NEW CONDITIONS FOR CENTRAL LIMIT THEOREMS

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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1968
Accession Number
AD0677200

Entities

People

  • Percy A. Pierre

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Control Systems Engineering
  • Convergence
  • Distribution Functions
  • Engineering
  • Normal Distribution
  • Probability
  • Probability Distribution Functions
  • Probability Distributions
  • Random Variables
  • Step Functions

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.