Outline for the extreme value theory lecture, March 13


I intend to cover the following topics: 


(1)    The Poisson distribution as the "law of rare events" (known, cf. TK).

(2)     A motivating analogy: The central limit theorem (CLT) for suitably scaled sums X1 + ... + Xn, where {Xi} i.i.d. copies of X

(3)    Instead of sum{Xi}, what about maxima Mn = max{X1 + ... + Xn} (suitably scaled)? How are they distributed, asymptotically?

(4)    So scaled Mn → GEV in distribution, but which GEV?

(5)    Other characterizations, and connection to "excess over threshold"

(6)    Bringing it all together:

(7)    If time permits: Inference from data.