A New Statistical Randomness Test: Saturation Point Test

Abstract

In this work, we propose a new statistical randomness test, the Saturation Point Test, which can be applied to integer sequences as well as binary sequences and is designed to increase the number of tests for short sequences. The subject of Saturation Point Test is the index of integer, denoted by SP, where all possible integers occur in the given sequence. We evaluate the probability Pr(SP=t) using Stirling numbers of the second kind and give a procedure to produce a p-value using this probability. Moreover, we state a pseudocode for the new test and evaluate the subinterval probabilities to apply chi^2 goodness of fit test.