# Questions tagged [multivariate-distribution]

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

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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 $\... • 11 1 vote 1 answer 229 views ### How do you count degrees of freedom in multivariate distributions? When dealing with a multivariate distribution (e.g., a multivariate t-distribution), how does dimensionality play into degrees of freedom? Let's say you have N measurements of a d-dimensional vector, ... • 11 5 votes 3 answers 544 views ### Generate multivariate distributions of lognormal and normal distribution in python I need to generate random numbers from 3 correlated distributions. First two of them are lognormal and the final one is normal, i.e. for X, ... • 193 6 votes 1 answer 461 views ### multicomp package and emmeans package produce different adjust pvalues for Dunnett procedure [closed] For Dunnett adjustment, multicomp package and emmeans package in R give different results. Anyone knows why? Thanks. Please see ... • 1,173 1 vote 1 answer 40 views ### Estimate multivariate distribution with several variables on real data (continuous and categoricals) and sample from it I have a complex dataset, collected through a survey, with both continuous (such as Age, Body mass index, etc..) and categorical variables (i.e. Gender, Education, etc..). I want to estimate their ... 5 votes 0 answers 74 views ### Difference between random vector and joint distribution My definition of a random vector is a vector$(x_{1},...,x_{n})$that maps from a sample space to${R}^{n}$. An example of this (in my understanding) would be a random process such as drawing one card ... • 51 3 votes 1 answer 76 views ### Multivariate and integral representations explanation I would to understand more on the multivariate and integral representations. I am fascinated by the possibility of a multivariate distribution like this one: $$\mathbb{P}(X_1 \le Z + a, X_2 \le Z + a, ... 1 vote 1 answer 110 views ### Calculation of multivariate probability mass function How to calculate the following multivariate probability mass function: P(X_1-X = n, X_2-X = n, ..., X_{N-1}-X = n) Where n and N are positive integers, and X_i and X are iid random variables ... 2 votes 1 answer 125 views ### Quantile function of multivariate distributions from empirical samples Let's say I have a k-dimensional multivariate normal distribution MVN(0,\Sigma). Denote random vector X \sim MVN(0,\Sigma) as X = (x_1, x_2, \dots, x_k). It is trivial to find P(x_1 \leq c_1, ... • 147 0 votes 0 answers 14 views ### Approximating a bivariate distribution with another distribution, which method to use? Let X \sim F(;\theta) and Y \sim G(;\eta) be two independent continuous random variables. The greek symbols represent the parameters of those distributions. I can easily sample from these ... 0 votes 0 answers 39 views ### Find the conditional PDF of a multivariate normal distribution given a constraint [duplicate] Problem to solve We have a vector of random variables \textbf{X}=(X_1,X_2) issued from a bivariate normal distribution. In particular, \mu = \begin{bmatrix} 2 \\ 3 \end{bmatrix}, \Sigma = \begin{... 1 vote 0 answers 31 views ### Joint testing of proportions, analogous to the Hotelling T^2 test? Hotelling's T^2 test examine if two multivariate Gaussian distributions with the same covariance matrix have the same mean vector. Assuming the two distributions to have the same covariance matrix ... • 65.8k 1 vote 1 answer 160 views ### Standard deviation of a function of random variables I was a bit confused recently with why two jointly distributed variables will exhibit a smaller scatter as the correlation between the random variables increases (assuming only positive values for the ... • 413 0 votes 0 answers 99 views ### Probability distribution of the product of three dependent continuous random variables Given the joint probability distribution for three dependent continuous random variables, I want to find a formula to compute the probability distribution for the product of these 3 random variables. ... 9 votes 1 answer 690 views ### Kullback–Leibler divergence between two multivariate t distributions with different degrees of freedom? I want to calculate the Kullback–Leibler divergence between two multivariate t distributions with different degrees of freedom (say \nu_1 and \nu_2), but same location and scale matrix, for ... • 93 4 votes 1 answer 207 views ### Generate nonnegative variates with mean 1 and specified variance-covariance Problem In several applications in surveys, it would be helpful to be able to generate a set of R n-dimensional variates with the following properties: Has mean vector 1 Has a specified ... • 506 1 vote 0 answers 76 views ### Statistic for significance test comparing transition matrix to null I have several pitch sequences (mini songs), that look something like this when plotted as a pitch profile (piano roll): I've coded each sequence in terms of its constituent interval sizes, and ... • 2,332 1 vote 1 answer 76 views ### Measure the "actual" number of dimentions in a multivariate distribution Consider a 3D multivariate normal distribution x\sim N(0,\Sigma) where$$\Sigma=\begin{bmatrix}1 &1 &0 \\ 1&1&0 \\ 0 &0& 1 \end{bmatrix}$$Since x_1 and x_2 are fully ... • 1,230 2 votes 0 answers 53 views ### Test for multivariate stationarity Given a bivariate time series (X_{1t}, X_{2t}) with X_{it}\sim N(0,1), I want to know if there is a way of testing if the bivariate distribution does not change over time. This is, if F_{12}(x_1,... 