The bivariate tag has no wiki summary.
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28 views
Joint PDF change of variables
I now understand how to conduct a change of variables for a marginal PDF.
Now, given two functions that define parameter's spatially: $C_A(x)$ and $C_B(x)$, is it possible to construct the Joint PDF, ...
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1answer
33 views
Is it normal to obtain better (smaller) P values in multivariate analysis compared to bivariate one?
If a multivariate design controls for other predictors when calculating the effect of a predictor, shouldn't it give paler P values (less significant ones, or less vivid odds ratios)? I am seeing ...
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1answer
56 views
Given known bivariate normal means and variances, update correlation estimate, $P(\rho)$, with new data?
I'm dealing with two correlated random variables which are modeled via a bivariate normal distribution. I have values for the means ($\mu_x, \mu_y$) and individual variances ($\sigma_x, \sigma_y$) of ...
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0answers
25 views
marginal of the bivariate normal wrt correlation
What is the distribution that results by marginalizing the correlation coefficient of the bivariate normal distribution, assuming a uniform prior in angular space:
$$\int \; p(x,y|\mu,\Sigma(\theta)) ...
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1answer
40 views
Bivariate normal expectation of the sinus cardinal
I would like to get an analytical expression for
$$\mathbb{E}\left(\frac{\sin(aX)}{aX}\frac{\sin(bY)}{bY}\right)$$
or at least an analytical approximation thereof, when $a,b$ are positive reals, and
...
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0answers
75 views
bivariate probit with endogenous covariate testing
I am interested in learning more about testing for the bivariate probit model with an endogenous treatment regressor. I have figured some stuff out -- summary below, since I don't see much on this ...
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1answer
119 views
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 ...
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1answer
47 views
Finding an appropriate distance/divergence/similarity measure in a real 2D phase space
At first, I have to excuse my sloppy terminology, as I am pretty new to the whole topic.
Imagine a real twodimensional phase space representing climate-related properties. I have a set of N variables ...
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2answers
336 views
Analysis and writing up results
I am doing research for my Masters studies and am battling a bit with the statistical side of my study. I used a survey and have captured all the data into SPSS. I have no statistical background, I ...
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1answer
164 views
KL divergence or similar “distance” metric between two multivariate distributions
I have a large dataset composed of many samples; each sample is as follows:
imagine a grid indexed by i,j
for a sample k, I have Y_k, where Y_k(i,j) is the probability density for k at (i,j)
of ...
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121 views
Bivariate Poisson - Cant seem to understand it. Could someone pls tell me how to work it out in laymans terms?
Researching bivariate poisson over the web is no easy task unless you can make sense of the greek symbols.
I am familiar with poisson and have a deep understanding of it. So could someone explain ...
3
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1answer
101 views
$X$ and $Y \sim U(0,1)$; by letting $Z=g(X,Y)$, how to derive $F_Z(z), E(Z)$ and $E(Z | X^2+X^2 > 1 )$
$X$ and $Y \sim U(0,1)$.
Let $$\eqalign{
g(x,y) &= x &\text{ if } &x^2+y^2 \le 1 \\
&=2 &\text{ if } &x^2+y^2 \gt 1
}$$
and $Z = g(X,Y)$. How to find $F_Z(z), ...
1
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1answer
106 views
Farlie-Gumbel-Morgenstern Bivariate Gamma Distirbution
Given the variables $X$ and $Y$, which are correlated, $X\ge0$, $Y\ge0$ and each follow a gamma distribution with different shape parameters, i.e.,$X\sim Gamma(a_1,\alpha)$ and $Y\sim ...
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3answers
315 views
Probability of collision (two bivariate normal distributions)
I am trying to solve this problem on and off for the past couple of months but to no success. This was supposed to be a very small part of my PhD thesis in navigation but I guess I underestimated the ...
2
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1answer
253 views
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, ...
2
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2answers
252 views
Correlation of bivariate grouped data?
