Extreme value theory
BMETE95MM16
2019/20. 2nd semester
Classes: Wed 12.15-13.45 H45A (before the distance learning period)
Evaluation
The evaluation rules have been changed due to the introduction of distance learning at BME.
The new rules are the following:
Three homework assignments are given during the semester with three exercises each.
Each exercises is worth 3 points, 27 points can be collected in total which is scaled by 1.5 in the end yielding 30% of the final score.
No minimal requirement is imposed.
Problems and dealines are below at the exercises.
An oral exam is held in the examination period giving 70% of the final score.
In the exam, both theory and exercises can be asked with roughly equal weights.
The theoretical part is what was covered in the lectures, possible exercises are the ones from the list below and its variants.
Exercises
Distance learning information
Distance learning videos
Content of lectures
- Lecture 6. 25th Mar: examples for MDA of Gumbel distribution, normal distribution, limit for sum and max of iid. symmetric Pareto random variables
- Lecture 7. 1st Apr: generalized extreme value distributions, max-domains of attraction, generalized Pareto distribution (GPD), exceedances, kth largest maxima
- Lecture 8. 8th Apr: limit laws for record values, Poisson point process limit, law of large numbers for record times
- Lecture 9. 15th Apr: process convergence for record times, classification of limit laws for record values
- Lectrue 10. 22nd Apr: multivariate max-infinitely divisible distributions
- Lecture 11. 29th Apr: multivariate extreme value distributions
- Lecture 12. 6th May: Exercises 2, 3b, 5, 7, 9, 11, 12
- Lecture 13. 13th May: Exercises 14, 15, 16, 17, 18
Hand-written lecture notes
- Domains of attraction for sums, stable laws
- Limit laws for normalized maxima, max-stable laws
- Fisher-Tippett theorem
- Maximum domains of attraction
- Generalized extreme value (GEV) distributions, kth largest maxima, records
- Multivariate extreme value distributions
2016 lecture notes in one file
Literature