Nonlinear and Linear Growth of Cumulative Effects of Natural Disasters

Abstract

As was shown earlier, the economic losses and casualties from natural disasters are often fitted by self-similar power-law distributions with heavy tails. If the exponent β of such a distribution does not exceed unity, β ≤ 1, then the mathematical expectation is infinite. In this case, the standard statistical tools, such as sample mean and sample standard deviation, are highly unstable (see Table 1.1). The increase of sample size, in contrast to the ordinary case of finite expectation, does not enhance the accuracy of the sample mean. The large statistical scatter of sample means (which are widely used until today, see e.g., [O1, O2, O3]) makes them inadequate for practical use in problems of loss reduction. We discuss below some approaches to the reliable estimation and prediction of total effects for the cases in which the standard statistical tools are inefficient.