ABSTRACT
This chapter discusses families of distributions which are defined through functional form assumption, either on density function, or on characteristic function, or invariance property. These families of distributions were defined by Marshall and Olkin, and Sivazlian. They include Dirichlet distributions, and have found applications in compositional data, and life time data. The chapter discusses some properties of these distributions. It presents the matrix variate generalizations of these families, and thus begins by defining matrix variate spherical distribution studied by Dawid and Fang and Chen. The chapter examines the stochastic representation of spherical distribution. The class of matrix variate spherical distributions studied here are generalizations of multivariate spherical distributions. There are several other classes of matrix variate generalizations of multivariate spherical distributions studied by Jensen and Good, Fang and Chen and Fang and Anderson.
