Properties of the vacancy statistic in the discrete circle covering problem.

*(English)*Zbl 1336.60011
Choudhary, Pankaj K. (ed.) et al., Ordered data analysis, modeling and health research methods. In honor of H. N. Nagaraja’s 60th birthday. Selected papers based on the presentations at the international conference, Austin, TX, USA, March 7–9, 2014. Cham: Springer (ISBN 978-3-319-25431-9/hbk; 978-3-319-25433-3/ebook). Springer Proceedings in Mathematics & Statistics 149, 121-146 (2015).

Summary: L. Holst [in: Contributions to probability and statistics, Hon. G. Blom, 169–177 (1985; Zbl 0572.60014)] 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.

For the entire collection see [Zbl 1337.92005].

For the entire collection see [Zbl 1337.92005].

##### Keywords:

occupancy problems; spacings; Bose-Einstein distribution; sampling without replacement; sampling with replacement
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\textit{G. Barlevy} and \textit{H. N. Nagaraja}, in: Ordered data analysis, modeling and health research methods. In honor of H. N. Nagaraja's 60th birthday. Selected papers based on the presentations at the international conference, Austin, TX, USA, March 7--9, 2014. Cham: Springer. 121--146 (2015; Zbl 1336.60011)

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