In the present paper we study some statistical parameter spaces which have a special role in the information geometry. Both analytical and geometrical representations of each of them are found out. The rotational surfaces of constant negative Gauss curvature are also considered and parametrically represented. We prove that the pseudo-sphere is actually a particular case of all of those surfaces. The pseuso-sphere is used for characterizing the statistical parameter spaces constituted by the normal, the exponential and the logistic density functions. A comparative representation of these three parameter spaces is given as well.