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I made ten measurements and obtained 10 best fit values as well as errors associated with each of the best fit values. The uncertainty in each of the measurements is known to be asymmetrically distributed, so the confidence intervals are asymmetric.

These best fit values are expected to be linearly proportional to an independent variable, let's say, time. Thus I want to fit the data to a linear function. However, I couldn't find a Python library that supports a fitting with asymmetric uncertainty.

I believe this kind of problem is common in statistics. Is there a reasonably simple way to fit a linear model to data with an underlying non-normal/asymmetric distribution?

Nathan
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Nownuri
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  • Possible duplicate of Linear model Heteroscedasticity – E. Sommer Jul 01 '19 at 07:53
  • It is possible to fit 10 data points where 2 large errors were negative and 8 small errors were positive. Is this the type of situation you are asking about? – James Phillips Jul 01 '19 at 11:58
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    @JamesPhillips No I meant the error bar for each data point is asymmetric around the data point. It's not +/- y but +y_1, -y_2. – Nownuri Jul 01 '19 at 12:18
  • Thank you for clarifying, I think the "on hold" status can be removed. I have never considered this and find the question very interesting. – James Phillips Jul 01 '19 at 19:17
  • @E.Sommer the Original Poster clarifying comment is that the uncertainties or errors in the dependent data are known to be asymmetrical about each data point's given value, so this does not appear to be a duplicate and seems unrelated to heteroskedasticity. I personally had never considered that this might be possible. – James Phillips Jul 01 '19 at 20:39
  • What are your data? Can you post them?My first guess is that they are from a different distribution than the normal, & you could address the issue possibly with a transformation of y, possibly with a GLM w/ an appropriate response distribution, or possibly some other way. But we can't tell without more information. – gung - Reinstate Monica Jul 03 '19 at 02:10
  • This can be done with a custom non-linear solver, where within each iteration of the solver each individual data point's error is examined to determine which of the two uncertainties is to be applied to that individual error. I have never seen this type of per-data-point asymmetric uncertainty and know of no existing library to use it, but it seems reasonably possible to make such a regression as I describe. – James Phillips Jul 05 '19 at 01:34

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