On the Poisson variate with beta prior distribution and a numerical method in estimating the resulting unconditional distribution
Dat, Le Tien
Zweig, Hans J.
Moore, Louis R., III
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A discrete distribution arises from a Poisson distruibution with parameter A, when the distribution of A itself is of the form cA(a-1)(b-A)(B-1) Ae(C,b), where o is sa scaling factor and a,B,b are strictly positive parameters. However, the functional for of the resulting unconditional distribution is not particularly tractable, hence the study of the statistical properties of the unconditional distribution is limited in the study of its mean and its variance. In regards to the modeling of a real situation, an estimation procedure of the parameters involved in cA(a-1)(b-A) (B-1) is discussed and a closed form of the probability distribution is derived. In addition, when accuracy is desired a numerical analysis of the probability distribution is also presented. The development of the results is continued in Appendix A, as a preparation in computerizing the calculation. Finally, an application to real data is discussed for the purpose of illustrating the model.
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