On a Nonparametric Homogeneity Criterion for k Samples
Iosif Ilyich Gikhman · Theory of Probability and Its Applications · 1957
As a criterion for homogeneity for k samples (under the assumption that the distribution function of the random variable is continuous) the statistic $D_k (1)$ is suggested; here $\tilde F_j (x)$ stands for the empirical distribution function of the j-th sample, $j = 1,2, \cdots ,k$. Its asymptotic distribution $(n_j \to \infty ,j = 1,2, \cdots ,k)$ is given by formula (2). In the special case $k = 2$, N. V. Smirnov’s criterion is obtained.