when generating normally-distributed random values, what is the most efficient way to define the range?
gaussian, javascript, math, normal-distribution, random
Solution
Subtracting two random numbers doesn't give you a normal distribution, it will give you numbers that decline linearly on both sides of zero. See the red diagram in this fiddle:
http://jsfiddle.net/Guffa/tvt5K/
To get a good approximation of normal distribution, add six random numbers together. See the green diagram in the fiddle.
So, to get normally distributed random numbers, use:
((Math.random() + Math.random() + Math.random() + Math.random() + Math.random() + Math.random()) - 3) / 3
This method is based on the central limit theorem, outlined as the second method here: http://en.wikipedia.org/wiki/Normal_distribution#Generating_values_from_normal_distribution
Problem
FYI: random == pseudo-random A. when generating uniformly-random numbers, I can specify a range, i.e.: ``` (Math.random()-Math.random())*10+5 //generates numbers between -5 and 15 ``` B. generating a set of random values with a version of Gaussian-esque normal randomness: ``` //pass in the mean and standard deviation function randomNorm(mean, stdev) { return Math.round((Math.random()*2-1)+(Math.random()*2-1)+(Math.random()*2-1))*stdev+mean); } //using the following values: { mean:400, standard_deviation:1 //results in a range of 397-403, or +-range of 3 }, { mean:400, standard_deviation:10 //results in a range of 372-429, or +-range of 30 }, { mean:400, standard_deviation:25 //results in a range of 326-471, or +-range of 75 } ``` each one gives me a range of approximately standard_deviation*(+-3) (assuming I left the program running longer). C. I can calculate this range as follows: - assuming I want a range from 300-500, so var total_range = 200; - my mean is 400, my +-range is total_range/2 (var r = 100) - so standard_deviation would be r/3 or in this case 33.333. This seems to be working, but I have no idea what I'm doing with math so I feel like an idiot, this solution feels kludgy and not totally accurate. My question: is there some formula that I'm dancing around that can help me here? my requirements are as follows: - must be able to define a range of numbers accurately. - must be done in JavaScript, as efficiently as possible. I think maybe I'm close but it's not quite there.