# Questions tagged [bivariate]

Concerning two random variables

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### Should one account for the known variance of fixed X when estimating its relationship with random Y?

In Aldrich (2005), and specifically in sections 10 and 11, the author describes the sufficient statistic for the parameter $\beta$ in the simple regression of random $Y$ on fixed $X$, with a bivariate ...
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### R implementation of Bivariate Test by Maronna

Does anyone know an R package that implements the Bivariate Test by Maronna and Yohai, 1978? Or maybe a derivate like the adaption from Potter, 1981 ? Or a baysian adaption ? Was not able to find an ...
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### Convolution with a pathological distribution

Problem definition Consider the following random bivariate vector \begin{aligned} y&=z+v \\ z&\sim p_z(z;c) \\ v&\sim p_v(v) \end{aligned} where $p_z$ ...
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### What type of statistical analysis is recommended for examining variations in risk and protective factors across male and female offending groups

I want to understand how risk and protective factors vary across separate male and female offending groups I have classified them into using group-based trajectory modelling (GBTM). Using GBTM, I ...
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### Simulate bivariate bernoulli responses with predefined beta coefficients

I have a specific data matrix with features (mainly categorical). I want to simulate a multivariate bernoulli response, for example bivariate, but with a predefined vector of beta coefficients (most ...
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### Estimation of bivariate function with one variable being constricted

Suppose the following classical supervised regression setting, $$y_{i} = f(x_{i}) + \epsilon_{i}, \quad i=1,\cdots,n,$$ where $\epsilon_{i}$ are i.i.d. zero mean Gaussian noise. The above regression ...
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### U -statistics for bi variate sample problem

Let $(X_1, Y_1), (X_2, Y_2),....,(X_n, Y_n)$ be iid random variables with joint distribution function $F(x, y)$ and $F(x), G(x)$ be the marginal distribution functions of $X_1$ and $Y_1$ respectively. ...
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### BIvariate Normal and Conditional Expectation

I am working on a problem where I must show that the conditional distribution of Y given X follows the distribution with mean and variance shown below. In the previous question, we were given that X ...
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### How to address endogeneity concerns using a recursive bivariate probit model?

I read a paper that addresses endogeneity concerns related to a binary moderator using recursive bivariate probit models. Their approach is: Analyze data using a recursive bivariate probit model. Get ...
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### Expectation and variance of bivariate skew normal distribution

I am fitting a bivariate skew normal distribution to a 2D data through the sn package in R. I get a $2 \times 1$ vector of ...
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### How to find the distribution of a function of two random variables?

I have the joint pdf $$f(x_1,x_2)=\begin{cases}\frac{1}{4}\;,\ -1<x_1,x_2<1\\ 0\;,\ \text{otherwise.}\end{cases}$$ I have to find the distribution of $Y=\frac{X_2}{1+X_1^2}.$ I have tried to ...
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1 vote
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### Test for bivariate normality assumption [duplicate]

Assume two time series $X_1$ and $X_2$, where $X_i=(x_{i,1},...,x_{i,T})$. How can we test the assumption of bivariate normality for these time series? (Assume each of the time series are stationary ...
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### How can population variance be estimated from a bivariate sample?

Let's assume a bivariate population with a correlation $\rho$ and a common $\sigma$ so that $\Sigma = \sigma^2 \begin{pmatrix}1 & \rho \\ \rho & 1\end{pmatrix}$. I would like to know the ...
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### Fitting bivariate normal distribution with covariate-dependent correlation parameters

Suppose we fit  \begin{bmatrix} X \\ Y \end{bmatrix} \sim \mathcal{N} \left( \begin{bmatrix} 0 \\ 0 \end{bmatrix}, \begin{bmatrix} 1 & \rho(C) ...
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Suppose $(X,Y)$ are two jointly normally distributed random variables. Suppose further that we want to calculate the density of $(X=x,Y=y)$. Is it possible to calculate this density if we do not have ...
Let's say you have a parameter vector $(p,q)$ consisting of two proportions, and you want to find a confidence region for the estimator $(\hat{p},\hat{q})$. Define H(x,y,p,q)=\frac{n}{...