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

«Approximate $\phi$-Entropy Test» is a generalization of «Approximate Entropy Test» and «Serial Test» of the NIST package. In the present paper we obtained the limit joint distribution of the statistic of «Approximate $\phi$-Entropy Test» and statistics $T_{\mathrm{mon}}$ and $T_{\mathrm{fr}}$ of the NIST package tests «Monobit Test» and «Frequency Test within a Block» respectively, in case when the tested sequence is «close» to a sequence of independent Bernoulli trials with parameter $\frac12$. The limiting value of the power of the test based on the simultaneous use of these three statistics was obtained. The limit joint distribution of the statistics $T_{\mathrm{mon}}$, $T_{\mathrm{fr}}$ and the statistics of «Approximate Entropy Test» and «Serial Test» was obtained.