Application of Convergence to Types: Limit Distributions for Extremes
Hsin-Chieh WongNCU 10:00–11:00 Hongjing Hall M107Abstract
A beautiful example of the use of the convergence to types theorem is
the derivation of the extreme value distributions. These are the possible limit
distributions of centered and scaled maxima of i.i.d. random variables. Surprisingly,
there are only three types of limiting distributions, the Gumbel, Frechet, and
Weibull distributions, known collectively as the extreme value distributions.
In this talk, we will state and prove the celebrated Extremal Types Theorem.
Keywords: maximum domain of attraction, extremal types theorem,
convergence to types theorem.