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Ordered Data Analysis, Modeling and Health Research Methods pp 121–146Cite as

Properties of the Vacancy Statistic in the Discrete Circle Covering Problem

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 149))

Abstract

Holst [10] introduced a discrete spacings model that is related to the Bose-Einstein distribution and obtained the distribution of the number of vacant positions in an associated circle covering problem. We correct his expression for its probability mass function, obtain the first two moments, and describe their limiting properties. We then examine the properties of the vacancy statistic when the number of covering arcs in the associated circle covering problem is random. We also discuss applications of our results to a study of contagion in networks.

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Notes

  1. 1.

    These cases are of interest because the unconditional probability that a bank is bad is higher than, equal to, and lower than the probability that a bank is bad conditional on news that another bank is good when M is degenerate, binomial, and a mixture of binomials, respectively. These distinctions turn out to matter when there is some possibility that news about some banks might be revealed.

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Author information

Authors and Affiliations

  1. Economic Research Department, Federal Reserve Bank of Chicago, 230 South LaSalle, Chicago, 60604, USA

    Gadi Barlevy

  2. College of Public Health Division of Biostatistics, The Ohio State University, 1841 Neil Avenue, Columbus, 43210-1351, USA

    H. N. Nagaraja

Authors
  1. Gadi Barlevy
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  2. H. N. Nagaraja
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Corresponding author

Correspondence to Gadi Barlevy .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences FO 35, University of Texas at Dallas, Richardson, Texas, USA

    Pankaj Choudhary

  2. Fordham University, New York, New York, USA

    Chaitra H. Nagaraja

  3. Southern Methodist University, Dallas, Texas, USA

    Hon Keung Tony Ng

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Barlevy, G., Nagaraja, H.N. (2015). Properties of the Vacancy Statistic in the Discrete Circle Covering Problem. In: Choudhary, P., Nagaraja, C., Ng, H. (eds) Ordered Data Analysis, Modeling and Health Research Methods. Springer Proceedings in Mathematics & Statistics, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-319-25433-3_8

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