[R] Fitting data from a spectrophotometer.

[Peter Dalgaard]

Gabor Grothendieck <ggrothendieck at 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   
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