Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [bivariate]

Concerning two random variables

For questions concerning two random variables, e.g. modeling their joint distribution.

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Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?

Somebody asked me this question in a job interview and I replied that their joint distribution is always Gaussian. I thought that I can always write a bivariate Gaussian with their means and variance and covariances. I am wondering if there can be a…
MarkSAlen
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Implementation of CoVaR (a systemic risk measure) in R

I'm trying to estimate CoVaR using bivariate DCC GARCH in R. The concept of CoVaR is the dependence adjusted of VaR, which was first introduced by Adrian and Brunnermeier (2011). However, this original definition of CoVaR presented some limitations,…
drawar
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How to get ellipse region from bivariate normal distributed data?

I have data which looks like: I tried to apply normal distribution (kernel density estimation works better, but I don't need such great precision) on it and it works quite well. Density plot makes a ellipse. I need to get that ellipse function to…
matejuh
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Is joint normality a necessary condition for the sum of normal random variables to be normal?

In comments following this answer of mine to a related question, Users ssdecontrol and Glen_b asked whether joint normality of $X$ and $Y$ is necessary for asserting the normality of the sum $X+Y$? That joint normality is sufficient is, of course,…
Dilip Sarwate
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Where is density estimation useful?

After going through some slightly terse mathematics, I think I have a slight intuition of kernel density estimation. But I am also aware that estimating multivariate density for more than three variables might not be a good idea, in terms of the…
lovekesh
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What is the maximum likelihood estimate of the covariance of bivariate normal data when mean and variance are known?

Suppose we have a random sample from a bivariate normal distribution which has zeroes as means and ones as variances, so the only unknown parameter is the covariance. What is the MLE of the covariance? I know it should be something like $\frac{1}{n}…
Stacy
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What is a 'bagplot', or 'bivariate boxplot'?

I've found a paper which introduces the multidimensional (bivariate here) version of the boxplot - a bagplot. What is that bagplot exactly? I can see the series of nested polygons based on vertices, one of those polygons being declared as a bagplot.…
mbaitoff
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calculation threshold for minimum risk classifier?

Suppose Two Class $C_1$ and $C_2$ has an attribute $x$ and has distribution $ \cal{N} (0, 0.5)$ and $ \cal{N} (1, 0.5)$. if we have equal prior $P(C_1)=P(C_2)=0.5$ for following cost matrix: $L= \begin{bmatrix} 0 & 0.5 \\ 1 & 0 \end{bmatrix}$ why,…
user153695
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Why can't one generalize the Kolmogorov-Smirnov test to 2 or more dimensions?

The question says it all. I've read both that one can't generalize KS to a dimension equal or larger than two, and that famous implementations like that in Numerical Recipes are simply wrong. Could you please explain why is so?
pedrofigueira
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Example of two *correlated* normal variables whose sum is not normal

I am aware of some nice examples of pairs of correlated random variables which are marginally normal but not jointly normal. See this answer by Dilip Sarwate, and this one by Cardinal. I am also aware of an example of two normal random variables…
mww
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Properties of bivariate standard normal and implied conditional probability in the Roy model

Sorry for the long title, but my problem is quite specific and hard to explain in one title. I am currently learning about the Roy Model (treatment effect analysis). There is one derivation step at my slides, which I do not understand. We calculate…
Ivanov
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Obtaining marginal distributions from the bivariate normal

Let $(X, Y)$ have a normal distribution with mean $(\mu_X, \mu_Y)$, variance $(\sigma_X^2, \sigma_Y^2)$ and correlation $\rho$. I want to know the corresponding marginal densities. All I found so far was the well-known density expressions for $X\sim…
Luke
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What kind of distribution is this? $\text{Cov}(X, Y)=0$ but $\text{Corr}(X, Y)=1$

I faced a limiting distribution with zero covariance between two variables but their correlation is $1$. Is there such a distribution? How it can be explained? You are right may I need give more detail. OK, X and Y are bivariate normal distribution…
Behgol
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Find data and confidence "ellipses" (regions?) for a bivariate median?

I'm wondering about ways to compute data and confidence ellipses around a bivariate median. For example, I can easily compute a data ellipse or a confidence ellipse for the bivariate mean of the following data (here just showing a data…
Gavin Simpson
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Limits on conditional expectation with normal margins and specified (Pearson) correlation

I saw the following question on another forum: "Suppose that both height and weight of adult men can be described with normal models, and that the correlation between these variables is 0.65. If a man's height places him at the 60th percentile, at…
Glen_b
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