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Matched pairs in independent Poisson processes

Published online by Cambridge University Press:  14 July 2016

David Oakes
David Oakes*
Affiliation:
London School of Hygiene and Tropical Medicine
*
∗Postal address: TUC Centenary Institute of Occupational Health, London School of Hygiene and Tropical Medicine, Keppel St (Gower St), London WC1E 7HT, U.K.
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Abstract

Given two independent Poisson processes 𝒜 and ℬ with rates respectively α and β (α < β) we match each point of 𝒜 with the closest point of ℬ that has not already been matched. The points of 𝒜 are taken in random order. It is shown that the point process of unmatched points of ℬ is a renewal process with the same interval distribution as the busy period of an M/M/1 queue. The distribution and moments of the distance between a typical point of 𝒜 and the corresponding matched point of ℬ are obtained. Variants of the matching process in which the assigned point of ℬ must lie to the right of the point of 𝒜, and in which the matching distance must be less than a fixed tolerance are studied. The use of matched samples to control for bias in observational studies is discussed.

Keywords

MATCHINGPAIR-MATCHINGCALIPER MATCHINGNEAREST AVAILABLE MATCHINGBUSY PERIOD
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 780 - 793
Copyright
Copyright © Applied Probability Trust 1979 

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