We’re rewarding the question askers & reputations are being recalculated! Read more.

# Questions tagged [extreme-value-theorem]

The tag has no usage guidance.

78 questions
Filter by
Sorted by
Tagged with
30 views

### What is the maximum possible value for $f(x)$ for $x \in [0,1]$? [on hold]

A function $f(x)$ is continuous and differentiable in $[0,1]$. If $f'(x) \le 10$ for all $x \in [0, 1]$ and $f(0) = 0$, what is the maximum possible value of $f(x)$ for $x$ in $[0, 1]$?
65 views

80 views

### Difficulty finding Lagrange multiplier because of $\leq$

Let $f: \mathbb R^3 \to \mathbb R$ be defined by $$f(x,y,z)=x-y+z$$ and $$E:=\{(x,y,z)\in \mathbb R^{3} \mid x^2+2y^2+2z^2\leq1\}$$ Find the extrema of $f$ on $E$. Path: I have already proven that ...
75 views

108 views

### What does it mean centering a Gumbel distribution?

Consider $M$ i.i.d. random variables $V_1,..., V_M$ distributed as Gumbel with location $\lambda$ and scale $\beta$. We know that (see proof at the end of the question)  E(\max_{k\in \mathcal{Y}} ...
87 views

### Extreme value theory - proof this is a poisson point process

Let $(X_n)_{n \geq 1}$ be an i.i.d sequence of real valued RVs with continous distribution function f and $M_n:=\max \{X_1,...,X_n \}$. Let $U_n:=\inf \{ k \in \mathbb{N} | X_k>X_{U_{n-1}} \}$ be ...
I know this is part of the Extreme Value Theorem but I want to tackle this one bit first, focusing on the maximum case. For a function $f$ continuous over interval $[a,b]$, it has a max value over ...
I'm trying to understand the functional form of the Generalized Pareto distribution (GPD) presented in Wikipedia. In the "Definition" section location parameter $\mu$ does not appear in the function, ...