A dependent \(F^ \alpha\)-scheme
type: Item
instance of: scholarly article
title: A dependent \(F^ \alpha\)-scheme
zbMATH Open document ID: 0817.60058
DOI: 10.1016/0167-7152(94)90053-1
author: Rocco Ballerini
published in: Statistics \& Probability Letters
publication date: 1994-11-06T00:00:00Z
review text: An \(F^ \alpha\)-scheme is a sequence of random variables \(\{X_ n\), \(n \geq 1\}\), where \(X_ n\) has cdf \(F^{\alpha_ n}\) for some sequence \(\{\alpha_ n\), \(n \geq 1\}\). For the independent \(F^ \alpha\)-scheme where the \(X_ n\)'s are independent, the sequence \{Maximum\((X_ 1, \dots, X_ n)\), \(n \geq 1\}\) and the sequence of record indicators are mutually independent. By using Archimedean copula function a dependent \(F^ \alpha\)-scheme is constructed that retains this property. Thus some of the results for the independent \(F^ \alpha\) scheme hold for such a dependent scheme. This has some implications on the secretary problem.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60G40
zbMATH DE Number: 681915
zbMATH Keywords: records
zbMATH Keywords: extremal process
zbMATH Keywords: Archimedian copula
zbMATH Keywords: secretary problem
reviewed by: H. N. Nagaraja
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)90053-1
OpenAlex ID: W1575769074
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description: scientific article; zbMATH DE number 681915