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With relevance to "functional data analysis", I am looking for some approach which can give an intermediate function among these five different function plots, where this "average function" has the closest distance at each point on the x-axis to each of the five plots.

The plots are shown here for the purpose of the question:

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Are there any particular methods one can use?

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    $\begingroup$ Re: "... this "average function" has the closest distance at each point on the x-axis to each of the five plots.", this is given by the function which is simply the pointwise average of your functions. $\endgroup$ Dec 28, 2022 at 19:02
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    $\begingroup$ @JohnMadden Because of the log scaling of the above figures would you recommend the geometric mean for the "pointwise average"? $\endgroup$
    – JimB
    Dec 28, 2022 at 21:14
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    $\begingroup$ @JimB hahaha got me :) indeed, if you want it to be close on the log scale, we should average in logspace. $\endgroup$ Dec 28, 2022 at 21:25
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    $\begingroup$ @JohnMadden Just checking to see if I was out of touch. I gave that advice to the OP when that exact same question (but for a potential implementation in Mathematica) was asked at mathematica.stackexchange.com/questions/277880/…. $\endgroup$
    – JimB
    Dec 28, 2022 at 21:29

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