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# Re: st: RE: inflection point of sigmoid curves

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: RE: inflection point of sigmoid curves Date Tue, 15 Jun 2010 12:32:24 -0400

```Tony--
But the normal pdf is not sigmoid (the cdf is, and its inflection
point is at the mean, so if the function is given then no Stata
(apparently?) sigmoid curve; if you know the functional form, it is
easy to derive the inflection point with paper and pencil, which was
Nick's point.  I offered a pair of "silly" examples of computing
inflection points of y=f(x) for some unknown sigmoid f() by estimating
a cubic function x=g(y) and then computing the inflection point in
terms of y (called ybar).

The examples are silly because y is assumed measured without error in
the regression, which contradicts any other regressions you might
consider where y is a function of x. Also, a cubic has the right sort
of shape but may not fit a particular function well at all (the
tangent and atan functions spring to mind). There is also a mistake in
the code... one should use -predict- instead of interpolation to get
xbar, like so:

drawnorm x, mean(10) n(1000) clear
sort x
g y=(_n+1)/(_N+2)
reg x c.y##c.y##c.y
loc ybar=-2*_b[c.y#c.y]/(6*_b[c.y#c.y#c.y])
set obs `=_N+1'
replace y=`ybar' in l
predict px
loc xbar=px[_N]
lpoly y x, nosc xli(`xbar')

webuse nhanes2, clear
ren  bpsystol y
ren age x
reg x c.y##c.y##c.y
loc ybar=-2*_b[c.y#c.y]/(6*_b[c.y#c.y#c.y])
set obs `=_N+1'
replace y=`ybar' in l
predict px
loc xbar=px[_N]
lpoly y x, nosc xli(`xbar')
tw function -12+_b[c.y]*x+_b[c.y#c.y]*x^2+_b[c.y#c.y#c.y]*x^3, ra(-200
300) || sc y x,  xli(`xbar')

On Tue, Jun 15, 2010 at 11:53 AM, Lachenbruch, Peter
<Peter.Lachenbruch@oregonstate.edu> wrote:
> If you wish the inflection point of a normal curve you can take the second derivative of a normal density and find the inflection points are at mu+sigma and mu-sigma.
>
> Tony
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```