问题
Let's say I have an algorithm that is supposed to represent a coin flip. How do I determine the bias of this coin? Specifically, I have written the algorithm in this JSFiddle.
The fiddle runs a series of 20 tests. Each test flips the coin 100 times and tallies the results. At the end of the series it reports Heads/Tails for the total number of flips across all tests. This result seems to be approaching 1 (from both sides), but I have not done any rigorous testing of this.
Note, this is not homework. This is purely a personal interest.
回答1:
You can't come up with a way to guarantee detecting a bias, but you can determine it to a certain degree of certainty (say 95%). What you do is test n times and count how many times you get heads, call this variable h.
Then if h / n < 0.5 - 1.96 * sqrt(0.25 / n) then the coin is biased towards tails (with a 95% probability) and if h / n > 0.5 + 1.96 * sqrt(0.25 / n) then the coin is biased towards heads.
This decision is based on something called normal approximation to a binomial distribution, you can read more about it here: http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Normal_approximation_interval
回答2:
George Marsaglia Diehard Tests
if you consider your Head/Tail as generating 0 1 bits. Using them you can generate random numbers and test their randomness
来源：https://stackoverflow.com/questions/8014607/how-do-i-determine-the-bias-of-an-algorithm