# Questions tagged [extreme-value-analysis]

This tag is for questions pertaining to the probabilistic/statistical theory of extreme deviations from the median of probability distributions. A central result of this theory is the Fisher–Tippett–Gnedenko theorem. It is not to be confused with the extreme-value-theorem tag that refers to a theorem for real valued continuous functions on a closed and bounded interval.

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### A basic property of slowly varying functions

It seems that a fundamental property of a slowly varying function is that for all $\delta > 0$ $$\lim_{x\to \infty} L(x) \, x^{-\delta} = 0.$$ How to prove this? The only book I found (that was ...
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### Expectation of maxima of $n$ Erlang-distributed (Gamma-distributed) random variables for small $n$

Say I have $n$ i.i.d. random variables $\mathbf{X}_n = \{X_1,X_2,\ldots,X_n\}$, where $X_i \sim \operatorname{Erlang}(k,\theta)$ or $\Gamma(k,\theta)$. Define $$Z_n := \max \mathbf{X}_n$$ I know that ...
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### AM GM inequality using conditional extrema

Given: $\prod_{i=1}^n x_i = 1$ leads to constraint function $G(x_1,x_2,...,x_n)=\prod_{i=1}^n x_i-1$ ($\prod_{i=1}^n x_i =x_1 x_2...x_n$) Task is to to find the minimum using conditional extrema of ...
### How to find extrema for given implicit function of $(x,y,z)$ variables?
Given the equation $$z^3 - 33xyz - 27 = 0,$$ we know that $z=z(x,y)$. As $z$ is function of both $x$ and $y$, I don't really know how to search for extremeum, because of three variables. I only ...