how to generate a gaussian distribution using mysql user-defined function

Question

I like to use MySQL to do quantitative analysis and statistics. I would like to make a MySQL user-defined function of the form: sample_gaussian(mean, stdev) that returns a single randomized value sampled from a gaussian distribution having mean and standard deviation of the user-entered arguments. MySQL already has a function rand() that returns a random number, so I just need to know some pseudocode for constraining/transforming that value so that it falls into the right distribution. Any suggestions?

BTW- This is my first stackoverflow question, so please forgive me if this question is asking too much of users on this site.

Answer 1

In answer to my own question, here is a MySQL user-defined function that returns a single random value sampled from a Gaussian distribution with a given mean and standard deviation.

DROP FUNCTION IF EXISTS gauss;
DELIMITER //
CREATE FUNCTION gauss(mean float, stdev float) RETURNS float
BEGIN
set @x=rand(), @y=rand();
set @gaus = ((sqrt(-2*log(@x))*cos(2*pi()*@y))*stdev)+mean;
return @gaus;
END
//
DELIMITER ;

To verify that this is in fact returning a Gaussian distribution, you can generate a series of these, then plot a histogram:

create temporary table temp (id int, rando float);
insert into temp (rando) select gauss(2,1); # repeat this operation 500 times
insert into temp (rando) select gauss(2,1) from any_table_with_500+_entries limit 500;
select round(temp,1), count(*) from temp group by round(temp,1) # creates a histogram

If you plot that histogram in excel or graphing tool of choice, you'll see the bell shaped normal curve.