Heavy-tailed distribution; arithmetic

Measurements are never absolutely accurate; so, it is important to estimate how the measurement uncertainty affects the result of data processing. Traditionally, this problem is solved under the assumption that the probability distributions of measurement errors are normal -- or at least are concentrated, with high certainty, on a reasonably small interval. In practice, the distribution of measurement errors is sometimes heavy-tailed, when very large values have a reasonable probability. In this paper, we analyze the corresponding problem of estimating the tail of the result of data processing in such situations.