# Questions tagged [multivariate-distribution]

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

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### n-th quantile for bivariate variable

I generate a 2000 bivariate random samples which are negative correlated. I used np.quantile to generate 10 quantile from this random samples. The related point is marked in the following figure. I am ...
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### t-Copula MLE on nu (DoF) only - log-likelihood function possibly convex?

I am working with t-Copula's to generate random synthetic data eventually. The paper I use as the foundation is Benali et al., 2021. To determine the best fitting t-Copula, they propose determining ...
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### Overlap coefficient for two multidimensional normal distributions

For two PDFs $f_1(x)$ and $f_2(x)$ the overlap coefficient (OVL) measures the similarity between two distributions through the overlapping area of their distribution functions and is given by the ...
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### Analogous result to Isserlis' theorem for mixed absolute product-moments of multivariate normal distribution

Suppose that $(X_1, \cdots, X_n)$ have a joint normal distribution. If $n = 2m + 1$, then $\mathbb{E} \left[ \prod_{j=1}^n X_j \right] = 0$. This can be argued from the symmetry of the multivariate ...
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### quantile surface of a mulitvariate distribution made of multiplication of marginal distributions assuming independence

How to perform quantile regression in a more elegant fashion? As discussed above, quantSheets() can only deal with one explanatory variable for computing quantile ...
1 vote
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### Distribution of Geometric Brownian Motion drawdowns from realizations of multivariate Normal and Laplace distributions

I am trying to simulate the distribution of Geometric Brownian Motion drawdowns from realizations of multivariate Normal and Laplace distributions under the same covariance structure. Drawdowns are ...
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Assume M follows an Inverse Wishart distribution (known parameters), what is the conditional distribution of X given Y and Z in the below (where Y and Z are square sub-matrices)? $$M = \... 0 votes 0 answers 30 views ### What is the sample size required to estimate a multivariate joint histogram? The required sample size for estimating a multivariate joint histogram is something that I expect to depend on multiple factors such as the distributional properties of the data-generating process (e.... 0 votes 1 answer 76 views ### Generate a multivariate normal vector I'm working in R and I was wondering, let's say I want to generate a random vector X \in \mathbb{R^p}, with X \sim N(0,I) where I is the identity matriz in \mathbb{R}^{p \times p}. The ... 0 votes 0 answers 41 views ### Combining marginal bivariate probability distributions into a single multivariate one Consider a set of 3 correlated random variables X, Y and Z. I have calculated bivariate marginal distributions over any pairs of these random variables. That is, I know probability density ... 1 vote 0 answers 16 views ### How to determine if a multi-dimensional vector comes from a multi-variate distribution or not? I have a complex multivariate distribution given by a multivariate random number generator (black box). In other words, whenever I call the "generator" I get a random vector containing ... 3 votes 2 answers 118 views ### Can a random variable be uncorrelated with its product with a correlated random variable? I have a random variable X. I want to find a random variable Y such that Y is correlated with X, but Y is not correlated with the product of X and Y. Is it always possible? 0 votes 0 answers 32 views ### Test goodness of fit of a multivariate distribution via testing GOF of linear combinations of components I am modeling a continuous bivariate distribution of a random vector (X_1,X_2) using a copula. I would like to assess how well I am doing. Given a data sample, I could probably do a bivariate ... 4 votes 1 answer 796 views ### KL divergence for joint probability distributions? I have a pair of joint probability distributions. I want to measure their similarity/dissimilarity. If they were single-dimensional probability distributions, then I could measure the Kullback–Leibler ... 1 vote 1 answer 357 views ### What is a generalisation of t-test to the case of multivariate distribution? When we have a sample of numbers, one of the most basic tests is the t-test, in which we check the null hypothesis that the population mean is equal to zero. I am interested in a generalisation of ... 3 votes 0 answers 151 views ### Mutual information relationship to copula entropy is borked? I have posted a related Question based on a paper, Ma, Jian, and Zengqi Sun. "Mutual information is copula entropy." Tsinghua Science & Technology 16.1 (2011): 51-54. In the paper, they ... 6 votes 0 answers 97 views ### 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-... 4 votes 1 answer 797 views ### What is the best way to sample points from an arbitrary 2D distribution? I want to sample points (x,y) randomly according to the Himmelblau function$$f(x,y) = (x^2 + y - 11)^2 + (x + y^2 - 7)^2\qquad -5\le x,y\le 5 which I treat as a multivariate probability density ...
Suppose I have $X_{n} \sim MVN(\underline{\mu},\Sigma)$ where $n$ is large (several thousands). However, the $\mu_i's$ and the elements of $\Sigma$ are such that almost every simulation from $X_n$ ...