Questions tagged [multivariate-distribution]
Probability distribution over vectors (as opposed to univariate distributions that are over numbers).
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Covariance of multivariate negative binomial with random effects
I am fitting a negative binomial-2 regression model where there is a multivariate normal random effects term. I would like to find an equation for the covariance of two outcomes. In "the ...
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Correlation and $z$-Transformation for Vectors With Correlation Structure
Consider a set of $p$ pairs $(x_1,y_1),...,(x_p,y_p)$, the sample correlation coefficient is
$$r=\frac{\sum_{i=1}^p (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^p (x_i-\bar{x})^2} \sqrt{\sum_{i=1}^p (...
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Modelling the joint pmf of 2 correlated variables as p(x)*pmf(E(y|x))
Let x,y be 2 correlated counts. We want to model the joint pmf p(x,y). We know that p(x,y) = p(x)p(y|x) = p(y)(x|y). However, what happens when we don't know y|x, but we can estimate E(y|x)? Can't we ...
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How may I find the distribution of a transformation of multivariate random variables?
Forgive me if this question has already been asked on here, but I could only find posts if the multivariate random variables were multivariate Gaussian.
Suppose we have two multivariate random ...
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Hotelling's $T^2$ chart for subgroups with unequal size
I have been reading about Hotelling's $T^2$ control charts and I'm unsure on how to deal with the case where the mean observations come from unequal-sized subgroups.
Consider $m$ observations $\mathbf{...
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Optimizing parameters for a non-standard probability density function
We have a non-standard multivariate probability density function, P(x | q), where x is a vector, and q are the parameters of the density. I get events ...
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PMF of the Independent Multivariate Bernoulli Distribution
I was reading this paper on the Multivariate Bernoulli Distribution, which provides the general form of the PMF in equation 3.1. The paper refers to this as the probability distribution function, but ...
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Sampling from multivariate probability distribution
What's the best way to sample from multivariate probability density functions that are proportional to $\exp(-\|x\|_2)$ or $\|x\|_2^p \exp(-\|x\|_2)$ for some positive integer $p$ with $x \in \mathbb{...
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Multivariate Normal Distribution. How do we apply this to dataset?
I am having a hard time understanding the concept of a multivariate normal distribution.
From my understanding, it assumes each group is normally distributed, making one joint normal distribution with ...
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Parametric copulas with marginals that are regressions
In Dependence Modeling with Copulas (Harry Joe) I'm struggling to interpret the meaning of a statement. In Chaper 5.1, it is stated:
Parametric inference for copulas
For dependence modeling with ...
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Multivariate sample covariance
I have a set of $X_1,...,X_n$ samples with covariance $\Sigma_1,...,\Sigma_n$.
The multivariate sample mean is then $$ \left(\sum_{i=1}^n \Sigma_i^{-1} \right)^{-1} \left(\sum_{i=1}^n \Sigma_i^{-1} ...
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Product of Two t-distribution Formulas
Does the product of two t-distribution formulas with same degrees of freedom simplify?
$T_v(x; \mu_1, \Sigma_1)T_v(x; \mu_2, \Sigma_2) =\ ?...$
In the normal case it simplifies to:
$\mathcal{N}(x; \...
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Distribution of covariance parameter resulting from sum of known- and unknown-covariance noise processes
Let's say I have a set $X$ of $N$ random $p$-dimensional vectors generated by $\mathbf{x}_i = \boldsymbol{\mu} + \Psi_i^{1/2} \boldsymbol{\xi}_i + \Sigma^{1/2} \boldsymbol{\zeta}_i$, where $\...
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How do you count degrees of freedom in multivariate distributions?
When dealing with a multivariate distribution (e.g., a multivariate t-distribution), how does dimensionality play into degrees of freedom? Let's say you have N measurements of a d-dimensional vector, ...
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Generate multivariate distributions of lognormal and normal distribution in python
I need to generate random numbers from 3 correlated distributions. First two of them are lognormal and the final one is normal, i.e. for X, ...
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