# Questions tagged [bivariate]

Concerning two random variables

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1answer
28 views

### Correlation between nominal and ordinal variables

In my survey data I have two variables: One is an ordinal variable with 5-scale scoring from Agree to Disagree. My second variable is an nominal variable where the participants had to choose from 7 ...
0answers
12 views

### Find skewness and kurtosis of a bivariate scatterplot

I was reading this paper in the medical field which proposes a method using two radiological parameters in order to distinguish benign and malignant lesions. In their paper the Authors show this plot ...
1answer
34 views

### Joint entropy of a bivariate Gamma probability density function

In Nadarajah and Kotz, 2009 (https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-39/issue-1/Four-Bivariate-Distributions-with-Gamma-Type-Marginals/10.1216/RMJ-2009-39-1-231....
0answers
13 views

### Covariance in Robot Pose from Covariance in Line Segments

The solution to this might be completely obvious, so I apologize beforehand. The purpose of this question is for me to get better intuition on how to use covariance matrices of correlated variables in ...
1answer
35 views

### Proving that a random vector is not bivariate normal

Suppose X,Y are random variables and their joint pdf is given by: f(x,y)=2g(x)g(y) where x*y>0, and zero otherwise. g(x) and g(y) are pdfs of standard normal distribution. I was first able to prove ...
3answers
160 views

### How to find the variance(s) of a bivariate normal density such that 95% of the mass is within a certain radius from the mean defined by a point A?

I would like to find the variance of a bivariate normal density (BND), centered at the mean M, such that 95% of its mass is within a certain radius, which depends on the position of a point, A. (Note: ...
2answers
243 views

### EM algorithm for MLE from a bivariate normal sample with missing data: Stuck on M-step

I'm trying to understand applying the EM algorithm to compute the MLE in a missing data problem. Specifically, suppose $(x_1,y_1),\ldots,(x_n,y_n)$ is a random sample from the bivariate normal ...
0answers
22 views

### Mean of uniform two-dimensional probability density function

I am trying to calculate the mean of a two-dimensional probability density function, which looks like: and is defined by I know that I can calculate this by However, this is where I get stuck, as I ...
1answer
123 views

### Linear least-square fitting of two variables with uncertainty on both

I am trying to find an R function to calculate the linear least-square fitting of two variables when both have an error (expressed as standard deviation). I have found this problem referred to in half ...
1answer
36 views

### “Information” Correlation

(Let $X$ and $Y$ be random variables, sufficiently nice for my question to make sense.) $$\text{Correlation}$$ $$\rho(X, Y) = \dfrac{\text{cov}(X, Y)}{\sqrt{\text{var}(X)}\sqrt{\text{var}(Y)}}$$ ...
0answers
14 views

2answers
50 views

### Correlation between the linear combinations of bivariate normal distributed variables

How can I find the correlation (rho) between $U$ and $V$, Where $U = X_1+X_2$ and $V= X_1-2X_2$ $X_1$ and $X_2$ are normally distributed with $\mu= 1$ and $\sigma= 2$.
0answers
21 views

### Partial derivative of bivariate cdf

Suppose the bivariate cdf $F(a,b)=Pr(X\leq a, Y\leq b)$ is differentiable in $(a,b)$. Is it true that $\frac{\partial Pr(X\leq a, Y\leq b)}{\partial a}=Pr(X=a,Y\leq b)$?
2answers
28 views

### Relation between bivariate survial function and cumulative density function

I am trying to understand why $Pr(T_1> t_1,T_2 > 2)=1-F_1(t_1)-F_2(t_2)+F_{12}(t_1,t_2)$ My derivation is as follows: \begin{align} Pr(T_1> t_1,T_2 > t_2) &=Pr(T_1> t_1\mid T_2>...
1answer
111 views

### bivariate normal distribution meaning [duplicate]

Does bivariate normal distribution mean the two random variables have normal distributions? is that enough for two random variables to have a bivariate normal distribution or are there some other ...
1answer
64 views

2answers
105 views

### Show the bivariate normal cdf evaluated at (0,0) is increasing in the correlation coefficient

$\begin{bmatrix}\epsilon_{1}\\ \epsilon_{2}\end{bmatrix}\sim N(\begin{bmatrix}0\\0\end{bmatrix},\begin{bmatrix}1,\rho\\ \rho, 1\end{bmatrix})$. Show that the joint cdf evaluated at (0,0), i.e., \$F_{\...
1answer
386 views

### Ellipse region shape from standard deviations

I need to draw a bivariate normal distribution ellipse based on this article. It says In the case of the bivariate normal distribution, both approximate and exact methods are available for ...
0answers
32 views

### Unbiased estimators of bivariate gaussian means

What are the best unbiased estimators of bivariate gaussian means given covariance matrix? Is there any such estimator that makes explicit use of the covariance matrix, and which is superior by any ...