Generalized distributions are useful for applied statisticians, and some of the popular distributions can be extended in several ways. In this study, we introduce a new family of generalized symmetric distributions called the generalized symmetric T-R \(\{Y\}\) class. We use the quantile function of a generalized Weibull distribution to construct this class, and derive some of its properties, including explicit expressions for the quantile function, Shannon entropy, moments, and mean deviation. We also derive a generalized t-student distribution as a special member of the generalized family by taking the t-student and exponential distributions for R and T, respectively, and investigate its properties. This distribution can be symmetric, left-skewed, or right-skewed. We demonstrate the usefulness of the generated distribution and its regression model by applying them to three datasets.
