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I create a 4th or 5th degree fit curve to find the extrema point of distribution. However, how will I calculate the margin of error of the extrema on x values? Is there any statistical method or function to calculate this?

The picture below, shows the light change over time of an astronomical event. Red vertical line represent the extrema point. How can I find the margin of error on the x-axis of the extrema point? Because the position of the extrema point will also change due to the margin of error in the y values.

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  • $\begingroup$ If you don't find an analytic solutions, you can bootstrap. $\endgroup$
    – Peter Flom
    Commented Jul 9 at 10:35
  • $\begingroup$ @PeterFlom I find the numerical value of the extrema point, but I am investigating the margin of error of this value. $\endgroup$
    – Erkan Güler
    Commented Jul 9 at 10:55
  • $\begingroup$ Yes, I realize that. That is the question I answered. $\endgroup$
    – Peter Flom
    Commented Jul 9 at 11:04
  • $\begingroup$ @PeterFlom Can you give detailed information ? I don't know how bootsrap will help. $\endgroup$
    – Erkan Güler
    Commented Jul 9 at 12:31
  • $\begingroup$ Bootstrapping is neither needed nor justified with such a small dataset. But for such a nice fit as indicated in the illustration, it would likely yield a reasonable result. You could use the permutation distribution of the residuals, for instance. $\endgroup$
    – whuber ♦
    Commented Jul 9 at 14:55

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