Questions tagged [bivariate]
Concerning two random variables
321
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Is it possible to winsorize bivariate outliers?
After examining the scatterplot of my dependent variable against my independent variable, it appears that there are some bivariate outliers. I also looked at the scatterplot of residuals against ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $$E\left[XY\Big|X| \leq z_{\alpha/2}, |Y| \...
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More correlated information is... more informative?
Suppose I am trying to make inference about a parameter $\mu$. I have a prior
$$
\mu \sim N(0,\sigma^2),
$$
and I observe two correlated signals about $\mu,$ namely $x_1, x_2$ where
$$
\begin{pmatrix}
...
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Proper Bivariate Joint Survival function
I have a joint survival function in the presence of 2 competing risks.
$S(t_1, t_2) = \exp\{−λ_1t_1 − λ_2t_2 − νt_1t_2 − μ_1t_1^2
− μ_2t_2^2\} \ \ \ t_1,t_2\geq0$
For which parameter values is this a ...
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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 ...
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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 ...
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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 ...
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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
$\Sigma=\begin{pmatrix}
1 & \rho \\
\rho & 1
\end{pmatrix}$ ...
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problem forecasting in R using a VAR model : interpretation of characteristic polynomial roots
I have the following R code, I am fitting a VAR(10) models to a bivariate time series, comprising two variables, gaz and nuc. Yet, when trying to forecast, I had negative values, whereas my series is ...
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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....
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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.
...
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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 ...
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Which mgcv syntax for a bivariate smooth interaction with a random effect as predictors?
I want to predict the concentration of a biomarker (continuous) according to the interaction of white blood cells with time (both continuous), considering medical units as a random effect that may ...
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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 ...
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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 ...
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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 ...
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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 ...
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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....
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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 \...
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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 ...
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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 ...
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1
answer
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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 ...
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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)...
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1
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69
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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 ...
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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 ...
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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 ...
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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 ...
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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
$$
Z = XY\quad \left| {X,Y\;indep.} \...
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How to find the distribution of a function of two random variables?
I have the joint pdf
$$f(x_1,x_2)=\begin{cases}\frac{1}{4}\;,\ -1<x_1,x_2<1\\ 0\;,\ \text{otherwise.}\end{cases}$$
I have to find the distribution of $Y=\frac{X_2}{1+X_1^2}.$
I have tried to ...
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answers
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Test for bivariate normality assumption
Assume two time series $X_1$ and $X_2$, where $X_i=(x_{i,1},...,x_{i,T})$. How can we test the assumption of bivariate normality for these time series? (Assume each of the time series are stationary ...
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How can population variance be estimated from a bivariate sample?
Let's assume a bivariate population with a correlation $\rho$ and a common $\sigma$ so that $\Sigma = \sigma^2 \begin{pmatrix}1 & \rho \\ \rho & 1\end{pmatrix}$.
I would like to know the ...
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Fitting bivariate normal distribution with covariate-dependent correlation parameters
Suppose we fit
$$
\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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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 ...
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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}{...
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Is a bivariate copula relevant in this physics setting manifesting uniform univariate marginals--and, if so, how can it be constructed?
To quickly place our probabilistic (copula) question in its subject matter setting, we note that a fundamental concept in quantum theory is that of entanglement QuantumEntanglement.
The states of ...
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What are examples of symmetric copulas $f(x,y)=f(y,x)$ having relative minima for $f(x,x)$?
In a previous posting on this site RepulsiveBehavior I attempted to detail
a quantum-information-theoretic separability/entanglement problem I am pursuing. Detailed issues of sampling sizes for a data ...
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Do any standard copulas fit well these sampled bivariate data--exhibiting repulsive behavior--having uniform marginals
I'm currently developing a data set that consists of two $50 \times 50$ matrices, which I designate as q1 and Q1.
I strongly believe (bordering on formal proof [cf. Corollary 1 in marginalinvariance]) ...
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Calculate chance of radius being smaller then X in a bivariate normal distribution
If I have two variables X and Y that are both normally distributed with the same standard deviation σ and the same mean 0. They come together to form a circular bivariate normal distribution. How can ...
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Your class has 100 students and they have 5 elective courses to choose from. In each course, the proportion of students is equal in population
I am actually unable to understand the question and would appreciate it if someone can help with that. For the above problem statement, there are three questions that I need to answer
Make a ...
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57
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Bivariate Distribution for Milstein Scheme
I am seeking a density for $$Y_{t+1}\mid Y_{t},$$
where $$Y_{t}=\begin{pmatrix}Y_{t}^1\\
Y_{t}^2
\end{pmatrix},$$
and for $i=1,2$, the $i$th component of the 2-dimensional Milstein scheme is given ...
1
vote
1
answer
82
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Covariance between partitions of a normal distribution
A bit of a contrived example, but if I had a sample of $X_1,\dots,X_n \stackrel{iid}{\sim} N(\mu,\sigma^2)$ (in this case $\mu$ is unknown but $\sigma^2$ is known), and then calculated the arithmetic ...
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Derivative of a Bivariate normal CDF with respect to its variables
Following up on the question (and answers) here, I'm trying to derive $\frac{\partial \Phi(x_1, x_2|\mathbf{\underline{\theta}})}{\partial x_1}$ and $\frac{\partial \Phi(x_1, x_2|\mathbf{\underline{\...
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Multivariate Analysis and AOR
Hello All, I understand how we can calculate the Bivariate analyses using the table 3 in table 4. But can anyone please help me understand how to calculate Multivariate analyses using AOR. Are there ...
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Does an R-based implementation of Fasano and Franceschini's (1987) 2D Kolmogorov-Smirnov test exist? [closed]
First I would like to recognize that similar versions of this question have been asked before, however these either did not pertain to Fasano and Franceschini's (1987) modification of the 2D KS test ...
