# [PD] cumulative distribution?

Mathieu Bouchard matju at artengine.ca
Thu Nov 10 23:26:37 CET 2005

```On Thu, 10 Nov 2005, Jacob Last wrote:
> In fact I don't think you can compute the cumulative gaussian
> distribution from a closed formula...

It depends which are the allowed building blocks for the formula. If all
you have is +,-,*,/,pow,exp,log,cos, then you can't.

then the MacLaurin expansion of integral(exp(-x*x)) is:

Sum of x(-x*x)^k / (k+1)! for k=0 and upwards

Which is a bitch to compute, since it needs so many terms to get it
accurate.

However, <math.h> has a function erf() which computes exactly that, and
it's prolly a good optimisation over computing the series naïvely.

> i think that a sigmoid function might be better suited than the
> hyperbolic tangent....

The hyperbolic tangent *IS* a sigmoid!

tanh(t) = 1-2*P(-2*t)

____________________________________________________________________
Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
Freelance Digital Arts Engineer, Montréal QC Canada

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