Generating Normally Distributed Random Numbers in JavaScript

JavaScript's pseudo-random number generator Math.random() outputs what you want a pseudo-random number generator to output: a random number uniformly distributed between 0 and 1. Great, but say you are in a situation where you don't want every number to be equally likely, you want them evenly distributed about a mean. You want a normally distributed random number. To get this you can use the Box-Muller transformation on two uniformly distributed random numbers. Problem solved!

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In this demonstration I use the Box-Muller transformation on numbers generated by JavaScript's Math.random() and use the Kolmogorov-Smirnov test to compare the result against a normal cdf table generated by Mathematica to see if they actually come out normally distributed.

As for results, generating anywhere between 50 and 1000 almost always passes the test with α=0.005. More than 1000 and it almost always fails. This could be for a number of reasons. First, in a word(s), rounding error. Second, I am using sqrt(1.63)/N to estimate the critical value for the test statistic because the tables for the Kolmogorov distribution I have only go up to 50. I suspect this estimate gets to be pretty far off by N=1000. Just eyeballing the resulting distribution after generating a large number (hundreds of thousands) it is consistently 3% heavy around the middle. Unacceptable? Depends, what do you need a browser to generate a normally distributed random number with more than 97% confidence for?