Questions tagged [extreme-value-theorem]

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19 questions
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Can the ratio of the two smallest element of an iid sample converge to 1 if the support of $X$ is positive?

We have: $\mathbb P(X \leq 0)=0$ and $\mathbb P (X \leq a)>0$ for any $a>0$.
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Finding points which are not local maximum or minimum

Consider the picture below: This is the levels curves for a function $f(x,y)$ where: Blue line is the partial derivative of $f(x,y)$ with respect to x Red line is the partial derivative of $f(x,y)$ ...
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Showing that the pointwise limit of continuous functions equals its supremum somewhere on compact domain

I'd appreciate hints on proving the following theorem: If $f(x) = \lim_{n\to\infty} f_n(x)$ for each $x \in [0,1]$ and $M = \sup_{x\in[0,1]} f(x)$, then there is $t \in [0,1]$ such that $f(t) = M$. ...
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Critical point of a multivariable function

For the function $f(x,y)=x^2y^2 + \frac{1}{y} + \ln(\frac{1}{x})$ I get two critical points, namely $P_1 =\left(\sqrt{\frac{1}{2}},1 \right)$ and $P_2 =\left(-\sqrt{\frac{1}{2}},1 \right)$. However ...
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Rate of convergence of the maxium of a random sequence

I came across a problem which requires the rate of convergence of $\sup_{1\le j \le N} |\sum_{i=1}^{N}X_{i,j}/N|$. If sup over a finite number of objects, this is a simple application of LLN. However, ...
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Frechet distribution function compared to empirical data

So basically I am trying to evaluate VaR on the Tesla stock using a Block Maxima method. I.e. I assume that the worst weekly log returns follow a generalized extreme value distrubtion with the shape ...