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Suppose you have a general random Gaussian vector $\mathbf{X}\sim\mathcal{N}\left(\boldsymbol{\mu},\boldsymbol{\Sigma}\right)$. I'm looking for the simple way to calculate the distribution of the max …

Let $k<d$ two positive integers, and $\{p_i\}_{i=1}^d$ a series of probabilities, with $p_i \in (0,1)$ and $\sum_{i=1}^d p_i = k$. We wish to sample exactly $k$ distinct indices $\mathcal{I}\triangleq …

Suppose you have a general $n$-th dimensional random Gaussian vector with probability distribution function $\mathcal{N}\left(\mathbf{x}|\boldsymbol{\mu},\boldsymbol{\Sigma}\right)$. What is the compu …

I'm looking for fast convergence rates for the central limit theorem - when we are not near the tails of the distribution. Specifically, from the general convergence rates stated in the Berry–Esseen …

Let $X \in \mathbb{R}^{m \times n}$ and $Y \in \mathbb{R}^{n \times k} $ be two independent Gaussian random matrices, i.e., with entries independently sampled from $\mathcal{N}(0,1)$ (a normal distrib …

Problem: Let $\phi(x)$ be the normal probability density function (pdf), and $\Phi(x)$ the normal cumulative distribution (cdf). I'm interested in the asymptotic behavior of the following integral $I( …