Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [multivariate-distribution]

Probability distribution over vectors (as opposed to univariate distributions that are over numbers).

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How to determine quantiles (isolines?) of a multivariate normal distribution

I'm interested in how one can calculate a quantile of a multivariate distribution. In the figures, I have drawn the 5% and 95% quantiles of a given univariate normal distribution (left). For the right multivariate normal distribution, I am…
Marc in the box
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Is this causation?

Consider the following joint distribution for the random variables $A$ and $B$: $$ \begin{array} {|r|r|}\hline & B=1 & B=2 \\ \hline A=1 & 49\% & 1\% \\ \hline A=2 & 49\% & 1\% \\ \hline \end{array}$$ Intuitively, if I know A, I can predict very…
elemolotiv
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Algorithms for computing multivariate Empirical distribution function (ECDF)?

One dimensional ECDF is fairly easy to compute. When it comes to two dimensions and up, however, online resources become sparse and hard to reach. Can anyone suggest, define and/or present efficient algorithms (not ready made implementation) for…
AlexanderF
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Multivariate Laplace distribution

I find it strange, but I can't find what multivariate Laplace distribution looks like. What is its pdf? I googled for a while but couldn't find a good description. I wasn't paying attention to Laplace. Now, all of a sudden when I need it, I can't…
user34790
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Is multivariate Cauchy stable?

I am trying to prove (if possible), for given $A_{n\times n}$ and $B_{n\times n}$, there exists a $C_{n\times n}$ satisfying $$A\pmb{X}_1 + B\pmb{X}_2 \stackrel{D}{=} C\pmb{X},$$ where $X_1, ~X_2$, and $X$ are independently and identically…
Shanks
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Generating Multivariate Uniform Distribution in R

Let $d$ a positive integer How to generate a sample of $n$ random variables with a multivariate uniform distribution on the cube $[a,b]^d$ in R? I don't know what to do. I know that I need a covariance matrix for the random vectors that I will…
Juan Corredor
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Generate a random set of numbers with fixed sum and desired means and variances?

The Dirichlet distribution allows you to generate a sample of numbers $x_i$ with a prescribed sum, say $\sum_i x_i = 1$. Moreover, the parameters $\alpha$ allow some degree of control on the means of the individual $x_i$. I also want to generate…
becko
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Probability distribution associated with nuclear norm?

The $\ell_1$ norm of model parameters is often added to loss functions because it induces sparsity in the solution of the overall cost function: $$ c(\theta) = -\log L(x|\theta) + \lambda ||\theta||_1$$ The fact that the added loss term can be…
John Madden
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Copula entropy: calculation is borked?

I came across a pretty cool paper whose idea makes a lot of sense to me. Ma, Jian, and Zengqi Sun. "Mutual information is copula entropy." Tsinghua Science & Technology 16.1 (2011): 51-54. The gist is that the copula is the "rest" of the…
Dave
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multivariate Student's t distribution: intuition for non-independence?

Consider a multivariate Student's t distribution, with parameters $\nu$ (d.f.), $\mu$ (location) and $\Sigma$ (shape). Does anyone have a good intuition for the individual components not being statistically independent, even when $\Sigma$ is a…
Colin Rowat
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How to show that $\left|\left|E\left[\frac{x-X}{||x-X||}\right]\right|\right|\xrightarrow{||x||\to\infty}1$ for a multivariate distribution?

I am trying to prove that $\left|\left|E\left[\frac{x-X}{||x-X||}\right]\right|\right|\xrightarrow{||x||\to\infty}1$ for any multivariate distribution. My Progress: I have proved the result for univariate distributions as the variable…
Martund
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Something like Mahalanobis distance when the copula is not Gaussian

Mahalanobis distance accounts for different variances of the marginal variables and correlations between the marginal variables. However, there is an implicit (maybe explicit) assumption that correlation is the right measure of dependence between…
Dave
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How to compare a new measurement to an existing multivariate distribution?

I have a dataset that describes the position and rotation of an object at different points in time using four dimensions. I want to use this sample of observations to get a sense of what positions and rotations are possible/likely for this…
Jeffrey Girard
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Can we apply a constraint on the distribution of the layer output?

As far I understood, the hidden layer outputs can be anything based on the learning algorithm or optimization rules. I was wondering if it possible to some constraints on the layer output. For instance, say, I want my layer outputs (for a particular…
talk2speech
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Multivariate Chebyshev's inequality with Mahalanobis distance

In Chebyshev's inequality, we can generalize the 68-95-99.7 rule from normal distributions to bound how much density is within a certain number of standard deviations from the…
Dave
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