Heavy-Tailed Distributions in Disaster Analysis (eBook)

V. Pisarenko, M. Rodkin (Autoren)

eBook Download: PDF

2010 | 2010
XIV, 190 Seiten
Springer Netherland (Verlag)
978-90-481-9171-0 (ISBN)

Infos

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.

Inhalt

Introduction 6
Contents 12
Chapter 1: Distributions of Characteristics of Natural Disasters: Data and Classification 16
1.1 The Problem of Parameterization and Classification of Disasters 16
1.2 Empirical Distributions of Physical Parameters of Natural Disasters 19
1.3 Distributions of Death Tolls and Losses Due to Disasters 29
1.4 The Classification and Parameterization of Disasters 32
1.5 The Main Results 36
Chapter 2: Models for the Generation of Distributions of Different Types 38
2.1 Why Are the Characteristic Types of Distribution Prevalent? 38
2.2 The Multiplicative Model of Disasters 48
2.3 The Mixed Models 49
2.4 The Main Results 51
Chapter 3: Nonparametric Methods in the Study of Distributions 53
3.1 Application to Earthquake Catalogs 53
3.2 Estimates of the Lower and Upper Bounds for the Tail of a Distribution Function 55
3.3 Confidence Intervals for the Intensity of a Poisson Process 58
3.4 Probability of Exceeding a Past Record in a Future Time Interval 61
3.5 Distribution of the Time to the Nearest Event Exceeding the Past Maximum 63
3.6 Main Results 66
Chapter 4: Nonlinear and Linear Growth of Cumulative Effects of Natural Disasters 68
4.1 Nonlinear Growth of Cumulative Effects in a Stationary Model with the Power (Pareto) Distribution 68
4.1.1 The Existence of a Nonlinear Growth of Cumulative Effects in a Stationary Model with the Pareto Distribution 68
4.1.2 The Evaluation of the Maximum Individual Loss 70
4.1.3 The Relation Between the Total Loss and the Maximum Individual Loss for the Pareto Law 72
4.2 The Growth of Total Earthquake Loss 76
4.2.1 The Raw Data on Seismic Disasters 76
4.2.2 The Nature of Nonlinear Growth of Cumulative Earthquake Loss 79
4.2.3 The Limits of Applicability of the Pareto Law to the Estimation of Earthquake Losses 88
4.3 Main Results 95
Chapter 5: The Nonlinear and Linear Modes of Growth of the Cumulative Seismic Moment 97
5.1 Nonlinear Mode of Growth of Cumulative Seismic Moment 97
5.2 Change in the Rate at Which the Cumulative Seismic Moment Increases with Time 106
5.3 Characteristic Maximum Earthquake: Definition and Properties 109
5.4 The Characteristic Maximum Earthquake: Estimation and Application 114
5.5 The Seismic Moment-Frequency Relation: Universal? 119
5.6 Nonlinear Mode of Growth of Cumulative Seismotectonic Deformation 122
5.7 Main Results 124
Chapter 6: Estimating the Uppermost Tail of a Distribution 126
6.1 The Problem of Evaluation of the ``Maximum Possible´´ Earthquake Mmax 126
6.2 Estimation of Quantiles Qq(tau) with the Help of Theorem 1 (Fitting the GEV Distribution) 133
6.3 Estimation of Quantiles Qq(tau) with the Help of Theorem 2 (Fitting the GPD Distribution) 134
6.4 Application of the GEV and GPD to the Estimation of Quantiles Qq(tau). The Global Harvard Catalog of Scalar Seismic Moments 137
6.5 Application of the GEV and GPD to the Estimation of Quantiles Qq(tau) for Catalogs of Binned Magnitudes 145
6.5.1 Catalog of the Japan Meteorological Agency (JMA) 147
6.5.1.1 The GPD Fitting 150
6.5.1.2 The GEV Fitting 150
6.5.2 Fennoscandia Catalog 155
6.5.2.1 The GPD Fitting 157
6.5.2.2 The GEV Fitting 160
6.6 Main Results 163
Appendix A: Application of the Kolmogorov Test to the Densities That Depending on a Parameter 165
Appendix B: Estimation of the Parameters (mu,sigma, xi) of the GEV Distribution Function: The Method of Moments (MM) 166
Appendix C: Estimation of Parameters (s,xi) of the GPD by Maximum Likelihood (ML) Method 167
Chapter 7: Relationship Between Earthquake Losses and Social and Economic Situation 169
7.1 Variation in the Number of Casualties and Economic Loss from Natural Disasters 169
7.2 Dependence of Losses on Per Capita National Product Values 175
7.3 Damage Values and Social Cataclysms 177
7.4 The Natural Disasters and the Concept of Sustainable Development 180
7.5 Main Results 181
Summary and a Review 183
References 190
Index 198

Produkt-Details

• Erscheint lt. Verlag: 20.7.2010
• Reihe/Serie: Advances in Natural and Technological Hazards Research
• Reihe/Serie: Advances in Natural and Technological Hazards Research
• Zusatzinfo: XIV, 190 p.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Naturwissenschaften ► Biologie ► Ökologie / Naturschutz
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geologie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• Schlagworte: Analysis • Earthquake • earthquakes • Hazards • Mmax-values • natural disaster • Natural hazards and society • Rare strong events statistics • Seismic risk assessment
• ISBN-10: 90-481-9171-8 / 9048191718
• ISBN-13: 978-90-481-9171-0 / 9789048191710