A NON-ELEMENTARY PROOF BY DIFFERENTIAL EQUATION FOR THE CENTRAL LIMIT THEOREM

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KORKMAZ A., Onemli M. B.

PAKISTAN JOURNAL OF STATISTICS, vol.29, no.3, pp.307-313, 2013 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 29 Issue: 3
  • Publication Date: 2013
  • Journal Name: PAKISTAN JOURNAL OF STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.307-313
  • Keywords: Central Limit Theorem, Elementary Proof, Non-Elementary Proof
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

The proofs of the central limit theorem are divided into two categories: elementary
and non-elementary. Proofs using the characteristic function are called non-elementary
while the other proofs are called elementary. Using differential equation, this paper gives
a new non-elementary proof for the central limit theorem. This proof is based on a
differential equation and does not use second order Taylor expansion of any characteristic function. It is apparent that given proof may only have a pedagogical importance.

The proofs of the central limit theorem are divided into two categories: elementary and non-elementary. Proofs using the characteristic function are called non-elementary while the other proofs are called elementary. Using differential equation, this paper gives a new non-elementary proof for the central limit theorem. This proof is based on a differential equation and does not use second order Taylor expansion of any characteristic function. It is apparent that given proof may only have a pedagogical importance.