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The contents of the paper is concerned with the two-sample problem where and are two empirical distribution functions. The difference changes only at an , corresponding to one of the observations. Let denote the subscript for which achieves its maximum value for the th time . The paper deals with the probabilities for and for the vector under , thus generalizing the results of Steck-Simmons (1973). These results have been derived by applying the random walk model.
Suppose that in a ballot candidate scores votes and candidate scores votes and that all possible voting sequences are equally probable. Denote by and by the number of votes registered for and for , respectively, among the first votes recorded, . The purpose of this paper is to derive, for , the probability distributions of the random variables defined as the number of subscripts for which (i) , (ii) but , (iii) but and , where .
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