Maple Logistic was Charge Distribution

[brian whatcott <inet@INTELLISYS.NET>]

At 22:20 11/16/99 -0500, Ludwik wrote:
> /snip/ Knowing
> positions you can calculate PE at once. No need to iterate till
> the minimum is found, as I did. Was this what you used
> Maple for?
>
> Ludwik Kowalski

Flying off at a distinct tangent - the Maple mention reminded me of
dredging up an email correspondence about the logistic curve as
worked by Maple and by some calculators in the course of a search on
 the keyword "logistic".  (There is apparently a proprietary slick
approach to forming the logistic on some calculators.)
 I'm not at all sure why a calculator should feature the logistic,
though it is a natural expression of growth limited by some constraint.

I saw this expression mentioned:
y = P0/(1 + exp(P1 + P2*x))

Comparing a genetic solution with a non linear regression, I saw that for
a curve not based on zero, this expression given above was not quite
optimal (though one could obtain high F and low sum of deviations squared).
 For a curve increasing from 5 and curving up to 15 for example, adding an
offset parameter (of 4.8) improved the accounting to 99%+
This gives the following equation:

y = P4 + P0/(1 + exp(P1 + P2*x))

In spite of the improved fit, the F value declines....having one more
degree of freedom. I recall that this is the drug of regression modellers:
they want to account for more and more of the variation, though each extra
term may add no predictive value.


brian whatcott <inet@intellisys.net>
Altus OK