On a class of symmetric distributions associated with the product of two correlated t variables

This article introduces a class of symmetric non-Gaussian distributions associated with the product of two correlated t variables. The distributions are obtained from the conditioning method. They are symmetric, possibly bimodal, and the marginal distributions of a nonlinearly truncated bivariate Student tν-distribution. The class is studied from several aspects, such as association with other distributions, nonlinear selection mechanism, and scale mixture scheme. The relationships among these aspects are given, and various properties of the class are also considered. Bayesian estimation of the class is discussed and three applications utilizing the class of distributions are also provided.