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Characterizations using record moments in a random record model and applications

Part of:Distribution theoryNonparametric inferenceStochastic processes

Published online by Cambridge University Press:  14 July 2016

H. N. Nagaraja and
Gadi Barlevy
H. N. Nagaraja*
Affiliation:
Ohio State University
Gadi Barlevy*
Affiliation:
Northwestern University
*
∗ Postal address: Department of Statistics, Ohio State University, 1958 Neil Avenue, Columbus, OH 43210-1247, USA. Email address: hnn@stat.ohio-state.edu
∗∗ Current address: Economic Research Department, Federal Reserve Bank of Chicago, 230 South LaSalle Street, Chicago, IL 60604-1413, USA
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Abstract

We consider a random record model from a continuous parent X with cumulative distribution function F, where the number of available observations is geometrically distributed. We show that, if E(|X|) is finite, then so is E(|R n |) whenever R n , the nth upper record value, exists. We prove that appropriately chosen subsequences of E(R n ) characterize F and subsequences of E(R n − R n−1) identify F up to a location shift. We discuss some applications to the identification of wage-offer distributions in job search models.

Keywords

Moment sequencerecord spacingorder statisticsgeometric distributionjob search model

MSC classification

Primary:62E10: Characterization and structure theory
Secondary:60G70: Extreme value theory; extremal processes62G30: Order statistics; empirical distribution functions

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003, pp. 826 - 833
Copyright
Copyright © Applied Probability Trust 2003 

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