The Beta Distribution is almost exclusively used for situations, after range normalization, wherein a continuous random variable is defined on the closed range [0, 1]. Since the beta distribution is intrinsically a two parameter distribution, this creates problems in some applications where specification of more than one parameter is difficult. In this note, two new classes of single parameter continuous probability distributions on a closed interval are introduced. These distributions remove some of the theoretical and practical problems of using the Beta Distribution for applications. The Burr Type XI Distribution has desirable characteristics for many applications especially when there is ambiguity in the definition of the specified parameter.