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gnuplotuncertainty

How to do a weighted fit for a with a set of data containing f(x) +- df(x)?

I have a function f(x) = a/x and I have a set of data containing values for f(x) +- df(x) and x +- dx. How do I tell gnuplot to do a weighted fit for a with that?

I know that fitaccepts the using term and this works for df(x), but it does not work for dx. It seems gnuplot treats the error I have for x as the error for the whole RHS of my function (a/x +- dx).

How do I do a weighted fit that fits f(x) +- df(x) = a/(x +- dx) to find the optimal a?

Solution

  • Since version 5.0, gnuplot has an explicit provision for taking uncertainty in the independent variable into account

    fit f(x) datafile using 1:2:3:4 xyerror

    using "Orear's effective variance method".

    (Above command expects data in the form x y dx dy.)