Re: [R] Fitting data from a spectrophotometer.

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From: Peter Dalgaard (p.dalgaard@biostat.ku.dk)
Date: Thu 13 May 2004 - 11:02:40 EST


Message-id: <x2sme55ebz.fsf@biostat.ku.dk>

Gabor Grothendieck <ggrothendieck@myway.com> writes:

> Perhaps you really prefer something with a continuous first derivative?
> In that case, all the continuous cumulative distribution functions have
> a sigmoidal shape and might be suitable. You could fit pnorm, plogis or tanh
> with suitable scaling and location parameters using nls. An example
> of fitting a logistic is at
>
> https://stat.ethz.ch/pipermail/r-help/2004-April/048385.html

Actually, an exponential dampening towards an asymptote is what comes
out in simple models of saturation. If the detector is 1/3 full, you'd
expect 2/3 marginal sensitivity to changes in the input, or more
generally (y: output, x: input)

  dy/dx = 1 - y/ymax

taking reciprocals and integrating both sides wrt. y gives

 x = -ymax * log(1-y/ymax) + C

and C has to be zero if you want a curve through the origin so you
wind up with

 y = ymax*(1-exp(-x/ymax))

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)             FAX: (+45) 35327907

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