COMPOSITION LIMIT THEOREMS FOR PROBABILITY GENERATING FUNCTIONS.
Abstract
Let (f sub k), k = 1 to k = infinity be any sequence of probability generating functions. It is established that sequential composition in the order f sub 1 (f sub 2(...(f sub k)...)) generates a convergent sequence of functions, and that composition in the order f sub k (f sub (k-1)(...(f sub 1)...)) generates a sequence of functions which converges when the values at zero converge. Properties of the limit functions are related to properties of (f sub k), k = 1 to k = infinity. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1967
- Accession Number
- AD0660508
Entities
People
- J. D. Church
Organizations
- University of Wisconsin–Madison