A Generalised Matching Distribution for the Problem of Coincidences

This paper examines the classical matching distribution arising in the “problem of coincidences”. We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed probability, and remaining non-matched items are allocated usin...

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Bibliographic Details
Published inMethodology and computing in applied probability Vol. 25; no. 4; p. 93
Main Author O’Neill, Ben
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2023
Springer Nature B.V
Subjects
Binomial distribution
Business and Management
Economics
Electrical Engineering
Life Sciences
Matching
Mathematics and Statistics
Probability
Random sampling
Statistics
Problem of coincidences
60C05
Secret-santa problem
60E99
Generalised matching distribution
Matching test
Matching statistic
Hat-check problem
Classical matching distribution
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Summary:This paper examines the classical matching distribution arising in the “problem of coincidences”. We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed probability, and remaining non-matched items are allocated using simple random sampling without replacement. Our generalised matching distribution is a convolution of the classical matching distribution and the binomial distribution. We examine the properties of this latter distribution and show how its probability functions can be computed. We also show how to use the distribution for matching tests and inferences of matching ability.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-023-10067-6