# 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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### Sparse representation of a distribution with independent and correlated variables

Here's what I'm trying to do: Imagine a probability distribution over $\mathbf{R}^2$, $P(x,y)$. I can approximate $P(x,y)$ with set of $N$ points $\{(x,y)_i\}$ drawn from $P$. By approximate, I mean ...
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### When is taking an average (mean) an algebraic operation in the sense of monads?

Taking the average of a sequence of numbers is not an "algebraic" operation, in the following sense. Given sequences $X_1,X_2,\ldots,X_n$ of numbers, one could either take the average of each one, ...
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### finding numbers at k hamming distance

Guys, I have N < 2^n randomly generated n-bit numbers stored in a file the lookup for which is expensive. Given a number Y, I have to search for a number in the file that is at most k hamming dist....
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### On random Dirichlet distributions

Fix a dimension $d\ge2$. Let $Q_d$ denote the positive quadrant of $\mathbb{R}^d$, that is, $Q_d$ is the set of points $\mathbf{x}=(x_i)_i$ in $\mathbb{R}^d$ such that $x_i>0$ for every $i$. For ...
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### low-discrepancy sequences for sampling of distributions

Hi everybody, I am writing of physics simulation that traces charged particles. I need to set up these particles in phase space ( 3 space dimension + 3 momentum dimensions) following distributions. ...
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### For what sub-$\sigma$-algebra are these two measures equivalent?

In two statistics papers (linked inline below) I have come across two definitions of certain probability measures. I conjecture that for particular choices of the construction that they are ...
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### Statistics of a simple Markov chain

Imagine a two-state Markov chain which hops between the states $\pm 1$ with probability $p<1/2$, so that the autocorrelation function after $k$ steps is $\rho_k = (2p-1)^k$ If I take an ...
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### Weighted Distribution [closed]

Hello, here's my basic problem - I would appreciate any help. We use a weighted system based on 1 (developing) ,2 (performing) ,3 (leading) to evaluate an employee's rating using various metrics. Each ...
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### What are the origin and applications of this result?

In a course taught by Morris Eaton on multivariate statistics that dealt mostly with the Wishart distribution, I learned this proposition: Suppose  M = \begin{bmatrix} A & B \\\\ B^T & C \...
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### Constraints for different probability measures to have the same expectation.

Take different $D_i \in \mathbb{R} \rightarrow \mathbb{R}$ functions $f_1, f_2$ (i.e. $\exists x : f_1(x) \neq f_2(x)$). We have $E[f_1(x)] = E[f_2(x)]$ Are there conditions that $f_1, f_2$ must ...
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### Resultant probability distribution when taking the cosine of gaussian distributed variable

I am trying to do a measurement uncertainty calculation. I have a gaussian distributed phase angle (theta) with a mean of 0 and standard deviation of 16.6666 micro radians. The variance is the ...
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### Density function for a multivariate Bernoulli-like distribution

I'm looking for a distribution to model a vector of $k$ binary random variables, $X_1, \ldots, X_k$. Suppose I have observed that $\sum_i X_i = n$. In this case I do not want to treat them as ...
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### “Square root” of Beta(a,b) distribution

Under what conditions on a and b is there a distribution $f_{a,b}$ such that the product $XY$ of two independent realizations $X$ and $Y$ from $f_{a,b}$ has a Beta(a,b) distribution? A standard ...
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### Probability distribution needed [closed]

Let me clarify my needs. The PDF must comply to: 1. The mean is always in the shorter tail 2. Should have an inverse function 3. Be defined in the interval [0, 1] 4. Should have a shape parameter that ...
Prove that the Normal (Gaussian) Distribution with a given Variance ${\sigma}^{2}$ maximizes the Differential Entropy among all distributions with defined and finite 1st Moment and Variance which ...