Recently, analysis of circular data has become a very dynamic development area. This goes from the construction of new probability models that describe this type of data, to the proposal of methods to carry out both frequentist and Bayesian inferences in the proposed models. One approach that has proved attractive for its simplicity in constructing circular distributions is the radial projection method. That consists of radially projecting a bivariate density, defined in \(\mathbb {R}^2\) , onto the unit circle \(\mathbb {S}\) . Although that method of construction is relatively simple, the crucial point is to have families of distributions initially defined in \(\mathbb {R}^2\) that allow generating sufficiently flexible circular densities to describe data on \(\mathbb {S}\) . An additional problem arises when we want to have distributions defined only on a subset of \(\mathbb {S}\) . This chapter presents a new bivariate model defined in \(\mathbb {R}^2\) , as well as the corresponding circular model obtained from its radial projection. It should be mentioned that the projected model obtained is able to describe circular data defined only in the first orthant of \(\mathbb {S}\) and is more flexible than those proposed in the literature. It also shows how to carry out Bayesian inferences for all parameters of the proposed bivariate model and describes some properties of the obtained circular model.