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Breaking bivariate records

Part of: Geometric probability and stochastic geometry Stochastic processes Limit theorems

Published online by Cambridge University Press:  18 August 2020

James Allen Fill
James Allen Fill*
Affiliation:
Department of Applied Mathematics and Statistics, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD21218, USA
*
Email: [email protected]
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Abstract

We establish a fundamental property of bivariate Pareto records for independent observations uniformly distributed in the unit square. We prove that the asymptotic conditional distribution of the number of records broken by an observation given that the observation sets a record is Geometric with parameter 1/2.

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60F05: Central limit and other weak theorems 60F15: Strong theorems 60G17: Sample path properties
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 30 , Issue 1 , January 2021 , pp. 105 - 123
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

†

Research supported by the Acheson J. Duncan Fund for the Advancement of Research in Statistics.

References

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