On the conditional noncentral beta distribution

Abstract

The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easiness of interpretation and versatility in modeling different types of data. However, the flexibility of its density at the endpoints of the support is poor enough to prevent from properly modeling the data portions having values next to zero and one. Such a drawback can be overcome by resorting to the class of the noncentral beta distributions. Indeed, the latter allows the density to take on arbitrary positive and finite limits which have a really simple form. Nevertheless, the analytical and mathematical complexity of this distribution poses strong limitations on its use as a model for data on the real interval (0, 1). That said, an in‐depth study of a newly found analogue of the noncentral beta distribution is carried out in this article. The latter preserves the applicative potential of the standard noncentral beta class but with the advantage of showing a more straightforward and easily handleable density.