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Characterizations in a random record model with a nonidentically distributed initial record

Part of: Distribution theory Nonparametric inference Stochastic processes

Published online by Cambridge University Press:  14 July 2016

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

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We consider a sequence, of random length M, of independent, continuous observations Xi, 1 ≤ i ≤ M, where M is geometric, X1 has cumulative distribution function (CDF) G, and Xi, i ≥ 2, have CDF F. Let N be the number of upper records and let Rn, n ≥ 1, be the nth record value. We show that N is independent of F if and only if G(x) = G0(F(x)) for some CDF G0, and that if E(|X2|) is finite then so is E(|Rn|), n ≥ 2, whenever N ≥ n or N = n. We prove that the distribution of N, along with appropriately chosen subsequences of E(Rn), characterize F and G and, along with subsequences of E(Rn - Rn-1), characterize F and G up to a common location shift. We discuss some applications to the identification of the wage offer distribution in job search models.

Keywords

Moment sequencenumber of recordsrecord spacinggeometric distributionMüntz-Szász theoremTitchmarsh convolution theoremjob search model

MSC classification

Primary: 62E10: Characterization and structure theory
Secondary: 60G70: Extreme value theory; extremal processes 62G32: Statistics of extreme values; tail inference
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 1119 - 1136
Copyright
© Applied Probability Trust 2006 

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