Accession Number : AD0721453

Title :   Nonlinear Extensions of a Limit Theorem,

Corporate Author : PRINCETON UNIV N J DEPT OF ELECTRICAL ENGINEERING

Personal Author(s) : Lugannani,Robert

Report Date : FEB 1971

Pagination or Media Count : 13

Abstract : A sequence of random variables (xn) is given together with centering and normalizing constants (an) and (bn), and it is assumed that the distribution of (xn-an)/bn coverges weakly (as n approaches infinity) to distribution F. The purpose of the present paper is to extend this convergence property to the sequence (V(xn)) where V is a given linear function. Specifically it is desired to find centering and normalizing constants (alpha n) and (beta n) such that the distribution of (V(xn)-alpha n)/beta n converges weakly to a limit G and to evaluate this limit. Sufficient conditions are presented that ensure the existence of the limit G, and it is shown that G is simply related to F. To illustrate the variety of limit laws that can arise, several examples are considered. (Author)

Descriptors :   (*DISTRIBUTION THEORY, THEOREMS), RANDOM VARIABLES, SEQUENCES(MATHEMATICS), PROBABILITY, CONVERGENCE

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE