# [PD] cumulative distribution?

Martin Peach martinrp at vax2.concordia.ca
Thu Nov 10 17:56:47 CET 2005

```Jacob Last wrote:

>In fact I don't think you can compute the cumulative gaussian
>distribution from a closed formula...
>
>

You can.

>i think that a sigmoid function might be better suited than the
>hyperbolic tangent.... take a look at
>http://en.wikipedia.org/wiki/Sigmoid_function for more.
>

The wiki article says:
"Besides the logistic function, sigmoid functions include the ordinary
arc-tangent <http://en.wikipedia.org/wiki/Trigonometric_function>, the
hyperbolic tangent <http://en.wikipedia.org/wiki/Hyperbolic_tangent>,
and the error function <http://en.wikipedia.org/wiki/Error_function>."
The tanh and sigmoid are essentially the same thing. Practically it
could represent the weight at successive times as you smoothly pour sand
from a bucket onto a scale, or the number of photons captured from a
pulse of light. which is what the cumulative gaussian distribution is
about. atan is the same shape going along the y axis. You can multiply
the argument of tanh by a constant to get different "sharpness" of the
S, and multiply and add constants to position and scale it "vertically".

Martin

```