# FMSN55/MASM15: Statistical Modeling of Extreme Values

## General information:

• ### This course is prerequisite for Statistical Modeling of Multivariate Extremes (FMSN15/MASM23) which runs in the second period of fall semester 2019.

• Credits: 7.5hp/7.5 ECTS credits.

• Requirements: Mathematical Statistics, basic course. Note that the course on probability theory is NOT required; see also the department's home page here for course requirements.

• Time period: Study period 4.

• Course Description:
Extreme value theory concerns mathematical modelling of extreme events. Recent developments have introduced very flexible and theoretically well motivated semi-parametric models for extreme values which now are at the stage where they can be used to address important technological problems on handling risks in areas such as wind engineering, hydrology, flood monitoring and prediction, climatic changes, structural reliability, corrosion modelling, and large insurance claims or large fluctuations in financial data (volatility). In many applications of extreme-value theory, predictive inference for unobserved events is the main interest. One wishes to make inference about events over a time period much longer than that for which data are available. For example, insurance companies are interested in the maximum amount of claims due to storm damage during, say, the next 30 years, based on data from the past 10-15 years. In bridge design a major factor is the maximum wind speed that can occur in any direction during the life of the bridge. However, the dataset used to estimate a return value for high wind speeds is often recorded over a much shorter time period than the expected lifetime of the bridge. Statistical modelling of extreme events has been subject of much practical and theoretical work in the last few years. The course will give an overview of a number of different topics in modern extreme value theory including the following topics:
• Statistical methods for extremal events,
• Some examples of application of the theory in large insurance claims due to windstorms, flood monitoring and pit corrosion,
• Exercises on detailed ``step-by-step'' use of extreme value modelling, and
• Discussion of some open problems in the field.

• Course syllabus: English ,Swedish

• Teacher: Nader Tajvidi, tfn 046/2229612

• Language: The course will be given in English.

• Computer assignments: There are three mandatory computer laboratory sessions in the course.
• Exams : Please check upcoming exams in the Centre for Mathematical Sciences or Lund University's exam schedule TimeEdit for scheduled exams. For information on advanced registration for re-take exams see this page.

• Allowed aids in the exam:

• Collection of formulas and tables pdf, ps and Appendix 2 on ``Some distributions and their characteristics".
• Copy of Chapter 4 entitled ``Order Statistics'' from A. Gut (1995) An Intermediate Course in Probability Theory, Springer-Verlag, New York.
• Calculator.
• Dictionaries for translation.