Modelling bivariate astronomical data with multiple components and non-linear relationships.

A common approach towards modelling bivariate scatterplots is decomposition into Gaussian components, i.e. Gaussian mixture modelling. This implicitly assumes linear relationships between the variables within each of the components in the mixture. An alternative, namely dependence modelling by mixtures of copulas, is advocated in this paper. This approach allows separate modelling of the univariate marginal distributions and the dependence which can possibly be non-linear and/or asymmetric. It also accommodates the use of a variety of parametric families for modelling each component and for each variable. The variety of dependence structures can be extended by introducing rotated versions of the copulas. Gaussian mixture modelling on the one hand, and separate modelling of univariate marginal distributions and dependence on the other hand, are illustrated by application to pulsar period – period-derivative observations. Parameter estimation for mixtures of copulas is performed using the method of maximum likelihood and selected copula models are subjected to non-parametric goodness-of-fit testing. [ABSTRACT FROM AUTHOR]