Let a 1's and b 0's be randomly arranged in a row; k is defined to be the largest number of 1's appearing within any m consecutive points in the arrangement. We find Pk*(k) = Pr{k a/2, and give upper 5% points on k for some choices of a, b, and m. This generalization of the classical birthday problem corresponds to a test for nonrandom clustering that is a discrete analogue to a scan test for clustering of points on the line discussed by Nous [4].
No takes yet. Share an insight, caveat, or question.
Bernard Saperstein (1972) studied this question.