Accession Number:

AD0677200

Title:

NEW CONDITIONS FOR CENTRAL LIMIT THEOREMS

Descriptive Note:

Corporate Author:

RAND CORP SANTA MONICA CA

Personal Author(s):

Report Date:

1968-10-01

Pagination or Media Count:

6.0

Abstract:

A general formulation of the central limit problem for sums of independent random variables is given. By assuming the existence of fourth- order moments, one is able to prove new necessary and sufficient conditions for both Normal and Poisson convergence which involve only moments. The proof of the theorem makes use of a characterization of the Normal distribution among infinitely divisible laws which was perhaps first recognized by Borges and later independently by the author.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE