Circular and spherical projected Cauchy distributions

Two new distributions are proposed: the circular projected and the spherical projected Cauchy distributions. A special case of the circular projected Cauchy coincides with the wrapped Cauchy distribution, and for this, a generalization is suggested that offers better fit via the inclusion of an extra parameter. For the spherical case, by imposing two conditions on the scatter matrix we end up with an elliptically symmetric distribution. All distributions allow for a closed-form normalizing constant and straightforward random values generation, while their parameters can be estimated via maximum likelihood. The bias of the estimated parameters is assessed via numerical studies, while exhibitions using real data compare them further to some existing models indicating better fits.