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I'm trying to generate some random numbers with simple non-uniform probability to mimic lifelike data for testing purposes. I'm looking for a function that accepts mu and sigma as parameters and returns x where the probably of x being within certain ranges follows a standard bell curve, or thereabouts. It needn't be super precise or even efficient. The resulting dataset needn't match the exact mu and sigma that I set. I'm just looking for a relatively simple non-uniform random number generator. Limiting the set of possible return values to ints would be fine. I've seen many suggestions out there, but none that seem to fit this simple case.

ellisbben
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jdunk
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  • There are several existing questions that answer this...I'll run one or more down shortly. [Generate random numbers following a normal distribution in C/C++ ](http://stackoverflow.com/questions/2325472/), [Converting a Uniform Distribution to a Normal Distribution](http://stackoverflow.com/questions/75677/), [C++: generate gaussian distribution](http://stackoverflow.com/questions/1109446/) – dmckee --- ex-moderator kitten Oct 13 '10 at 02:18

2 Answers2

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Box-Muller transform in a nutshell:

First, get two independent, uniform random numbers from the interval (0, 1], call them U and V.

Then you can get two independent, unit-normal distributed random numbers from the formulae

X = sqrt(-2 * log(U)) * cos(2 * pi * V);
Y = sqrt(-2 * log(U)) * sin(2 * pi * V);

This gives you iid random numbers for mu = 0, sigma = 1; to set sigma = s, multiply your random numbers by s; to set mu = m, add m to your random numbers.

ellisbben
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My first thought is why can't you use an existing library? I'm sure that most languages already have a library for generating Normal random numbers.

If for some reason you can't use an existing library, then the method outlined by @ellisbben is fairly simple to program. An even simpler (approximate) algorithm is just to sum 12 uniform numbers:

X = -6 ## We set X to be -mean value of 12 uniforms
for i in 1 to 12:
   X += U

The value of X is approximately normal. The following figure shows 10^5 draws from this algorithm compared to the Normal distribution.

enter image description here

csgillespie
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