Gabor Grothendieck <[EMAIL PROTECTED]> 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 ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
