Study of a new bivariate trigonometric Gaussian distribution

Abstract

This article introduces a new bivariate distribution derived by extending the standard independent Gaussian framework with trigonometric components. The proposed distribution, known as the bivariate trigonometric Gaussian distribution, enhances the classical Gaussian distribution structure while maintaining key analytical tractability. We outline its key theoretical properties, including the explicit forms of the marginal distributions and several structural characteristics of the joint probability density function. Graphical illustrations highlight the influence of the trigonometric parameters on the shapes of the distributions. Finally, we demonstrate the practical value of this theoretical framework by analyzing a real-world turbine dataset. Our findings demonstrate the empirical superiority of the bivariate trigonometric Gaussian distribution over classical distributions when it comes to fitting complex, nonlinear physical phenomena.