# Questions tagged [multivariate-normal-distribution]

The multivariate normal distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. (Also called, multivariate Gaussian)

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### derive multivariate pdf from matrix variate pdf

I am working on the proof part in Definition section of https://en.wikipedia.org/wiki/Matrix_normal_distribution. I can understand what s going on, except for the last part how inv(V(kron)U) becomes ...
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### Jointly complete and sufficient statistics for multivariate normal distribution [duplicate]

Consider the random sample X from the multivariate normal distribution where xi are i.i.d as N(µ,Σ). *Show that the sample mean x̄ and Sample covariance matrix S are jointly complete and sufficient ...
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### Generating samples from high-dimensional multivariate Gaussian with few training samples

Say I have a $n\times d$ dataset $D$ where $n\ll d$ ($n$ number of observations, $d$ number of dimensions). Currently, if I want $m$ samples from $D$ assuming it is multivariate Gaussian, I can do ...
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### Distribution of residuals of LME models

I'm asking if you can help me please. I have a random slope model with longitudinal data, where I consider two times (time 1 and time 2). As a result I have residuals for each subject at both time 1 ...
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### Multinormal assessment of residuals (Multilevel models)

I need some help. my_model<-lme(OUTCOME ~ VISIT + TREATMENT+ VISIT*TREATMENT, random= ~ 1+VISIT | ID, my_data) I built this multilevel random slope model (above), where we have two visits for each ...
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### Numerical computation of the means and covariance in a truncated bivariate normal distribution

How can I compute the means and covariance of a truncated bivariate normal distribution? I am particularly worried about the case when the truncation occurs very far from the mean. Is there a robust ...
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### DFT of Multivariate Normal Random Vector

I have a real zero-mean multivariate rv $X \sim \mathcal{N}(0, \Sigma)$, with $N^d$ entries. $X \in \mathbb{R}^{N^d}$ is the flattened representation of a $d$-dimensional signal, of "side length&...
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### Assumptions of Path Analysis - Multivariate Normality inspite Univariate Non Normality

I am currently checking if my data meets the assumptions for path analysis: mainly multivariate normality of the three endogenous variables $m_1,m_2,y$ (As recommended by e.g. Streiner, 2005). I ...
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### Standard Gaussianity test for high dimensional data

I'm using a Gaussianity assumption over 500-dimensional data in my work and I wanted to check the validity of my assumption. I developed a transformation that relies on this assumption and I have good ...
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Following up on the question (and answers) here, I'm trying to derive $\frac{\partial \Phi(x_1, x_2|\mathbf{\underline{\theta}})}{\partial x_1}$ and $\frac{\partial \Phi(x_1, x_2|\mathbf{\underline{\... 1answer 984 views ### Implication of relationship between multivariate normal distribution and chi-square distribution I am wondering what is the implication of the above relation/theorem. I know how to prove this using "sphering$Y$" but I am failing to get intuitive understanding of the theorem. What does it mean ... 2answers 72 views ### Find the variance-covariance matrix for a linear combination of multiple bivariate normal distribution? I have an arbitrary number of independnet bivariate normal distributions with$\mu_i = [x_i,z_i]$&$ \Sigma_i= \left(\begin{array}{cc} \sigma^2_{x_i} & \sigma^2_{x_i,z_i}\\\ \sigma^2_{x_i, ...
How could I fit data with observations from one Dirac delta component and $n$ normal distributed components? Where $n$ usually is between 1 and 5. My prior knowledge is that one component really is a ...