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Properties of the vacancy statistic in the discrete circle covering problem

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  • Gadi Barlevy
  • H. N. Nagaraja

Abstract

Holst (1985) introduced a discrete spacings model that is related to the Bose-Einstein distribution and obtained the distribution of the number of vacant slots 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 also discuss an application of our results to a study of contagion in banking networks.

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  • Gadi Barlevy & H. N. Nagaraja, 2013. "Properties of the vacancy statistic in the discrete circle covering problem," Working Paper Series WP-2013-05, Federal Reserve Bank of Chicago.
    • Handle: RePEc:fip:fedhwp:wp-2013-05
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    1. Ricardo J. Caballero & Alp Simsek, 2013. "Fire Sales in a Model of Complexity," Journal of Finance, American Finance Association, vol. 68(6), pages 2549-2587, December.
    2. J. A. Wellner, 1994. "Covariance formulas via marginal martingales," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 48(3), pages 201-207, November.
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    1. Alvarez, Fernando & Barlevy, Gadi, 2021. "Mandatory disclosure and financial contagion," Journal of Economic Theory, Elsevier, vol. 194(C).

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