On the pointwise central limit theorem and mixtures of stable distributions

I. Berkes, E. Csáki

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let X1, X2, . . . be i.i.d. r.v.'s with EX1 = 0, EX21 = 1 and put Sn = X1 + ··· + Xn. We investigate the a.s. limiting behavior of (equation presented) for general norming sequences (ak). The pointwise central limit theorem shows that LN converges a.s. to the normal distribution if ak - √k; in our paper we prove the surprising result that for suitably chosen (ak) the expression LN can converge also to non-Gaussian limits, in particular, any symmetric stable distribution is a possible limit of LN. We shall determine the class of limit distributions of LN and extend the result to the case when Xn belong to the domain of attraction of a stable law.

Original languageEnglish
Pages (from-to)361-368
Number of pages8
JournalStatistics and Probability Letters
Volume29
Issue number4
DOIs
Publication statusPublished - Sep 16 1996

Fingerprint

Stable Distribution
Central limit theorem
Converge
Stable Laws
Symmetric Distributions
Domain of Attraction
Limiting Behavior
Limit Distribution
Gaussian distribution
Stable distribution
Class
Normal distribution
Attraction
Limit distribution

Keywords

  • Mixtures
  • Pointwise central limit theorem
  • Stable distributions

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

On the pointwise central limit theorem and mixtures of stable distributions. / Berkes, I.; Csáki, E.

In: Statistics and Probability Letters, Vol. 29, No. 4, 16.09.1996, p. 361-368.

Research output: Contribution to journalArticle

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