Theory on a new bivariate trigonometric Gaussian distribution
Christophe Chesneau
Abstract
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.
Topics & Concepts
MathematicsBivariate analysisGaussianIndependence (probability theory)Marginal distributionApplied mathematicsConditional probability distributionNormal-gamma distributionJoint probability distributionTrigonometric functionsDistribution (mathematics)Multivariate normal distributionConditional independenceProbability density functionGaussian random fieldProbability distributionRandom variableDifferentiation of trigonometric functionsTrigonometryStatisticsStatistical physicsGaussian processGeneralized inverse Gaussian distributionAlgorithmStatistical Distribution Estimation and ApplicationsBayesian Methods and Mixture Models