Binomial mixtures with continous mixing priors

Abstract

In this work, we consider a class of mixture distributions generated by randomizing the success parameter p of a Binomial distribution. We derive the density functions of the mixture distributions, and in some cases, give their simple properties, such as the mean and variance. We also derive the density functions of mixing distributions that may be new to the reader. This is important because these densities are then used in the mixing procedure. The reader can then follow through with the process and calculations therein. We find that the Beta distribution is a most tractable mixer for the Binomial, and therefore dedicate a whole Chapter to various Beta generalizations in the unit interval, and their derived Binomial mixtures. Chapter three then looks at viable alternatives to the Beta in this regard. The remaining Chapters are dedicated to various transformations that enable us to move beyond the unit interval in which the parameter p is restricted. A summary of our findings and further areas of research is given in Chapter eight.