Distributions of Characteristics of Natural Disasters: Data and Classification

Abstract

This chapter is devoted to a review of empirical data on natural disasters, to a discussion of distribution laws for disaster size and to the description of the approaches used for parameterization and classification of disasters. We wish, first, to acquaint the reader with the great variety of statistical and physical characteristics used to describe different kinds of natural and man-induced disasters. As a result of this review, it appears possible to specify the place occupied in the variety of different kinds of disasters and adverse phenomena by a special class of disasters, namely, those described by distributions with “heavy tails”. The present book is mainly devoted to results of research in the statistical characteristics of just this kind of disaster. The term “heavy-tailed distribution” is commonly used for a distribution density that decreases at infinity slowly enough, for example, more slowly than any exponent. We will use the term in a narrower sense, namely, for distributions with an infinite mathematical expectation. For such distributions the law of large numbers and the central limit theorem in the theory of probability do not hold, and thus the standard statistical characteristics such as sample mean and variance are inapplicable. The distributions possessing this property – being theoretically with an infinite mean - will be called heavy-tailed distributions in what follows.