Note on a clustering problem

B. Saperstein

doi:10.2307/3212882

Abstract

Consider the clustering statistic, k* defined to be the maximum number of 1's to appear within any m consecutive positions in a random arrangement of a 1's and M–a 0's. Pr(k* – k) was found for the case k ≧ ½ a by the author [4], and then for m/M = 1/L, L an integer, by Naus [3]. Here, we generalise Naus's method to obtain the distribution of k* under no special restrictions on a, k, m or M.

References

[1] Hwang, F. K. (1974) A discrete clustering problem. Unpublished memorandum.Google Scholar

[2] Karlin, S. and Mcgregor, J. (1959) Coincidence probabilities. Pacific J. Math. 9, 1141–1164.CrossRef Google Scholar

[3] Naus, J. I. (1974) Probabilities for a generalized birthday problem. J. Amer. Statist. Assoc. 69, 810–815.CrossRef Google Scholar

[4] Saperstein, B. (1974) The generalized birthday problem. J. Amer. Statist. Assoc. 67, 425–428.CrossRef Google Scholar

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Note on a clustering problem

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