Power of the test based on joint application of «Monobit Test», «Frequency Test within a Block» and «Serial Test»

We consider the problem of testing the hypothesis $H_0$: «tested sequence is a sequence of independent random variables having a Bernoulli distribution with parameter $\frac12$, in the scheme of series» against alternative $H_1$, which approaches $H_0$ as the sample size increases. In particular, an alternative is considered in which the tested sequence is a high-order Markov chain. In case when $H_1$ is true the limiting joint distribution of statistics $T_1, T_2, T_3$ of the following tests of the NIST package was found: «Monobit Test», «Frequency Test within a Block» and «Serial Test». The limiting value of the power of the test based on the simultaneous use of these three statistics was obtained. In the case when the alternative hypothesis does not approach $H_0$, the limiting behavior of the vector $(T_1, T_2, T_3)$ is described.