A Good and SIMPLE Measure of Randomness

Question

What is the best algorithm to take a long sequence of integers (say 100,000 of them) and return a measurement of how random the sequence is?

The function should retu

Answer 1

You can treat you 100.000 outputs as possible outcomes of a random variable and calculate associated entropy of it. It will give you a measure of uncertainty. (Following image is from wikipedia and you can find more information on Entropy there.) Simply:

You just need to calculate the frequencies of each number in the sequence. That will give you p(xi) (e.g. If 10 appears 27 times p(10) = 27/L where L is 100.000 for your case.) This should give you the measure of entropy.

Although it will not give you a number between 0 to 1. Still 0 will be minimal uncertainty. However the upper bound will not be 1. You need to normalize the output to achieve that.