Note on a clustering problem

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.