# Article

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Keywords:
points of maximal deviation; two-sample Smirnov statistic; empirical distribution functions; joint distribution; random walk model
Summary:
The contents of the paper is concerned with the two-sample problem where \$F_m(x)\$ and \$G_n(x)\$ are two empirical distribution functions. The difference \$F_m(x)-G_n(x)\$ changes only at an \$x_i, i=1,2,\ldots, m+n\$, corresponding to one of the observations. Let \$R^+_{mn}(j)\$ denote the subscript \$i\$ for which \$F_m(x_i)-G_n(x_i)\$ achieves its maximum value \$D^+_{mn}\$ for the \$j\$th time \$(j=1,2,\ldots)\$. The paper deals with the probabilities for \$R^+_{mn}(j)\$ and for the vector \$(D^+_{mn}, R^+_{mn}(j))\$ under \$H_0 : F=G\$, thus generalizing the results of Steck-Simmons (1973). These results have been derived by applying the random walk model.
References:
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