Abstract
A new family of probability distributions is defined and applied for modeling symmetric real-life datasets. Some new bivariate type G families using Farlie-Gumbel-Morgenstern copula, modified Farlie-Gumbel-Morgenstern copula, Clayton copula and Renyi's entropy copula are derived. Moreover, some of its statistical properties are presented and studied. Next, the maximum likelihood estimation method is used. A graphical assessment based on biases and mean squared errors is introduced. Based on this assessment, the maximum likelihood method performs well and can be used for estimating the model parameters. Finally, two symmetric real-life applications to illustrate the importance and flexibility of the new family are proposed. The symmetricity of the real data is proved nonparametrically using the kernel density estimation method.