Theory on a new bivariate trigonometric Gaussian distribution

The main contribution of this article is the introduction of a new bivariate distribution, referred to as the bivariate cosine Gaussian   distribution. We develop its theoretical framework, deriving the marginal and conditional distributions, and analyzing the independence properties of the components of the associated random vector. A graphical study is provided to illustrate the behavior of various types of probability density functions, and a simulation procedure for generating samples from the distribution is also described. Together, these results establish the theoretical foundations for potential applications of the bivariate cosine Gaussian   distribution in two-dimensional modeling.