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