The fast increasing length of random number streams, the application of more powerful cores and emerging various Random Number Generators (RNGs) lead to a revolution from traditional RNGs. The authentic RNGs are mainly based on the physical environments, such as sound waves, light photons, etc. They obtain the advantage of unpredictable, and thus, are random with no doubt. However, in practical applications like Cryptography, lottery, and some academic requirements, etc., reproducibility is a very important attribute. People are searching different ways for generating random number streams to simulate the authentic ones. Because being generated not naturally, they are called Pseudo Random Number Generators (PRNGs). To distinguish the quality of these PRNGs, a level to gauge how similar are they as authentic random numbers is essential. Statistical tests are considered as accurate and efficient tests. Along with the fast development of RNGs and PRNGs, it takes a new theme that how to improve the statistical tests. In this article, we are introducing some practical test suites, including DIEHARD, NIST, TestU01, SPRNG, etc., and trying to elaborate how to use them. Meanwhile, I notice similar characteristics, which lead to the idea that tests in one suite could imitate tests in another suite. Then I've composed a combination file that could use all the testing suites. Due to the high comprehensiveness, TestU01 is used as mother board of this file. Afterward, I'll trace the newest trends of PRNGs, to detect the principle of counter-based PRNG - Random123, and show the testing results from both BigCrush test in TestU01 and combination file. Also, hardware RNGs, which generate authentic random numbers, are also tested to show the quality of statistical tests. Last but not least, parallel tests, whose advantages are more significant, especially when random number streams are getting bigger, are also discussed, and so are software and hardware support.
