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Questions tagged [multivariate-distribution]

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

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Multivariate $t$ ('mvt') - adjustment in emmeans in R

I am doing post-hoc comparisons of contrasts based on linear mixed models I built in R. I am using the emmeans package for the comparisons. One of the default ...
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multivariate normal distribution with mean vector 0 and covariance matrix Σ

I am newby in statistics and I have huge data with "p" variables and "n" samples. My data is a two dimensional matrix with "n" columns (each column is a sample) and "p" rows (each row is a variable). ...
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Unbiased estimator for Theta of a Normal Distribution

If $X_1,\ldots,X_n\sim \operatorname{iid} \operatorname N(\theta, \sigma^2)$, then verify that $\bar{X}_n$ is unbiased estimator for $\theta$ and that Cramer Rao bound is met? I am facing difficulty ...
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Finding joint probability distributions from marginal distributions

Question: I was solving test papers where I found this one. My doubt: I know to work with conditional probabilities and Jaccobian Transformation and part A and B can be done applying the above..But ...
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Multivariate Test for Mean Equivalence

I am looking for an equivalence test for multivariate means (arbitrary or normally distributed). Any suggestions or hints in the right direction are appreciated.
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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 $X_1, ~X_2$, ...
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Hessian of Log of Matrix-t distribution

I am trying to calculate the hessian of the log of the matrix-t distribution. I know that the log of the matrix-t distribution can be written: \log T_{N\times P}(X| \nu, M, \Sigma, \Omega) \propto -\...
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If $\mathbf{x} \sim N(\mathbf{0,I})$ and $\mathbf{y} = \mathbf{Ax}$, what does $\mathbf{A}^T \mathbf{A}$ represent?

If $\mathbf{x} \sim N(\mathbf{0,I})$ then $\mathbf{AA}^T$ is the covariance matrix of $\mathbf{y} = \mathbf{Ax}$, but what does $\mathbf{A}^T \mathbf{A}$ represent? In some places I have seen ...