[portland] Any Mathematical Coders Here?

Rich Shepard rshepard at appl-ecosys.com
Thu May 8 03:53:56 CEST 2008

   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 curve
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.


Richard B. Shepard, Ph.D.               |  Integrity            Credibility
Applied Ecosystem Services, Inc.        |            Innovation
<http://www.appl-ecosys.com>     Voice: 503-667-4517      Fax: 503-667-8863

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