All Questions
Tagged with extreme-value normal-distribution
14 questions
32
votes
3
answers
17k
views
Extreme Value Theory - Show: Normal to Gumbel
The Maximum of $X_1,\dots,X_n. \sim$ i.i.d. Standardnormals converges to the Standard Gumbel Distribution according to Extreme Value Theory.
How can we show that?
We have
$$P(\max X_i \leq x) = P(...
- 1,271
24
votes
2
answers
11k
views
Distribution of the maximum of two correlated normal variables
Say I have two standard normal random variables $X_1$ and $X_2$ that are jointly
normal with correlation coefficient $r$.
What is the distribution function of $\max(X_1, X_2)$?
- 2,295
15
votes
2
answers
21k
views
What is the distribution for the maximum (minimum) of two independent normal random variables?
Specifically, suppose $X$ and $Y$ are normal random variables (independent but not necessarily identically distributed). Given any particular $a$, is there a nice formula for $P(\max(X,Y)\leq x)$ or ...
- 355
3
votes
1
answer
870
views
$\mathbb{E}$ and Variance of the maximum of independent $\mathcal{N}(\mu_i, \sigma_i^2)$
I am interested in the expectation and the variance of the maximum of several independent, normal distributed variances. That is, given a set of $I$ different RVs with $X_i \sim \mathcal{N}(\mu_i, \...
- 14k
9
votes
1
answer
9k
views
Expected value of minimum order statistic from a normal sample
UPDATE Jan 25th 2014: the mistake is now corrected. Please ignore the calculated values of the Expected Value in the image uploaded - they are wrong- I don't delete the image because it has generated ...
- 60.8k
7
votes
2
answers
286
views
What is the distribution of a bivariate normal component conditional on the max of the other component?
Let $n$ be a large integer, and consider two independent multivariate Gaussian $n$-vectors $x, z$ with $x\sim\mathcal{N}\left(0,I\right),$ and $z\sim\mathcal{N}\left(0,\sigma^2 I\right)$. Let $y=x+z$. ...
- 563
3
votes
1
answer
5k
views
Expectation of max of two normal random variables
I have been reading this paper about the maximum and minimum of two normal distributed variables.
Inside the paper there is the formula for the expectation of this the maximum of the two variables. ...
- 133
9
votes
1
answer
2k
views
Approximating the mathematical expectation of the argmax of a Gaussian random vector
Let $X = \left( {{X_1},...,{X_n}} \right) \sim \mathcal{N}\left( {{\mathbf{\mu }},{\mathbf{\Sigma }}} \right)$ be a Gaussian random vector and $I = \mathop {\arg \max }\limits_{i = 1,n} {X_i}$.
$I$ ...
user193726
7
votes
1
answer
411
views
Estimation of a uniform distribution corrupted by Gaussian noise
Problem definition
I have a dataset composed by $m$ observations $y^{(1)},\dots,y^{(m)} \in \mathbb{R}^2$ generated as follow
\begin{equation*}\begin{aligned}
y &= z + v \newline
z & \sim\...
- 473
5
votes
2
answers
1k
views
CDF of maximum of $n$ correlated normal random variables
The maximum of $n$ normal i.i.d. random variables
$$Y=\max\{x_1,...,x_n\},$$
$$x_i \sim N[0,1]$$
has the CDF
$$P(Y\le y)=\Phi(y)^n $$
but how does the CDF look like, if the variables are identically ...
- 1,250
5
votes
1
answer
313
views
What is the maximum value in a finite selection of a normally distributed variable?
A parameter of an object is normally distributed with a mean m and a std. dev. s. If r such ...
- 153
4
votes
0
answers
189
views
Extreme value distribution for univariate normal: Derive parameters of the Gumbel [duplicate]
I have a question regarding the extreme value distribution corresponding to i.i.d. samples $X_i$ from a normal distribution, say $X_i\sim N(\mu, \sigma^2)$.
According to the theorem of Fisher-Tippett-...
- 41
3
votes
0
answers
770
views
GEV of Normal Distribution and relationship of the parameters
My question goes on Extreme Value Theory for the Normal distribution (www.math.ethz.ch/~embrecht/RM/chap7.pdf):
Which type of GEV (Generalized Extreme Value) distribution does the Normal distribution ...
- 1,271
2
votes
0
answers
1k
views
maximum gap between order statistics of normally distributed random variables [closed]
I am currently working on a not-that-easy problem involving order statistics. As I am unsure as to how I could solve it, I thought it might already possess a solution. So here I am, my questions is: ...
- 21