Heavy-tailed Distributions in Disaster Analysis

by Pisarenko, V.; Rodkin, M.

• ISBN13: 9789048191703
• ISBN10: 904819170X
• Format: Hardcover
• Copyright: 2010-08-29
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Distributions of Characteristics of Natural Disasters: Data and Classification	p. 1
The Problem of Parameterization and Classification of Disasters	p. 1
Empirical Distributions of Physical Parameters of Natural Disasters	p. 4
Distributions of Death Tolls and Losses Due to Disasters	p. 14
The Classification and Parameterization of Disasters	p. 17
The Main Results	p. 21
Models for the Generation of Distributions of Different Types	p. 23
Why Are the Characteristic Types of Distribution Prevalent?	p. 23
The Multiplicative Model of Disasters	p. 33
The Mixed Models	p. 34
The Main Results	p. 36
Nonparametric Methods in the Study of Distributions	p. 39
Application to Earthquake Catalogs	p. 39
Estimates of the Lower and Upper Bounds for the Tail of a Distribution Function	p. 41
Confidence Intervals for the Intensity of a Poisson Process	p. 44
Probability of Exceeding a Past Record in a Future Time Interval	p. 47
Distribution of the time to the Nearest Event Exceeding the Past Maximum	p. 49
Main Results	p. 52
Nonlinear and Linear Growth of Cumulative Effects of Natural Disasters	p. 55
Nonlinear Growth of Cumulative Effects in a Stationary Model with the Power (Pareto) Distribution	p. 55
The Existence of a Nonlinear Growth of Cumulative Effects in a Stationary Model with the Pareto Distribution	p. 55
The Evaluation of the Maximum Individual Loss	p. 57
The Relation Between the Total Loss and the Maximum Individual Loss for the Pareto Law	p. 59
The Growth of Total Earthquake Loss	p. 63
The Raw Data on Seismic Disasters	p. 63
The Nature of Nonlinear Growth of Cumulative Earthquake Loss	p. 66
The Limits of Applicability of the Pareto Law to the Estimation of Earthquake Losses	p. 75
Main Results	p. 82
The Nonlinear and Linear Modes of Growth of the Cumulative Seismic Moment	p. 85
Nonlinear Mode of Growth of Cumulative Seismic Moment	p. 85
Change in the Rate at which the Cumulative Seismic Moment Increases with Time	p. 94
Characteristic Maximum Earthquake: Definition and Properties	p. 97
The Characteristic Maximum Earthquake: Estimation and Application	p. 102
The Seismic Moment-Frequency Relation: Universal?	p. 107
Nonlinear Mode of Growth of Cumulative Seismotectonic Deformation	p. 110
Main Results	p. 112
Estimating the Uppermost Tail of a Distribution	p. 115
The Problem of Evaluation of the ôMaximum Possibleö Earthquake Mmax	p. 115
Estimation of Quantiles Qq(¿) with the Help of Theorem 1 (Fitting the GEV Distribution)	p. 122
Estimation of Quantiles Qq(¿) with the Help of Theorem 2 (Fitting the GPD Distribution)	p. 123
Application of the GEV and GPD to the Estimation of Quantiles Qq(¿). The Global Harvard Catalog of Scalar Seismic Moments	p. 126
Application of the GEV and GPD to the Estimation of Quantiles Qq(¿) for Catalogs of Binned Magnitudes	p. 134
Catalog of the Japan Meteorological Agency (JMA)	p. 136
Fennoscandia Catalog	p. 144
Main Results	p. 152
Application of the Kolmogorov Test to the Densities That Depending on a Parameter	p. 154
Estimation of the Parameters (¿,¿, ¿) of the GEV Distribution Function: The Method of Moments (MM)	p. 155
Estimation of Parameters (s,¿) of the GPD by Maximum Likelihood (ML) Method	p. 156
Relationship Between Earthquake Losses and Social and Economic Situation	p. 159
Variation in the Number of Casualties and Economic Loss from Natural Disasters	p. 159
Dependence of Losses on Per Capita National Product Values	p. 165
Damage Values and Social Cataclysms	p. 167
The Natural Disasters and the Concept of Sustainable Development	p. 170
Main Results	p. 171
Summary and a Review	p. 173
References	p. 181
Index	p. 189
Table of Contents provided by Ingram. All Rights Reserved.