I believe you are right about the logistic curve predating the distribution From what I recall it was first derived (using a firstorder nonlinear differential equation) by Verhulst to model population as an elaboration of Malthus' model, which is verbal but corresponds to the first order linear differential equation for exponential growth. Been a while since I read any of that stuff so my memory may be faulty. Verhulst's equation is a popular example for a nonlinear ODE that can be solved analytically. There are so few...
-----Original Message-----
From: "Nick Cox" <[email protected]>
To: [email protected]
Sent: 11/13/2008 8:25 AM
Subject: RE: st: A rose by any other name?
As a matter of history, I believe that logistic as a growth curve came
long before the logistic as a CDF, but as Jay implies, between friends
it's the same equation.
There are some historical references on this within
SJ-8-1 gr0032 . . . . . . . Stata tip 59: Plotting on any transformed
scale
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N.
J. Cox
Q1/08 SJ 8(1):142--145 (no
commands)
tip on how to graph data on a transformed scale
Nick
[email protected]
Verkuilen, Jay
>>To be more precise, the proposed model is a gamma density kernel, not
a
bonafide gamma density ,which integrates on 1. Of course in this
context, the function is used to model nonlinear trend, not a
probability distribution of some random variable.>>
Right, and thus it's not dissimilar from using the logistic CDF as a
model for growth between asymptotes, which is often done using, say,
Gaussian errors around the curve itself.
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