Skip to main content

Questions tagged [bivariate]

Concerning two random variables

Filter by
Sorted by
Tagged with
0 votes
0 answers
17 views

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 ...
virtuolie's user avatar
  • 642
0 votes
0 answers
21 views

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 ...
Dirk's user avatar
  • 3
3 votes
1 answer
96 views

Convolution with a pathological distribution

Problem definition Consider the following random bivariate vector \begin{equation} \begin{aligned} y&=z+v \\ z&\sim p_z(z;c) \\ v&\sim p_v(v) \end{aligned} \end{equation} where $p_z$ ...
matteogost's user avatar
0 votes
0 answers
23 views

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 ...
Ayda's user avatar
  • 1
0 votes
0 answers
34 views

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 ...
eddie8434's user avatar
0 votes
0 answers
10 views

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 ...
DoubleL's user avatar
  • 11
0 votes
0 answers
13 views

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. ...
user771946's user avatar
0 votes
0 answers
43 views

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 ...
Harry Lofi's user avatar
0 votes
0 answers
38 views

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 ...
Puneet Sachdeva's user avatar
2 votes
1 answer
59 views

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 ...
Kasthuri's user avatar
  • 163
2 votes
1 answer
42 views

Bivariate random variable and transformation

Let $X=(X_1,X_2)$ and $Y=(Y_1,Y_2)$ be non-negative absolutely continuous random vector and if $\phi(X_j)=Y_j$, $j=1,2$, are one-one transformation then $$H[Y;\phi(t_1),\phi(t_2)]=H(X;t_1,t_2)-E[\log ...
Unknown's user avatar
  • 173
0 votes
0 answers
22 views

Single or Multiple Bivariate analysis?

For the data structure, we are fitting the multilevel model to the data. Before fitting the model, we are eager to do bivariate analysis so that we can keep those independent variables in the ...
user232597's user avatar
0 votes
1 answer
42 views

best strategy to test bivariate data

Here's a revised version of your text: I have two sets of data: Intensity and Duration. For each set, I possess both observation data and model data, denoted as (I_obs, I_mod) and (D_obs, D_mod) ...
diedro's user avatar
  • 111
0 votes
0 answers
11 views

X and Y are correlated, errors in both X and Y but error variances unknown; How to predict X|Y or Y|X? Deming, bivariate gaussian ellipses, other?

Seeking relationships between two variable, both with random gaussian errors; ratio of error variances is unknown, no correlation of errors in X and Y, but another unknown variable Z (unmeasured) may ...
David's user avatar
  • 1
2 votes
1 answer
385 views

Why do my residual plot and scatterplot look the same and what does this mean?

I am investigating the relationship between device usage and screen time for my math assignment (my last ever high school math assignment, yay!), but after creating the residual plot, I realised it ...
Luca's user avatar
  • 23
1 vote
0 answers
35 views

How to generate random samples for the Poisson Bivariate Distribution like `np.random.poisson` in Numpy? [duplicate]

I am working with the Poisson Bivariate Distribution and I need to generate random samples to apply in a Monte Carlo simulation, but so far I haven't found too much about it on the internet. I saw ...
José Thomaz Antunes Soares's user avatar
0 votes
0 answers
43 views

What value bounds an ellipse of a bivariate population at one standard deviation?

I am trying to draw an ellipse that bounds a bivariate distribution by the shared 1 sigma in 2D space (i.e. points that fall within one standard deviation of both populations). The function in R I am ...
madroan's user avatar
1 vote
2 answers
56 views

Help with algebraic steps that my statistics text employed in confirming a conditional distribution [duplicate]

In the page from a statistics book pasted below the authors make the algebraic leap from the LHS to the RHS of the equals sign here: $\large \frac{(x_1 - \mu_1)^2}{\sigma_{11}} - 2\rho_{12} \frac{(x_1 ...
stevedepp's user avatar
0 votes
1 answer
37 views

Is it reasonable to use Chi Square data in a bivariate analysis?

I am currently working on a report about the frequency of hand types in Texas Hold'em and whether or not the frequencies change when there are multiple players involved. For example, is there a change ...
Alexander Svendsen-Conn's user avatar
0 votes
0 answers
38 views

How to calculate lambdas from Bivariate Poisson distribution?