0 votes 0 answers 36 views ### Distribution of iid variates with fixed sum I have n bins, and a pool containing N balls, N > n. I do a consecutive N times: I take one of the balls from the pool and put it into a bin randomly selected with uniform probability 1/n.... 1 vote 1 answer 204 views ### Creating multivariate distribution using marginal: can I use a copula? I am modeling a multivariate distribution, where I already have the distributions of the marginals. Let's call the marginals, f_{i}(x) for every i marginal distribution, where i=1,2,3. We ... • 243 1 vote 0 answers 136 views ### Contour lines for multivariate Laplace distribution In the p-variate normal distribution (\mathbf{N_p(\mu,\Sigma)}), the solid ellipsoid of x values satisfying (\mathbf{x-\mu)'\Sigma^{-1}(\mathbf{x}-\mu)}\leq \chi^2_p(\alpha) has probability 1-\... 2 votes 0 answers 134 views ### When to specify multivariate versus univariate priors on parameters? Suppose a linear regression model:$$y \sim Normal(\beta X, \sigma)$$For our purposes, assume y is a univariate outcome and X is a design matrix containing an intercept and one additional ... 2 votes 1 answer 149 views ### Joint Uniform Distribution Probability Problem Let X \sim U(0,1) and Y \sim U(0,x) . Calculate$$ \Pr(X >0.5 | Y= 0.25)$$Is this a trick question ? Since \Pr(Y = 0.25) = 0, right ? 0 votes 0 answers 27 views ### Mistake in Multivariable Transformation The answer is \frac{19}{24} but I don't know where is my mistake. The question is this. Let$$f_{X,Y}(x,y) = \begin{cases} x+y, \quad 0<x<1, 0<y<1 \\ 0, \quad \quad \quad \text{elsewhere}... 1 vote 1 answer 230 views ### Sampling from multivariate Bernoulli Suppose you have a vector p drawn from a multivariate Beta distribution (not a Dirichlet), such as the one described here ( How to construct a multivariate Beta distribution? ) with a Gaussian copula. ... • 103 1 vote 0 answers 422 views ### Why is it difficult to sample from a multivariate distribution? [closed] The Monte Carlo Markov Chain method requires sampling from a multivariate distribution. This is because the Markov Chain process requires dependent draws. See 1:55 at https://www.youtube.com/watch?v=... • 523 4 votes 0 answers 168 views ### How to fit a copula when zeros abound? I am modelling a joint distribution for two random variables:$F(x,y)$. I observe$n$data points$(x^{}_{i},y^{}_{i})^{N}_{i=1}$. I would like to model$F$as the product of its marginals and a ... • 103 2 votes 1 answer 692 views ### Fitting a copula vs. directly fitting a multivariate distribution I understand that the joint density of two random variables$f(x,y)$can be decomposed as the product of its marginals and a copula:$f(x,y) = g(x)k(y) \times c(G(x),K(y))$. Alternatively this may be ... • 103 0 votes 0 answers 149 views ### Probability of getting k different colored balls from an urn with K different colors of balls, each color has the same number of balls Let's say I have an urn with$n$balls, with$K$different colors of balls, where each color has the same number of balls:$\frac{n}{K}$. Given I reach into the urn and grab a ball (without ... 6 votes 1 answer 196 views ### What is the distribution of a random linear combination of gamma random variables? Let$U\sim \mathcal U(0, 1)$be a random variable uniformly distributed over the interval$[0, 1]$. Let$X_1, X_2\sim \Gamma(a, b)$be two iid random variables with a Gamma distribution. Now it is ... • 93 0 votes 0 answers 53 views ### generalization of univariate pdf under constraints I'm looking for generalizations of a univariate probability distribution function. The pdf is $$\varphi(x)=(2\sqrt{s}K_1(2\sqrt{s}))^{-1}e^{\frac{s}{\log x}}.$$ for$K_1$a modified Bessel function, ... 4 votes 2 answers 338 views ### Multivariate Probability Distribution with Linear Conditional Expectation I want to know what probability distribution has the linearity property of the conditional expectation. To be specific, suppose that we have three random variables named$v_1,\;v_2,\;v_3$. Then, if$[...
Let's say that I have a random variable $X$ that follows a singular Wishart distribution with $\nu$ degrees of freedom and a shape matrix $\Sigma$ that is $p\times p$. We can write "symbolically&...