This research proposes a new statistic for spectral testing, establishing its limiting distribution for binary sequences, highlighting improved hypothesis testing.
We consider the problem of testing the hypothesis that the tested sequence is a sequence of independent random variables that take values 1 and –1 with equal probability. To solve this problem, the Discrete Fourier Transform (spectral) test of the NIST package uses the statistic T Fourier , the exact limiting distribution of which is unknown. In this paper a new statistic is proposed and its limiting distribution is established. This new statistic is a slight modification of T Fourier . A hypothesis about the limit distribution of T Fourier is formulated, which is confirmed by numerical experiments presented by Pareschi F., Rovatti R. and Setti G.
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M P Savelov (2023) studied this question.
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