TST: A new randomness test method based on coupon collector’s problem

Abstract

In this paper we find that a random sequence is expected to obey a new interesting distribution, and the coefficient of variation of this distribution approximates the value of golden section ratio, the difference between these two numbers is only 0.000797. As this interesting property, this newfound distribution is derived from Coupon Collector’s Problem and founded by the uniformity of frequency. Based on this distribution a new method is proposed to evaluate the randomness of a given sequence. Through the new method, the binary and decimal expansions of e, π, √ 2, √ 3 and the bits generated by Matlab are concluded to be random. These sequences can pass NIST tests and also pass our test. At the same time, we test some sequences generated by a physical random number generator WNG8. However, these sequences can pass the NIST tests but cannot pass our test. In particular, the new test is easy to be implemented, very fast and thus well suited for practical applications. We hope this test method could be a supplement of other test methods.