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Bounding The Rates Of Convergence Towards The Extreme Value Distributions, James Palmer

Honors Program Theses and Projects

Extreme value theory is a branch of probability which examines the extreme outliers of probability distributions. Three extreme value distributions arise as the limits of the maxima of sequences of random variables with certain properties. In this paper, we will first give information about these three distributions and prove that they are the only limit distributions of maxima. After that, we switch to a discussion about Stein's method. Stein's method is commonly used to prove central limit theorems. Stein's method also develops bounds on the distance between probability distributions with regards to a probability metric. There are three essential steps …