Title: Counting Distributions with Recursion of Higher Order
Abstract: Chapter 2 circled around various forms of the recursion $$p(n)=\biggl(a+\frac{b}{n}\biggr)p(n-1)$$ for a distribution p on the non-negative integers. In the present chapter, we extend this recursion to $$p(n)=\sum_{i=1}^{k}\biggl(a(i)+\frac{b(i)}{n}\biggr)p(n-i),$$ and we study compound distributions where the counting distribution satisfies various forms of this recursion. A central part of the chapter is devoted to discussion of the properties of distributions that satisfy this recursion for n=1,2,…. Finally, we consider a recursion that can be applied for compound distributions when the generating function of the counting distribution is rational.
Publication Year: 2009
Publication Date: 2009-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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