View Full Version : Generating Normal Distribution Deviates

December 7th, 2008, 05:45 PM
Hey, Everyone :)
Does anyone possess a code which would help me to generate random numbers which are distributed normally.


int randomNumber = NormalDistribution.Next(mean, variance);

The function takes two parameters: mean and variance (optionally standart deviation) and returns a random number.
I would appreciate your help very much!
As for language... Java would be the best option but if you have any other implementations (except some exotic ones, e.g brainf*ck) I'd be pleased to see them also.
Thanks in advance!

December 7th, 2008, 06:33 PM
In python, with scipy:

>>> from scipy.stats import norm
>>> norm.rvs(size=5,loc=0,scale=0.5)
array([-0.44018532, 1.05318381, 1.0794372 , 0.52152627, 0.40720329])

"loc" is the mean, and "scale" is the standard deviation. "size" is the number of samples.

December 7th, 2008, 06:47 PM
Or in C, using the GNU Scientific Library:


#include <stdio.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>

int main (void)
const gsl_rng_type * T;
gsl_rng * r;

int i, n = 10;
double sigma = 0.25;

T = gsl_rng_default;
r = gsl_rng_alloc (T);

* Print n random variates chosen from the gaussian distribution
* with mean zero and standard deviation sigma.

for (i = 0; i < n; i++)
double x = gsl_ran_gaussian(r, sigma);
printf (" %f", x);
printf ("\n");
gsl_rng_free (r);
return 0;

Compile and run:

$ gcc gen_rand.c -lgsl -o gen_rand
$ ./gen_rand
0.033480 -0.022025 0.418602 0.183410 0.249381 -0.319376 -0.599179 -0.169820 -0.009773 0.223389

See the chapter on Random Number Distributions (http://www.gnu.org/software/gsl/manual/html_node/Random-Number-Distributions.html) in the GSL docs for more information and examples.

Lux Perpetua
December 7th, 2008, 08:15 PM
There's a standard way to generate normal deviates from uniform deviates using polar coordinates. You need two uniform deviates, but you get two normal deviates as a result, so it evens out.

If your two uniform deviates are u and v:

1. Let t = 2*pi*u, r = sqrt(-2*log(v)).
2. Let x = r*cos(t), y = r*sin(t).

Then x and y are your two standard normal deviates (mean 0, standard deviation 1). In general, if you want mean m and standard deviation s, return m + s*x, m + s*y instead of x, y.

As for getting uniform deviates, best case: your standard library offers a facility to generate random numbers uniformly distributed between 0 and 1. I know this is often not the case; in this case, you should generate a random positive integer and divide the result by RAND_MAX or the equivalent. (Actually, the best case is that your standard library offers normal deviates, since it is likely to be faster than the above method. :-))