distribution to construct thisclass, and derive some of its properties, including explicit expressions for the quantilefunction, Shannon entropy, moments, and mean deviation. We also derive a general-izedt-student distribution as a special member of the generalized family by takingthet-student and exponential distributions forRandT, respectively, and investigateits properties. This distribution can be symmetric, left-skewed, or right-skewed. Wedemonstrate the usefulness of the generated distribution and its regression model byapplying them to three datasets.