Accession Number : AD0660508

Title :   COMPOSITION LIMIT THEOREMS FOR PROBABILITY GENERATING FUNCTIONS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Church,J. D.

Report Date : MAR 1967

Pagination or Media Count : 41

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)

Descriptors :   (*FUNCTIONS(MATHEMATICS), PROBABILITY), (*SEQUENCES(MATHEMATICS), THEOREMS), RANDOM VARIABLES, CONVERGENCE, STOCHASTIC PROCESSES, EXPONENTIAL FUNCTIONS, SERIES(MATHEMATICS)

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE