[portland] Any Mathematical Coders Here?
markgross at thegnar.org
Thu May 8 04:59:56 CEST 2008
On Wed, May 07, 2008 at 06:53:56PM -0700, Rich Shepard wrote:
> Is anyone in the group highly conversant with distribution function
> algorithms? I've been spending too much time trying to find a
> formula/algorithm that will generate sigmoid curves (both S- or Z-shaped)
> given the two ends, the midpoint, and the inflection point.
> While the Boltzmann function appears to work if the width of the curve is
> about 50% the width of the x axis, it never reaches y=0.0 or y=1.0 with
> finite widths. And, the inflection point drops well below y=0.5 if the
> width is about 30% of the x-axis range.
> I've tried a bunch of other approaches (including some suggestions from a
> subscriber to the NumPy mail list), but those suggestions are just not
> working for me.
> The Hill function looked promising, but I've not been able to find what
> the theta and n represent in the formula.
> The arctangent function _almost_ works in a limited number of cases.
> It's been too many years since I fully understood the mathematics of
> distribution functions, and even then a lot of my attention was focused on
> the log-normal distribution.
I know enough to get into trouble. But I don't know what a sigmoind
cure is other than http://mathworld.wolfram.com/SigmoidFunction.html
which isn't very helpful.
If you are substituting in arctan's for this curve then I have to
think you are looking for something that "looks" like something as
opposed to something that means anything.
If you are just looking for a "shape" and not something that means
much you can do splines and besior(sp) curves.
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