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      Questions tagged [probability-distributions]

      In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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      votes
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      70 views

      Is there a name for “splitting a probability distribution into independent components”?

      Suppose I have a random variable $\theta=(\theta_1,\dotsc,\theta_n)$; where the $\theta_i$ might have pairwise correlations. I decompose it into $\theta=\hat\theta(\phi_1,\dotsc,\phi_k)$, where $\hat\...
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      votes
      0answers
      26 views

      Distribution of a post-selected random variable with power-law distribution

      Background Assume $X \sim \mathcal D$ is a random variable, distributed according to some distribution $\mathcal D$. Then postselection with respect to some set $A$ is defined as the conditional ...
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      vote
      0answers
      23 views

      Reference Request: Total Variation Between Dependent and Independent Bernoulli Processes

      Let $X$ be a random variable taking values in $\{0,1\}^n$ with the following distribution. For each coordinate $i$, we have $p_i = P(X_i = 1) = c/\sqrt n$, where $c$ is a (very small) constant. ...
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      votes
      0answers
      49 views

      Order statistics of correlated bivariate Gaussian

      Suppose $(X_1,Y_1),...,(X_n,Y_n)$ are i.i.d. bivariate Gaussian with mean zero. Each coordinate has variance 1 and correlation between coordinates is $\rho\in[-1,1]$. I'm interested in the following ...
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      votes
      1answer
      66 views

      Strictly Proper Scoring Rules and f-Divergences

      Let $S$ be a scoring rule for probability functions. Define $EXP_{S}(Q|P) = \sum \limits_{w} P(w)S(Q, w)$. Say that $S$ is striclty proper if and only if $P$ always minimises $EXP_{S}(Q|P)$ as a ...
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      votes
      3answers
      88 views

      A clean upper bound for the expectation of a function of a binomial random variable

      I wonder if there is a closed-form, or clean upper bound of this quantity: $\mathbb{E}[|X/n-p|]$, where $X\sim B(n,p)$.
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      0answers
      34 views

      Estimator example cube [closed]

      We make subsequent throws of a fake cubic cube for which the probability of falling out six is 1/6 - epsilon, the probability of falling out of one is 1/6 + epsilon and the others eyes drop out with ...
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      votes
      1answer
      80 views

      How to find a special random variable? [closed]

      Suppose random variables $X_1$ and $X_2$ have the same distribution under P, $Y_1$ is an arbitrary random variable,let $Z_1:=X_1+Y_1$.Can we find a r.v. $Y_2$ which has same distribution as $Y_1$,such ...
      2
      votes
      1answer
      63 views

      Asymptotic bound on the total variation distance between a standard multivariate normal and a simple mixture

      Let $P = N(\vec{0}, I^d)$ be a standard multivariate Gaussian distribution in $d$ dimensions. Let $Q$ be distributed the same as $P$, except that samples from $Q$ have one of their coordinates, chosen ...
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      vote
      0answers
      47 views

      About a class of expectations

      Consider being given a $n-$dimensional random vector with a distribution ${\cal D}$, vectors $a \in \mathbb{R}^k$, $\{ b_i \in \mathbb{R}^n \}_{i=1}^k$ and non-linear Lipschitz functions, $f_1,f_2 : \...
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      votes
      0answers
      29 views

      Looking for a generalization of Binomial distribution and it's properties

      In my research (coming from computer science), I have encountered a family of discrete probability distributions that seems to be some sort of generalization of the binomial distribution. A ...
      1
      vote
      1answer
      52 views

      Concentration inequality for quadratic form of Gaussian variables with non-idempotent matrix

      Given $y \sim N(0,\sigma^2 I)$, and $M$ that is a symmetric matrix (not necessarily idempotent) what is the distribution of ${y^T M y}$? is there a high probability bound on $|{y^T M y}|$? Most ...
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      votes
      1answer
      51 views

      Rate of decay in the multivariate Central Limit Theorem

      The celebrated Berry-Esseen inequality tells us that the rate of convergence in the univariate CLT is of magnitude $\frac{1}{\sqrt{n}}$ for sums $S_n=X_1+\cdots+X_n$ of independent random variables $...
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      votes
      1answer
      75 views

      Variance of sum of $m$ dependent random variables

      I originally posted this question in Mathstackexchange, but since I got no answer I'm posting it also here. Let $X_1,X_2,...$ be a sequence of identically distributed and $m$-dependent random ...
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      vote
      0answers
      92 views

      Different balls in bins: What is the probability distribution of the sum of the minimum of the two types of balls over all bins?

      Assume that there are $N$ different bins and two different kinds of balls, $R$ red balls and $W$ white balls. The red balls and the white balls are randomly distributed across the bins (that is, for ...

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