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st: non-linear least squares

From   "Metcalfe, Paul" <>
To   <>
Subject   st: non-linear least squares
Date   Wed, 26 Nov 2003 11:58:31 -0000

Dear statalisters,
A colleague of mine has asked for help with the following stata query:

Working with non-linear least squares regression, Stata 8 includes a couple of non-linear functions already programmed.  The logistic function:
	nl log3    Y = b1/(1 + exp(-b2*(X-b3)))
and the Gompertz:
	nl gom3    Y = b1*exp(-exp(-b2*(X-b3)))

However, looking at various econometric manuals, these functions are normally of the form:
	log        Y = b1/(1+(b2*exp(-b3*X)))
      gom        Y = b1*exp(-b2*exp(-b3*X)))

I can't find a mathematical way to move between the two; are the functions programmed into Stata a recognised alternative form, or is the help file incorrect?

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