How to calculate relative error when true value is zero? How do I calculate relative error when the true value is zero?
Say I have $x_{true} = 0$ and $x_{test}$. If I define relative error as:
$\text{relative error} = \frac{x_{true}-x_{test}}{x_{true}}$
Then the relative error is always undefined. If instead I use the definition:
$\text{relative error} = \frac{x_{true}-x_{test}}{x_{test}}$
Then the relative error is always 100%. Both methods seem useless. Is there another alternative?

If this is based on any kind of real-world situation, then there should be multiple $x_{test}$ measurements, i.e. a distribution.  Then it will have a standard deviation, or at least quantiles, and you can define the distance from the mean of the $x_{test}$ to $x_{true}$ in terms of these.  E.g., $(\mu_{test} - x_{true}) / \sigma_{test}$ will give you a sort of 'relativized error'.  You can also apply standard statistical tests for significance, e.g. the t-test.
