# Quality of randomness in generated random number

I have generated a list of 3 random number where each summed to 1. I would like to access the quality of randomness. What is the best mechanism to access this randomness? E.g my random numbers are. Any idea what tools can I use excel for this?

0.4 0.5 0.1
0.2 0.3 0.5
0.6 0.2 0.2
0.5 0.2 0.3
0.2 0.4 0.4
0.2 0.1 0.7
0.3 0.3 0.4
0.8 0.1 0.1
0.1 0.5 0.4
0.4 0.4 0.2

• There are an infinite number of ways in which a stream of numbers might be nonrandom. Given your sample size looks rather small, can you be more precise about what kinds of non-randomness you want to detect? Feb 20, 2014 at 10:45
• I would like to ensure they are equally distributed like first column having high value e.g. >0.7 followed by column 2 and last column 3. So I want to make sure its uniformly distributed to enable the weighting done on a proper probablistic Feb 20, 2014 at 10:48
• One of your problems is that the columns cannot be uniformly distributed and still sum to unity. You therefore must have a specific (multivariate) distribution in mind as a reference against which randomness will be assessed. If you don't know how to describe the distribution you would like to produce, that's ok, but you will still need to edit this question to give us enough quantitative information about what you're trying to do so that we can deduce what that distribution ought to be.
– whuber
Feb 20, 2014 at 16:27

## 1 Answer

Since you have a constraint your numbers are dependent and not uniformly distributed. You need to recover plausibly uniform i.i.d. numbers generating your set first, and then test those for randomness. If you consider the triplets as partitions of the unit interval, each one is also defined by two beta distributed values $\left( B(1,2) \text{ and B(2,1)} \right)$, which must be brought to uniform via the beta CDFs, and then you can test the outcomes e.g. with a Chi-square test or the DieHard testing suite. If the triplets were originated differently then you must derive a corresponding "uniformization" first, and then check for randomness.

• Given that these values appear to be discrete, I strongly suspect that even after such a transformation they will fail just about every randomness test with flying colors!
– whuber
Feb 20, 2014 at 16:13
• If they are indeed discrete and no example then the last "uniformization" step is just an entropy collection collection scheme on the line of arithmetic coding... and then build 32-bit chunks out of that. But for that one has to infer somehow what the distribution actually is, sure, if the uniform partition hypothesis does not stand. Feb 20, 2014 at 16:23