On the Mixing Property in the Sense of A. Rényi for the Statistics of Homogeneity Test

Аннотация

In this paper we present an R-mixing test for the sequence of random variables, introduced by A. Rényi, and prove a certain property of R-mixed sequences. It is proved that the statistics of homogeneity test has the R-mixing property with the limit chi-square distribution with k − 1 degrees of freedom. This result strengthens a well-known result on the asymptotic chi-square distribution of the statistics of homogeneity test.