Syllabus academic year 2011/2012
(Created 2011-09-01.)
Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course will be given in English on demand. Optional for: F5, Pi5. Course coordinator: Nader Tajvidi,, Mathematical Statistics. Prerequisites: FMS155 Statistical modelling of Extreme Values. The course might be cancelled if the number of applicants is less than 16. Assessment: Written exam and home assignments. Parts: 2. Further information: The course is also given at the faculty of science. Home page:

Multivariate extreme values occure in, e.g., economy, safety and reliability, insurance mathematics, hydrology, meteorology. environmental sciences, och ocenanography. They often show complicated dependencies between several variables, e.g. between wind speed, wind direction, wave height and ocean currents. This calls for special methods that can be used, e.g., for analysis of trends, calculation of flooding risks, and modelleling storm damage, corrosion speed, or financial risks. Climat and environmental changes, as well as an increasingly complicated financial market, pose new demands on deapend knowledge in these fields. This course is a countinuation of FMS155 Statistical Modelling of Extreme Values, and teaches methods for analysis of multivariate and spatial extreme values.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

Judgement and approach
For a passing grade the student must

Weak convergence for normalized extreme values of stochastic vectors, different characterisations of multivariate extreme value distributions, "peaks over threshold"-model in the multivariate case, different definitions of multivariate generalized Pareto distributions, statistical inference for multivariate extreme values, parametric and semi-parametric methods for multivariate extreme values, use of copula in modelling extreme values, point process characterisation of extreme values, prediction of extreme values, examples of applications of the theory, e.g., estimation of operational risk, climate changes and wind insurances.

Resnick, S.I. (2007) Extreme values, Regular Variation and Point Processes, Berlin: Springer-Verlag.
Harry, J. (1997) Multivariate Models and Multivariate Dependence Concepts, Chapman & Hall/CRC Monographs on Statistics & Applied Probability.


Code: 0111. Name: Written Examination.
Higher education credits: 6. Grading scale: TH. Assessment: Written examination.

Code: 0211. Name: Laboratory Work and Home Assignments.
Higher education credits: 1,5. Grading scale: UG. Assessment: Laboratory work and home assignments.