[Numpy-discussion] Combining Sigmoid Curves

[Rich Shepard]

On Fri, 2 May 2008, Angus McMorland wrote:

> How about multiplying two Boltzmann terms together, ala:
>
> f(x) = 1/(1+exp(-(x-flex1)/tau1)) * 1/(1+exp((x-flex2)/tau2))

> You'll find if your two flexion points get too close together, the peak
> will drop below the maximum for each individual curve, but the transition
> will be continuous.

Angus,

   With an x range from 0.0-100.0 (and the flexion points at 25.0 and 75.0),
the above formula provides a nice bell-shaped curve from x=0.0 to x=50.0,
and a maximum y of only 0.25 rather than 2.0.

   Modifying the above so the second term is subtracted from 1 before the
multiplication, or by negating the exponent in the second term, yields only
the first half: the ascending 'S' curve from 0-50.

Thanks,

Rich

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