SEQUENTIAL $ \chi^2$ CRITERIA
V. K. Zaharov, O. V. Sarmanov, V A Sevast'janov · Mathematics of the USSR-Sbornik · 1969
Independent trials with outcomes are considered. Let the probability of the th outcome be under the null hypothesis but be under the alternative hypothesis , . For testing the hypothesis samples with increasing size are formed. We denote the number of times that the th outcome appears in the first trials by . The statistics are introduced by formula (1.2). The hypothesis is rejected if x_i^*$ SRC=http://ej.iop.org/images/0025-5734/8/3/A08/tex_sm_2040_img13.gif/> for all , where is some critical value, and is accepted in the remaining cases. The limit, for , of the distribution of under the hypotheses and is given in the paper. These are used for the computation of the errors of the first and second kind, and , according to formulas (1.4) and (1.5). These distributions are multivariate generalizations of the central and noncentral -distributions.References: 4 titles.