Some Angular-Linear Distributions and Related Regression Models

Parametric models are proposed for the joint distribution of bivariate random variables when one variable is directional and one is scalar. These distributions are developed on the basis of the maximum entropy principle and by the specification of the marginal distributions. The properties of these distributions and the statistical analysis of regression models based on these distributions are explored. One model is extended to several variables in a form that justifies the use of least squares for estimation of parameters, conditional on the observed angles.