If the uncertainty of a function $f(x,y)$ is given by:

$$\delta f = |f_{best}|\sqrt{ \left( \frac{\delta x}{x_{best}} \right)^2 + \left( \frac{\delta y}{y_{best}} \right)^2}$$

what do we do if $x_{best}$ or $y_{best}$ are zero? Presumably, $\delta x$ and $\delta y$ need not be zero.

  • $\begingroup$ The formula you're using is not suitable for the kind of case you're applying it to. $\endgroup$ – Glen_b Apr 9 '14 at 2:44
  • $\begingroup$ @Glen_b Cool. Do you mind elaborating a little? Or providing a link? $\endgroup$ – confused guy Apr 9 '14 at 3:00
  • $\begingroup$ @Glen_b What is the equation one should use in that case...? $\endgroup$ – confused guy Apr 9 '14 at 3:01
  • $\begingroup$ Such formulas rely on assumptions; you've violated the assumptions of the one you used, but you don't indicate which assumptions should apply. [Further, with variables that can be non-positive, I'd suggest you probably want to consider absolute error rather than relative error.] $\endgroup$ – Glen_b Apr 9 '14 at 3:04
  • $\begingroup$ By the way, can you say where your formula came from? Did they explain anything about it? $\endgroup$ – Glen_b Apr 9 '14 at 3:04

you don't use relative error in this case: $\delta f=\sqrt{(\delta x)^2+(\delta y)^2}$

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    $\begingroup$ Cool. Do you mind elaborating just a bit? I know a little math, but I'm a total rookie when it comes to stats. $\endgroup$ – confused guy Apr 9 '14 at 2:19
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    $\begingroup$ Or if you can provide a link, that'd be okay too. $\endgroup$ – confused guy Apr 9 '14 at 2:25
  • $\begingroup$ For a standard guide in uncertainty propagation, see the GUM, Section 5. $\endgroup$ – Pascal Dec 13 '16 at 9:09

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