[R] Fitting data from a spectrophotometer.
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Thu May 13 03:02:40 CEST 2004
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
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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