Timothy, the only way I could find of doing what you want is called
'the polar form of the Box-Muller transformation'.
Fortunately, it's not as bad as it sounds. :)
I've copied an ADA implementation, and here it is:
function polarBoxMuller pLength, pMean, pSdev
put false into useLast
repeat pLength
repeat
put ((random(101) - 1) * 0.02) - 1 into x1 -- generate a
random number between -1 and +1
put ((random(101) - 1) * 0.02) - 1 into x2
put (x1 * x1) + (x2 * x2) into w
if w <= 1 then exit repeat
end repeat
if w <> 0 then put ln(w) * -2 into w -- rev barfs if w is zero
if w <> 0 then put sqrt(w) / w into w -- ditto
put x1 * w into y1
put x2 * w into y2
put pMean + y1 * pSdev & comma after tList
put pMean + y2 * pSdev & comma after tList
end repeat
return char 1 to -2 of tList
end polarBoxMuller
This should give you a comma delimited list of (fairly) normally
distributed numbers.
Best,
Mark
ps. I enjoy this sort of thing, so thanks for the question!
On 21 Oct 2008, at 23:03, Timothy Miller wrote:
Greetings,
I'm interested an a modest statistics demonstration, but I can't
figure out how do to the math myself.
I'd like to have a few lines of code that produces a sequence of
numbers. (whole numbers would probably be okay). I'd like to
specify the number of numbers generated. Let's call that Z.
I'd like also to specify the desired mean and standard deviation.
I'd like the function (is this a function??) to work in such a way
that if Z is large, the set of numbers generated, if graphed as a
frequency distribution, would be normally distributed, i.e., Gaussian.
If Z is rather small, then the mean and standard deviation of the
numbers produced will would only approximate the desired mean and
standard deviation. Different runs would produce different actual
means and standard deviations.
If Z is very small, like 3 or 4, the numbers will look almost random.
I hope I explained that clearly.
Optionally, I might also be able to enter a variable that would
specify the desired number of digits to the right of the decimal
point.
No favors are requested. I'd really be rather uncomfortable with a
generous gesture. However, if someone has some code like this
sitting around, and you're willing to share it, with a few notes
about how to use it, I'd appreciate it. If not, it can't be helped.
Hmmmm... I wonder if some website somewhere would do the work for
me. That could work... I looked around, but didn't find anything.
Thanks in advance.
Tim Miller
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