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Introduction to Extreme Value Theory: N=1000 Sample from Normal Distribution

Learn about Extreme Value Theory using N=1000 samples from a Normal Distribution N(0,1) and fitting a curve. Explore block-maxima and threshold approaches with asymptotic models, degenerate distributions, and maxima calculations with Frechet, Weibull, Gumbel densities. Understand Maxima I and II, Fisher Tippet theorem, and max-stable distributions. Discover the domain of attraction with examples like the standard exponential and uniform distributions.

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Introduction to Extreme Value Theory: N=1000 Sample from Normal Distribution

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  1. Extreme Value Theory: Part I Sample (N=1000) from a Normal Distribution N(0,1) and fitted curve

  2. Two main kind of Models: Block-maxima and Threshold approaches

  3. Asymptotics: Problems of degenerate distributions

  4. Asymptotic models for Maxima I:

  5. Example: Densities

  6. Densities of distribution: Frechet Weibull Gumbel

  7. Important relationship:

  8. Asymptotic models for Maxima II: From Fisher Tippet theorem:

  9. Class of non-degenerate limit distributions of maxima: Example: Standard exponential distribution In other words, a distribution is max-stable if, and only if, it is a generalized extreme value distribution.

  10. Maximum Domain of Attraction: Example: Standard exponential distribution

  11. Example: Uniform distribution

  12. End of Part I of Extreme Value Theory

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