[PD] cumulative distribution?

[Martin Peach]

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