Heavy-Tailed Distributions in Disaster Analysis

This book presents new approaches to seismic risk estimation and forecasting the damage caused by all types of earthquakes. It examines trends in the costs inferred by damage as related to changing social and economic situations for different regions.

Mathematically, natural disasters of all types are characterized by heavy tailed distributions. The analysis of such distributions with common methods, such as averages and dispersions, can therefore lead to erroneous conclusions. The statistical methods described in this book avoid such pitfalls. Seismic disasters are studied, primarily thanks to the availability of an ample statistical database. New approaches are presented to seismic risk estimation and forecasting the damage caused by earthquakes, ranging from typical, moderate events to very rare, extreme disasters. Analysis of these latter events is based on the limit theorems of probability and the duality of the generalized Pareto distribution and generalized extreme value distribution. It is shown that the parameter most widely used to estimate seismic risk Mmax, the maximum possible earthquake value is potentially non-robust. Robust analogues of this parameter are suggested and calculated for some seismic catalogues. Trends in the costs inferred by damage from natural disasters as related to changing social and economic situations are examined for different regions.

The results obtained argue for sustainable development, whereas entirely different, incorrect conclusions can be drawn if the specific properties of the heavy-tailed distribution and change in completeness of data on natural hazards are neglected.

This pioneering work is directed at risk assessment specialists in general, seismologists, administrators and all those interested in natural disasters and their impact on society.

Mathematical evidence of non-robustness of Mmax parameter are presented Robust analog of Mmax is presented Evidence in support of possible realization of sustainable development is presented Distribution laws typical for natural disasters are examined Includes supplementary material: sn.pub/extras

Zusammenfassung

From the reviews: "This book is, therefore, timely and should be welcomed by those working in earthquake forecasting ... . an important reference text that should be useful to those seeking to estimate loss and quantify probabilities of rare events using the conventional approach of nipping and tucking the seismic database to the Poissonian figure. Those seeking to model the real Earth seismic expression may also find it a useful start point." (Joan L. Latchman, Mathematical Geosciences, Vol. 43, 2011)

Inhalt
Distributions of Characteristics of Natural Disasters: Data and Classification.- Models for the Generation of Distributions of Different Types.- Nonparametric Methods in the Study of Distributions.- Nonlinear and Linear Growth of Cumulative Effects of Natural Disasters.- The Nonlinear and Linear Modes of Growth of the Cumulative Seismic Moment.- Estimating the Uppermost Tail of a Distribution.- Relationship Between Earthquake Losses and Social and Economic Situation.