(Created 2009-08-11.)

STATISTICAL MODELLING OF EXTREME VALUES | FMS155 |

**Aim**

The course aims to give theoretical knowledge in mathematical modelling of extreme events and discusses in detail how the theory can be applied in practice. Different courses of action for modelling of extreme values are discussed and guidance is given as to how the models can be modified to fit different practical situations. The students should also learn about more advanced models for extreme value analysis, including multivariate extreme value distributions and extreme values for non-stationary processes.

*Knowledge and understanding*

For a passing grade the student must

- be familiar with the fundamental results in univariate extreme value analysis,
- be able to describe the fundamental statistical methods of extreme value theory,
- understand the mathematical theory behind the methods and implications of the assumptions made in order to develop the theory, as well as understand the impact of these assumptions on application of theory,
- be able to describe the differences between the univariate and multivariate extreme value theory.

*Skills and abilities*

For a passing grade the student must

- identify those situations where extreme value theory can be used,
- know which computer packages are available for application of theory and also know how to use those discussed in the course,
- be able to estimate and predict extreme events in the univariate case,
- be able to explain the mathematical models and statistical methods for extreme value analysis,
- be able to explain what type of data is needed in order to apply the theory,
- assess whether the theory can be used on a specific problem,
- give some examples of application of the theory,
- explain, step by step, how the theory can be applied,
- know where to find more information about those models which have been discussed in detail in the course.

**Contents**

Extreme value theory concerns mathematical modelling of random extreme events. Recent development has introduced mathematical models for extreme values and statistical methods for them. Extreme values are of interest in, e.g., economics, safety and reliability, insurance mathematics, hydrology, meteorology, environmental sciences, and oceanography, as well as branches in statistics such as sequential analysis and robust statistics. The theory is used, e.g., for flood monitoring, construction of oil rigs, and calculation of insurance premiums for re-insurance of storm damage. Often extreme values can lead to very large consequences, both financial and in the loss of life and property. At the same time the experience of really extreme events is always very limited. Extreme value statistics is therefore forced to difficult and uncertain extrapolations, but is, none the less, necessary in order to use available experience in order to solve important problems.

The course will present the fundamental statistical methods for extreme value analysis, discuss examples of applications, i.a., regarding floods, storm damage, human life expectancy, and corrosion, provide practical use of the models, and point to some open problems and possible developments.

**Literature**

Coles, S: An Introduction to Statistical Modelling of Extreme Values. Springer-Verlag 2001.