ABSTRACT
The beta distribution is very much used in Bayesian statistics, mainly as a prior distribution for either a proportion, or the proba bility of occurrence of an event, or the value of any random variable with variation between 0 and 1, such as the coefficient of determi nation or the reliability of a component. But the non-central beta distribution, defined on the unit interval, is less frequently encoun tered. Having a more general expression, and defined on a finite interval of R, is the general beta distribution, which can represent the distribution of a random variable with finite bounds. For this reason, it is encountered in several applications in Engineering and Management Science. However, the Bayesian approach to its study is much more elaborate, and has seen only a limited number of results. Extensions of the beta to vector and matrix variate distributions are receiving increasing attention, and, with the recent advances in computing technology, have found applications in several domains. Their Bayesian treatment seems quite complex at the present time. We will distinguish mainly between the beta typel and beta type2.
