The limit joint distributions of statistics of four tests of the NIST package
Maksim P. Savelov · Discrete Mathematics and Applications · 2023
Abstract 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.