I have three random variables X1, X2, X3 which follow independent Poisson distributions with parameters λ1, λ2, λ3 >0 and then the random variables X = X1 + X3 and Y = X2 + X3 jointly follow a ...
Juan's user avatar
  • 57
2 votes
1 answer
121 views

Correlation of bivariate normal variables with truncated tails

What is the correlation of a bivariate normal distribution after truncating the tails of both variables at $\alpha$ standard deviations? In symbols, what is $$E\left[XY\Big|X| \leq z_{\alpha/2}, |Y| \...
POC's user avatar
  • 668
2 votes
1 answer
102 views

More correlated information is... more informative?

Suppose I am trying to make inference about a parameter $\mu$. I have a prior $$ \mu \sim N(0,\sigma^2), $$ and I observe two correlated signals about $\mu,$ namely $x_1, x_2$ where $$ \begin{pmatrix} ...
deej's user avatar
  • 21
0 votes
0 answers
55 views

Behavior of higher moments in the bivariate distribution

Given a bivariate joint distribution of random variable X and Y, $P(X,Y)$, consider the expectation value $E[(X-Y)^n]$ for different n values. If one observes that while the variance becomes smaller ...
Quantization's user avatar
3 votes
1 answer
49 views

Testing correlation coefficients from two bivarate poisson

I have datasets from two bivariate poisson distributions, $BVP_x(\lambda_1, \lambda_2, \lambda_{12})$, and $BVP_y(\lambda_3, \lambda_4, \lambda_{34})$ respectively. Now we know the correlation ...
Hirak Sarkar's user avatar
2 votes
1 answer
85 views

Testing correlation coefficient of two bivariate gaussian

I have datasets from two bivariate normal distributions, $\mathcal{N}(\mu_x, \Sigma_x)$, and $\mathcal{N}(\mu_y, \Sigma_y)$ respectively. Now we know the correlation coefficient for these two ...
Hirak Sarkar's user avatar
3 votes
1 answer
241 views

Upper bound for sum of dependent normal variables

I am having difficulties with the following problem: Assuming $X$ and $Y$ follow a bivariate normal distribution with $\mu = 0$ and $\Sigma=\begin{pmatrix} 1 & \rho \\ \rho & 1 \end{pmatrix}$ ...
Coach's user avatar
  • 33
0 votes
0 answers
34 views

Identifiability of a bivariate normal distribution with identified minimum

I am suffering from to understand a proof of a paper. (Nádas, Arthur. "The distribution of the identified minimum of a normal pair determines' the distribution of the pair." Technometrics 13....
MinChul Park's user avatar
1 vote
1 answer
48 views

Understanding of bivariate Gaussian distributions in connection with complex random variable

Say that we want to model a complex-valued signal using the RV $S$, where $S$ can be expressed by it's real and imaginary part, i.e. $S = X + iY$, where $X$ and $Y$ are real-valued random variables. ...
mr.hyde's user avatar
  • 13
1 vote
0 answers
35 views

Bivariate restricted probit in R

I want to estimate a bivariate restricted probit model in R. In particular, I want to restrict the correlation between the models to 0. Using the GJRM package & function, I was already able to ...
JanR's user avatar
  • 11
4 votes
2 answers
229 views

Transform bivariate uniform variable

Let $X_1 = U(0,1)$ and $X_2 = U(0,1)$. $X_1$ and $X_2$ are independent. Then $f(x_{1}, x_{2})=1, {0}\le{x_1}\le{1}, {0}\le{x_2}\le{1}$. Let $Y_1 = \arctan(X_{2}/X_{1})$, $Y_2 = X_2$. I need to find ...
Igor Yegin's user avatar
0 votes
0 answers
196 views

Deriving the Expectation of the conditional distribution for the bivariate lognormal distribution

For $(X_1,X_2)$ ~ $Normal(\mu, \Sigma)$: $$E(X_2|X_1)=\mu_2+\rho*\sigma_2\frac{X_1-\mu_1}{\sigma_1}$$ I am trying to derive the $E(Z_2|Z_1)$ for $(Z_1,Z_2)$~$LogNormal(\mu, \Sigma)$. I guess I could ...
ColorStatistics's user avatar
1 vote
0 answers
39 views

Bivariate correlation across subgroups

I have several variables and I would like to test for possible linear correlations between. However, the data is across 2 groups, and there is a significant group difference in these variables. I know ...
Julian Macoveanu's user avatar
0 votes
0 answers
39 views

Simulating using conditional density - is this correct?

