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.
Questions tagged [extreme-value-analysis]
104 questions
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Block size BMM when modeling Generalized Extreme Value distribution
I'm an Operations Research student who's trying to wrap his mind around extreme value theory. I've read into EVT and more specific into the first theorem of Fisher, Tippett and Gnedenko.
In their modeling approach, they apply block maximum modeling…
Mr. N
- 43
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The Marcum Q- function and the limit of Modified Bessel Functions
I've recently come across the following limit:
$$\lim_{n \to \infty} \left[\sum_{k=1}^{\infty} \left(\frac{a}{b}\right)^k \operatorname{I}_k(ab)\right]^n$$
where $\operatorname{I}_k$ are modified Bessel functions.
Is there a known solution for this…
lbagua
- 51
1
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1 answer
Question on Block Maxima Method for Extreme Value Theory
I am reading about extreme value theory. Let $X_1, X_2, ...$ be i.i.d. random variables and $M_n = \text{max}\{X_1,...,X_n\}$ as usual.
I understand that, by the Fisher-Tippett-Gnedenko theorem:
If there exist sequences $b_n \in \mathbb{R}$ and $a_n…
AdaLovelace
- 73
- 6
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1 answer
Is $(0,0,0)$ saddle point?
$f(x,y,z)=x^3+y^3+z^3-3xy-3yz$
Is $(0,0,0)$ saddle point?
$\nabla f(0,0,0)=0$, so $(0,0,0)$ is one of the stationary point.
Also, because of my posture The reason why $f(0,0,0)$ is not a extreme value. ,
$f(0,0,0)$ is not a extreme value.
Therefore,…
daㅤ
- 3,264
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0 answers
The reason why $f(0,0,0)$ is not a extreme value.
$f(x,y,z)=x^3+y^3+z^3-3xy-3yz$
According to wolfram alpha, $f(0,0,0)$ is not a extreme value.
I considered why $f(0,0,0)$ is not a extreme value.
Is this reason correct?
When $x$ is very close to $0$ with $y=x,…
daㅤ
- 3,264
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vote
1 answer
Finding global Max/Min in multi valued function with boundaries
so this is an exmaple from a book I have.
Find Max/Min of $f=\frac{x^2}{2} + \frac{y^2}{2}$ on $E=\big\{ (x,y)\in \mathbb R \big| \frac{x^2}{2} + y^2 \leq 1\big\}$
1. Step: We look at the Interior of E:
$df=(x,y)=0 \Rightarrow p_0 = (0,0)$
2. Step:…
xotix
- 887
0
votes
2 answers
Limit involving logarithms and an unknown function
I need to find a function $a(t)$ which is positive such that for some $\gamma > 0$ we have:
$$\lim_{{t \to \infty}}\frac1{a(t)}\left({-\frac{1}{{\ln(1-\frac{1}{{xt}})}} + \frac{1}{{\ln(1-\frac{1}{t})}}}\right) = \frac{x^{\gamma}-1}{\gamma}
$$
I know…
user979120
- 3
- 3
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values on the boundaries of a open interval
Say we have a simple function $f(x)=x\cdot e^{-10x}$, we want to obtain the maximum value of it in an open interval $x \in (0.2, 1)$. Loosely speaking, the maximum point is at $x=0.2$ which is not within the range. But I want to use the result…
weidade3721
- 145