All Questions
Tagged with extreme-value normal-distribution
14 questions with no upvoted or accepted answers
3
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Distribution of the minimum of the squared Euclidean norm of a $N(\mu,\Sigma)$ random variable
Suppose that $X^n := \{x_1, x_2, \ldots, x_n\}$ is a sample of $n$ i.i.d $p$-dimensional points, where $X \sim N(\mu, \Sigma)$.
What is known about the distribution of $\min_{x_i \in X^n} \|x_i\|^2_2$?...
- 802
3
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770
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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
1
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Distribution of the difference between the maximum of $n$ identical and correlated Gaussian random variables and any one of them
Suppose, there are $n$ identical and correlated Gaussian random variables namely, $X_1, X_2, ..., X_n$ with $X_i\sim\mathcal{N}(0,\sigma^2)$ for all $i\in\{1,2, ...n\}$. The correlation coefficient ...
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Given 5 variables, all independently normally distributed, what is the probaility that variable A is lower than the other 4 variables?
Suppose variables A B C D and E are independent, normally distributed, with known variance and mean.
What is the probability that A is less than B and C and D and E?
Essentially, I have model ...
- 11
1
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125
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Distribution of maximum of sample means
Let $X_1, ..., X_n$ be a sample from $N(\mu, 1)$. Fix $1 \leq m<n$ and define $$T_i= \frac{1}{m}\sum\limits_{j=i}^{i+m-1} X_j,$$ for $i \in \lbrace 1, ..., n-m+1 \rbrace$. We have the test that ...
- 111
1
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232
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Maximum absolute from complex Gaussian distribution
Consider a random variable $Y$ with complex Gaussian distribution, i.e $Y \sim \mathcal{C N}(\mu,\sigma^2)$. We can write $Y$ as real ($Y_r$) and imaginary component ($Y_j$) as $Y = Y_r + i Y_j$. ...
- 121
1
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142
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Expectation of a sequence of random variables based on a set of iid Gaussian random variables
This is a rather convoluted problem: I'll my best trying to explain it. So, we have $m$ iid standard Gaussian RVs $Q_i$. We get a realization from each of them, and these values $q_1,\dots,q_m$ are ...
- 18.4k
1
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46
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Probability that the Maximum of Many Normal Draws from Multiple Classes is of one Class
Given a set of $N=n_i+n_j+n_k$ draws from distributions $N(\mu_i,\sigma_i^2), N(\mu_j,\sigma_j^2), N(\mu_k,\sigma_k^2)$, what is the probability that the maximum drawn value was from distribution $i,j,...
- 11
1
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308
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Could the sum of two normally distributed random variables be a GEV distribution?
I'm playing with Matlab, I have got a test statistic $T$ wich is of the form :
$$T(x)=\sum_{i=1}^{n}f_{i}(x)+\sum_{i=1}^{n}g_{i}(x)+c $$
Where $f$ and $g$ are functions of the observations $x$, $n$ is ...
- 902
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25
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Separating components of a likelihood maximization
Apologies for the naive question, but I have a problem I would like to solve.
Suppose I have a two dimensional likelihood of the form
$L \propto \exp\{-\frac{1}{2}\} \begin{bmatrix}x & y\end{...
- 1
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41
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Identifiability of a bivariate normal distribution with identified minimum
I am suffering from to understand a proof of a paper.
(Nádas, Arthur. "The distribution of the identified minimum of a normal pair determines' the distribution of the pair." Technometrics 13....
- 441
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34
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Find maximum of bimodal posterior pdf
can you help find the maximum (analytically) of the following posterior pdf?
$p(\theta|x) = \frac{\alpha}{\sqrt{2\pi}}e^{-\frac{1}{2}(\theta-x)^2} + \frac{1-\alpha}{\sqrt{2\pi}}e^{-\frac{1}{2}(\theta+...
- 1
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51
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Estimate true mean of the maximum of N sample means
Let's say we have N distributions $\mathcal N(\mu_i, \sigma_i)$, each with unknown mean $\mu_i$ and unknown standard deviation $\sigma_i$, $i=0,...,N-1$.
For each $i$, $M$ independent random samples ...
- 1
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54
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Drawing the smallest value from a set of distributions
I have a specific number of normal distributions $N_D$ all with their own mean $\mu$ and std $\sigma$. Now I obtain a sample from all distributions which results in a set of $N_D$ samples. What is the ...
