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I'm calculating the error on $\theta$ from given PDG values for $f(\theta)=sin^2(2\theta) \pm \sigma_{f}$

Question: I'd like to calculate the errors (from the inverse function) as $$\sigma_{\theta}^{neg} = f - f^{-1}( f - \sigma_{f}^{neg} ) $$ $$\sigma_{\theta}^{pos} = f^{-1}( f + \sigma_{f}^{pos} ) - f $$

How is this procedure called officially? Does it have a commonly understood name?

I found here the name "(e) [...] The simple approach.", which does not sound descriptive of the procedure.

Comment: I'm not sure about the Gaussian error propagation in this case, since the error is asymmetric and the Gaussian approximation - which only gives a slope of the function at this point - does not describe the confidence interval well.

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  • $\begingroup$ I think this question is more suitable for mathematics forum. $\endgroup$ – hsinghal Jul 2 '16 at 18:35
  • $\begingroup$ I'm asking for a field-specific term, so the forum is fitting. $\endgroup$ – IljaBek Jul 2 '16 at 22:53

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