Concept

# Propagation of uncertainty

Summary
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function. The uncertainty u can be expressed in a number of ways. It may be defined by the absolute error Δx. Uncertainties can also be defined by the relative error (Δx)/x, which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, σ, which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval x ± u. However, the most general way of characterizing uncertainty is by specifying its probability distribution. If the probability dist
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