On the pointwise central limit theorem and mixtures of stable distributions

I. Berkes and E. Csáki

Statistics & Probability Letters, 1996, vol. 29, issue 4, 361-368

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 for general norming sequences (ak). The pointwise central limit theorem shows that LN converges a.s. to the normal distribution if ak = [radical sign]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.

Keywords: Pointwise; central; limit; theorem; Stable; distributions; Mixtures (search for similar items in EconPapers)
Date: 1996
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(95)00192-1
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:29:y:1996:i:4:p:361-368

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().