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 s

Answer 1

rand() returns a uniformly distributed random variable between 0 and 1 (you should verify this because i am not sure - this is how it works in Sybase). You can use rand() to generate one or more normally distributed random variables r with mean zero and standard deviation (and variance) one, i.e. r ~ N(0,1), implementing one of the methods mentioned here

When you have generated a random variable from N(0,1), you can de-standardize it (solve for X in the formula here) to get a random variable from N(my_mean,my_std), that is by multiplying it by my_std and then adding my_mean.

Answer 2

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.

Answer 3

The Box-Muller transform is a way to generate standard normal random variates using elementary functions. It generates two at a time, which is sometimes wasteful, but I find it very elegant.