NEW CONDITIONS FOR CENTRAL LIMIT THEOREMS
RAND CORP SANTA MONICA CA
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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.
- Statistics and Probability