As a criterion for homogeneity for k samples (under the assumption that the distribution function of the random variable is continuous) the statistic Dₖ (1) is suggested; here Fⱼ (x) stands for the empirical distribution function of the j-th sample, j = 1,2, ⋯ ,k. Its asymptotic distribution (nⱼ → ∞ ,j = 1,2, ⋯ ,k) is given by formula (2). In the special case $k = 2$, N. V. Smirnov’s criterion is obtained.
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I. I. Gikhman (1957) studied this question.
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