Solution of Deny convolution equation restricted to a halfr, R. A.: A functional law of the iterated logarithm for distributions in the domain of partial attraction of the normal distribution
type: Item
instance of: scholarly article
title: Solution of Deny convolution equation restricted to a halfr, R. A.: A functional law of the iterated logarithm for distributions in the domain of partial attraction of the normal distribution
zbMATH Open document ID: 0641.60019
author: Abdulhamid A. Alzaid
author: Ka-Sing Lau
author: Damodar Shanbhag
author: C. R. Rao
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: The main result is: partial sums of i.i.d. r.v. when suitably normed and centred \((S_ n-a_ n)/B_ n\) are in the domain of partial attraction of the normal distribution iff the set of almost sure limit points of the random polygon as a sequence in C[0,1] or of the partial sum process \((S_{[nt]}-a_{[nt]})/B_ n\) as a sequence in D[0,1], equals to the unit ball of absolutely continuous functions in \(L_ 2\) metric. It is proved that the same statement holds true after removing a fixed number of terms of largest modulus from \(S_ n\).
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4044836
zbMATH Keywords: functional law of iterated logarithm
zbMATH Keywords: trimmed variables
zbMATH Keywords: domain of partial attraction
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4044836