The limit joint distributions of statistics of four tests of the NIST package

For sequences of independent random variables having a Bernoulli distribution with parameter $p$ the limit joint distribution of statistics of four tests of the NIST statistical package («Monobit Test», «Frequency Test within a Block», «Runs Test» and a generalization of «Non-overlapping Template Matching Test») is obtained. Conditions of asymptotic uncorrelatedness and/or asymptotic independence of these statistics are given.