Is there any reasonably fast way of finding a function of the type
that best fits a given data, for some K and n? For example, the following data closely follows an inverse power law
data = {{98.6, 38.8, 29.2, 23.7, 20.5, 18.1, 17, 15.9, 15, 14.3}}
ListLogPlot[data]
How can I find an expression that fits it?
How about a sum of functions of that form?
Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/MonadicProgramming/MonadicQuantileRegression.m"]
func = First[
QRMonUnit[N@data] ⟹
QRMonEchoDataSummary[] ⟹
QRMonQuantileRegressionFit[lsBasis, 0.5, Method -> {LinearProgramming, Method -> "Simplex"}] ⟹
QRMonPlot[] ⟹
QRMonErrorPlots[PlotRange -> All] ⟹
QRMonTakeRegressionFunctions]
func[x]
(* 7.25308 + 30.0585/x^10. + 57.0715/x^1. + 4.21694/x^0.5 *)
Show[ListLogPlot[data], LogPlot[func[x], {x, 1, Length[data]}]]
ListLogLogPlot[data]where they should fall on a line if the relationship was indeed a power-law. This can be confirmed with fitting:fit = NonlinearModelFit[First@data, 1/(k v^n), {k, n}, v]; Show[ListPlot[data], Plot[fit[x], {x, 1, 10}]]The fit can be made better by including more terms:NonlinearModelFit[First@data, 1/(k1 v^n1) + 1/(k2 v^n2), {k1, n1, k2, n2}, v]$\endgroup$NonlinearModelFit, as suggested in the other comment. $\endgroup$