Course syllabus

# Statistisk modellering av extremvärden Statistical Modelling of Extreme Values

## FMS155, 7,5 credits, A (Second Cycle)

Valid for: 2012/13
Decided by: Education Board 1
Date of Decision: 2012-03-27

## General Information

Elective for: D4, F4, F4-fm, I4, I4-fir, Pi4, Pi4-fm, Pi4-mrk
Language of instruction: The course might be given in English

## 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 extreme values for non-stationary processes.

## Learning outcomes

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.

Competences and skills
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.

## Examination details

Assessment: Written exam and compulsory computer exercises.

Parts
Code: 0103. Name: Written examination.
Code: 0203. Name: Laboratory work.

• FMS012 Mathematical Statistics, Basic Course or FMS032 Mathematical Statistics, Basic Course or FMS035 Mathematical Statistics, Basic Course or FMS086 Mathematical Statistics or FMS140 Mathematical Statistics, Basic Course or FMSF01 Mathematical Statistics

Required prior knowledge: Probability theory corresponding to FMSF05.
The number of participants is limited to: No
The course might be cancelled: If the number of applicants is less than 16.
The course overlaps following course/s: MAS231, MASM15