Gatha Cognition®
Perception, Learning and Reasoning

#### Introduction

Statistical Theory of Extremes

1-10

Asymptotic behaviours , Asymptotic distribution , Exceedances , Order statistics , Weibull distribution , Stochastic Model , Experimental digression

Statistical Theory of Extremes deals with analysis and predict the aspects of natural phenomena using univariate or multivariate sampled data. Natural phenomena, as floods, large fire claims, heavy rains, gusts of winds, and large waves analysed using suitable or available samples of random sequences or of stochastic processes. Interplay between order statistics and exceedances. Exact distribution of order statistics. Asymptotic behaviour of the sample quantiles, i.e. of central order statistic, as an approximation tool for efficient estimation of “extreme” quantiles of the design of structures, evaluation of extreme conditions or forecasting catastrophes. The book deals with behaviour of maxima with conversion to minima results immediate.

The purpose of STATISTICAL THEORY OF EXTREMES is to deal with, analyze and predict (or forecast) aspects of natural phenomena that correspond to the largest or smallest values of sampled data, or to over - or under passing some level that sometimes lead to natural disasters.

Floods, large fire claims, heavy rains, gusts of wind, and large waves, are examples of maxima or largest values of samples, as well as droughts, breaking strength of materials, failure of equipment or apparatus, low temperatures, etc. are examples of minima or smallest values of samples.

In fact, in data analysis, we can sometimes proceed through a sequence of models, adapted to the case.

The applications will be based on the use of asymptotic distributions as to the description of extremes, useful for forecasting: so obtaining asymptotic distributions, as well some reference to the speed of convergence, plays an essential role in the book.

Case studies, as in the last chapter and in the statistical chapters of the book, may be of help to practitioners.