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So how do you properly test your random number generator? Frequency (Monobits) Test. Test For Frequency Within A Block. Runs Test. Test For The Longest Run Of Ones In A Block. Random Binary Matrix Rank Test. Discrete Fourier Transform (Spectral) Test. Non-Overlapping (Aperiodic) Template Matching Test. How to test randomness? - Test Engineering Notes github.io 2021/12/10 testing-ran github.io 2021/12/10 testing-ran
Chi-square is a statistical test that examines the differences between categorical variables from a random sample in order to determine whether the expected and observed results are well-fitting.
There are two phases to test the random number generator process. First you need a source of entropy[1] that is impossible to guess like the weather. Second you need a deterministic algorithm to expand the seed into a multitude of sequences for keys and the like. Testing usually starts with checking your entropy. Provable Randomness: How to Test RNGs | by Unitychain Medium unitychain provable-random Medium unitychain provable-random
The runs test is a statistical test to determine whether random selection has been made in the process of sample selection from an ordered population. The runs test is a type of non-parametric test and hence, there is no need for the assumption of a normal distribution to hold true. An Application of the Runs Test to Test for Randomness of Observations nih.gov articles PMC6422539 nih.gov articles PMC6422539
Run test of randomness is a statistical test that is used to know the randomness in data. Run test of randomness is sometimes called the Geary test, and it is a nonparametric test. Run test of randomness is an alternative test to test autocorrelation in the data.

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To test the quality of each of the random number generators, we can apply a multinomial test to determine if the null hypothesis that the parameters of a multinomial distribution are equal to specified values is correct. Quality of Random Number Generators - Maple Help - Maplesoft maplesoft.com help Maple view Rand maplesoft.com help Maple view Rand
The frequency (or frequency within a block) test is used to test the randomness of a sequence of zeroes and ones (Dataplot will covert a data set with exactly two distinct values to a sequence of zeroes and ones). The test is based on the proportion of zeroes and ones.
One measure for randomness is the entropy which can be defined for random variables. Consider a coin flip with probability p for head and 1-p for tails. The entropy in this case would be H = - [p log(p) + (1-p) log(1-p)]. This value takes it maximum for p=0.5.

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