A new two-parameter family of continuous univariate distributions on the interval (– 1, 1) is introduced, and some properties are given. It is shown that parameters θ andvare globally orthogonal in the Fisher information sense and that, to some extent, they have the properties of a location parameter and a precision parameter, respectively. A pivotal statistic is constructed whose distribution is independent of the location parameter. Finally, the connection with ultraspherical functions and Brownian motion is described.