On limit laws for sums of Pfeifer records
type: Item
instance of: scholarly article
title: On limit laws for sums of Pfeifer records
zbMATH Open document ID: 1164.62018
author: Barry C. Arnold
author: José A. Villaseñor
published in: Extremes
publication date: 2009-02-28T00:00:00Z
review text: Asymptotic normality is demonstrated for centered and normalized sums of the form \( w_n=\sum_{i=0}^n \psi\left(\sum_{j=0}^i\beta_j X_j\right) \), where \(X_j\) are i.i.d. non-negative r.v.s with finite moment generating function, \(\beta_j\) are positive constants, and \(\psi\) is a non-decreasing regularly varying function. This result is applied to the sums of Pfeifer records, i.e., records in initial observations which are i.i.d. with common survival function \((\bar F_0)^{\alpha_0}\) before the first record and with the survival function \((\bar F_0)^{\alpha_n}\), \(n=1,2,\dots\), at the intervals between the \(n\)-th and \(n+1\)-th records.
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 5520592
zbMATH Keywords: regularly varying functions
zbMATH Keywords: order statistics
MaRDI profile type: Publication
full work available at URL: s10687-007-0043-1
OpenAlex ID: W1994722709
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cites work: Q5545070
DOI: 10.1007/S10687-007-0043-1
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description: scientific article; zbMATH DE number 5520592