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RE: st: A rose by any other name?

From   jverkuilen <>
To   <>
Subject   RE: st: A rose by any other name?
Date   Thu, 13 Nov 2008 10:23:54 -0500

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" <>
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There are some historical references on this within 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
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N.
J. Cox
        Q1/08   SJ 8(1):142--145                                 (no
        tip on how to graph data on a transformed scale


Verkuilen, Jay

>>To be more precise, the proposed model is a gamma density kernel, not
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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