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From |
Austin Nichols <austinnichols@gmail.com> |

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 commands are required). The poster was asking about an arbitrary (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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: inflection point of sigmoid curves***From:*Johannes Schmid <d320838@dadlnet.dk>

**st: RE: inflection point of sigmoid curves***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**Re: st: RE: inflection point of sigmoid curves***From:*Austin Nichols <austinnichols@gmail.com>

**RE: st: RE: inflection point of sigmoid curves***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

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