Which test should I use, if I want to test the correlation between 2 bivariate grouped variables?
The case is: I have asked several hotel owners about their feelings about the occupational rate of ...
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0answers
83 views
Joint distribution of two distances
Suppose there are three points in 3D space, each with coordinates $A_i=(X_i,Y_i,Z_i)\leadsto \mathcal{N}(\mu_i,\tau^2\mathbb{I}_3)$. We compute the distance between the three points, e.g. $D_{ij} = ...
4
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1answer
163 views
Inequality for bivariate normal distribution
Let $X_1$ and $X_2$ be bivariate normal with mean $\mu=(0,\mu_2)$, for any $\mu_2$, and correlation $\rho$.
Consider the following inequality:
\begin{align*}
Pr\left\{|X_1| \ge ...
3
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1answer
159 views
When simulating a bivariate normal distribution, why is $\rho$ chosen instead of estimated from the data?
In a video lecture, MrProf shows the 3d-plot of a bivariate normal distribution $\mu_{x_1} = \mu_{x_2} = \sigma_1 = \sigma_2 = 1$ and chooses $\rho = 0.5$ .
If stick to Mathworld, $\rho$ simply is ...
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60 views
Exponential Downweighting in Bivpois [closed]
I basically want to model football results using bivpois. The package is easy to use but I wondered if anyone knew how (in R) to extend it to Downweight past results like Dixon Coles 97 suggests.
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95 views
Is it possible (or even usefull) to transform Log transformed data into Z-scores?
We have created a questionnaire. In this questionnaire there are different dimensions with different answering scales.
Because of our rightly skewed data we log transformed our data. But here is the ...
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0answers
35 views
Approach to testing difference from a bivariate null distribution generated by randomization
I would like to test if each of the red observations is more extreme in variable xy[,2] than 95% of a null hypothesis (black dots) generated by randomization.
I am ...
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2answers
412 views
Finding the Bayesian classifier for a bivariate Gaussian distribution
Very close to: Joint Gaussian of two Gaussians
I am trying to find the Bayesian classifier for two classes given by the following bivariate Gaussian distributions:
$$p(x|c_1) = N(\mu_1, ...
2
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1answer
318 views
Ellipse region shape from bivariate normal distributed data?
In my previous question I needed to help with ellipse region extraction and determine if point lies in that region or not.
I ended up with this code:
...
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4answers
3k views
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 ...
3
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2answers
240 views
McKay's Bivariate Gamma Distribution
Given the variables $X$ and $Y$, which are correlated, $X\ge0$, $Y\ge0$ and each follow a gamma distribution with different shape parameters, i.e.,$X\sim\Gamma(a_1,\alpha)$ and ...
2
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2answers
574 views
Bivariate Gamma distribution PDF
I'm analyzing a set of data, and I like to fit a gamma distribution. I know how to do it in one dimension, but the data that I'm analyzing now are two dimensional. Is there any way that I can have a ...
0
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1answer
223 views
How to relate the variance of a joint bivariate normal distribution to the variance of a single normal distribution?
I have $(X,Y_1)$ with joint bivariate normal distribution. Also, $Y_1$ is conditional on $X$. Therefore $\rho$ is non-zero. Suppose I have $Y_2$ that is also normally distributed and $\mu_{Y_2} = ...
3
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2answers
138 views
What is the relation between two IIN mean zero random variables?
I have trouble proving the following fact in my econometrics homework. The lecturer said that I should merely look at my statistics books, but I cannot seem to find it anywhere! Thus, sorry if it is ...
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1answer
417 views
What is the variance of the sum of components of a multivariate normal distribution?
I'm talking with my advisor about how to compute standard deviations for, say, combined standardized test scores for admissions purposes. For example, we'd be interested to compute the sum of the ...
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3answers
137 views
Comparing points in a bivariate space
I have bivariate data from which I have generated thousands of bootstrapped estimates within each of two conditions (pink & blue):
I'd like to determine whether these conditions' bivariate ...
