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source: Embrechts pg 165, 354 (3.52) G is Generalized Pareto Distribution

Base on that theorem, could I conclude that 1) if I have a data and the excess fit with Generalized Pareto Distribution, then the data fit Generalized Extreme Value Distribution? 2) the shape parameter of Generalized Pareto Distribution is the same as Generalized Extreme Value Distribution?

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Hi,

See Coles(2001) "An Introduction to Statistical Modeling of Extreme Values" Pgs. 75-76.

I think it can help. enter image description here

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    $\begingroup$ This looks potentially useful, Maria, but without the context of the referenced equations $(4.2)$ and $(4.3)$ it's not sufficiently clear to answer the question. Perhaps you could add an explanation of the quoted text? $\endgroup$
    – whuber ♦
    Oct 30, 2019 at 14:00

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