Consider the pair of random variables $(X, Y)$ whose density is given by $$f(x, y)=yx^{y-1}e^{-y}1_{(0, \infty)}(y)1_{(0, 1)}(x)$$ I was first asked to find the density of $Y$. This was simple, that's ...
JustAnAmateur's user avatar
0 votes
0 answers
497 views

Bivariate and multivariate analysis

Most of researcher when conducting binary logistic regression analysis they use to contradictory analysis Bivariate analysis or bivariable analysis to select variables that fit model,then 2....
Fufa Balcha 's user avatar
1 vote
0 answers
58 views

What is the joint distribution between the sample mean and sample mediant of rounded normal variables?

I am curious about the relationship between the arithmetic mean and the (generalized) mediant. I took $10^4$ samples (each of size $n=3$) of $\operatorname{Round}(X_i,\text{decimals}=3)$ where $X_i \...
Galen's user avatar
  • 9,361
0 votes
1 answer
52 views

Finding expectation through conditioning

I want to find $E(X^2Y^2)$. Now $Var(XY) = E(X^2Y^2)-E(XY)^2.$ Since $E(X)$ and $E(Y)$ both are 0, $Cov(X,Y) = E(XY)$ and $Cov(X,Y) = \rho \sigma_{x}\sigma_{y}. $ Therefore, $Cov(X,Y)=\rho.$ Therefore ...
Equation_Charmer's user avatar
0 votes
0 answers
44 views

Data association

I have a typical question if someone can help. Construct two bivariate data sets (choose number of cases to suit yourself), each with correlation above 0.9, so that the combined data set has negative ...
puth pura's user avatar
1 vote
1 answer
38 views

What is the meaning of percentage in parantheses and the p-value in this bivariate analysis of patients?

In this paper, Table 2 shows some values in parentheses. The paper doesn't seem to include an explanation. As an example, 82 patients out of 94 with Radial head fracture showed No HO (Heterogeneous ...
Ritesh Singh's user avatar
2 votes
1 answer
53 views

Best fit line of bivariate normal data passes through extrema of level sets

I am learning about the idea of correlation in statistics, and I came across the following Statement: the best fit line of bivariate normal data passes through extrema of level sets. That is, if $(X,Y)...
Benjamin Wang's user avatar
0 votes
1 answer
84 views

Expression of Kibble's bivariate Gamma distribution PDF

I'm studying the Kibble's bivariate Gamma distribution and found one inconsistency between different papers and I'm not sure which is correct. In the Smith et al. 1982, A bivariate Gamma Probability ...
Jason's user avatar
  • 103
1 vote
1 answer
42 views

Erroneous Argument for uncorrelated implies Independence

I've been working on the problem where for a bivariate normal random variable (X,Y), uncorrelated implies Independence. However, I realized that I didn't use the bivariate normal assumption, so there ...
MoneyPrinting's user avatar
0 votes
1 answer
179 views

From univariate to joint convergence in distribution

Let $X_n \rightarrow_d X$ and $Y_n \rightarrow_d Y$ where $X$ and $Y$ are i.i.d standard exponential random variables. However, I do not have that for any $n$, $X_n$ and $Y_n$ are independent. Can I ...
Eryna's user avatar
  • 319
2 votes
1 answer
2k views

Estimating the cumulative probability of a bivariate normal distribution

I have a quick question regarding working out the probabilities of a bivariate normal distribution. To my knowledge, there is no nice closed-form for a cumulative distribution function for the ...
Aleksey's user avatar
  • 23
2 votes
0 answers
35 views

A question about product and division of random variables

Taken three real continuous random variables $X,Y,Z$, non negative (to simplify the handling of the problem), with respective pdf's $p_X , p_Y , p_Z$ . Then if $$ Z = XY\quad \left| {X,Y\;indep.} \...
G Cab's user avatar
  • 131
2 votes
1 answer
565 views

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 ...
DevD's user avatar
  • 115
1 vote
0 answers
72 views

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 ...
statwoman's user avatar
  • 703
3 votes
1 answer
160 views

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 ...
Denis Cousineau's user avatar
0 votes
0 answers
46 views

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) ...
david's user avatar
  • 144
0 votes
1 answer
204 views

Is it possible to calculate a bivariate normal density using only the univariate normal density function? [duplicate]

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 ...
Felipe D.'s user avatar
  • 268
0 votes
0 answers
92 views

Two possible definitions of confidence regions: which one to choose?

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 \begin{equation} H(x,y,p,q)=\frac{n}{...
Vincent Granville's user avatar

1
2 3 4 5
7