Extremes

Introduction

The extreme value theory deals with the stochastic behavior of the minimum and the maximum of random variable. It involves a large variety of applications such as natural phenomena: rainfall, floods, atmospheric turbulence, corrosion...etc. The distribution proprieties of extremes and intermediate order statistics are determined by the upper and lower tails of the probability distribution.

Application of Extreme Value Theory :

  • Meteorology

    • extreme wind

    • heavy precipitation events

    • extreme in climate change

  • Hydrology

    • protection against flood

  • Finance

    • maximal daily lost

    • distribution of incomes

Probability distribution of temperature increment (red) measured in urban lake, compared with a Gaussian distribution (blue).
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