Caveats and Warnings
Error estimates for non-linear functions are biased on account of using a truncated series expansion. The extent of this bias depends on the nature of the function. For example, the bias on the error calculated for log x increases as x increases since the expansion to 1+x is a good approximation only when x is small.
In the special case of the inverse where, the distribution is a Cauchy distribution and there is no definable variance. For such ratio distributions, there can be defined probabilities for intervals which can be defined either by Monte Carlo simulation, or, in some cases, by using the Geary-Hinkley transformation.
Read more about this topic: Propagation Of Uncertainty
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