Questions tagged [bivariate]

Joint probability distribution of two variables.

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24 views

Integration of (Phi(x)-Phi(y))^2d(F(x, y)

How to integrate the following? Thanks
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1answer
19 views

Two simultaneous time series vars. Want “confidence” intervals for one's prediction (not forecast per se) of the other

Let me know if this is a duplicate. This seems to differ from other time series questions I've seen in that I'm not trying to forecast the future. Maybe that will mean only a difference in the ...
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1answer
16 views

Lcross Confidence Envelopes - R software

I have performed an Lcross examination in R with the following code: ...
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37 views

correlation coefficient bivariate normally distributed [duplicate]

Suppose that X,Y and X,Z are bivariate normally distributed. We have $E(X)=0, Var(X)=10$, $E(Y)=0, Var(Y)=6$ and $ρ_{xy}=0.87$ Moreover, $E(X)=0, Var(X)=10$, $E(Z)=0, Var(Z)=4$ and $ρ_{xz}=0.87$ ...
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27 views

Simplification of bivariate normal $\phi_2(x,y,\rho)$ at $y=y_F$ (i.e. fixing one of the axes)

Suppose we start off with the traditional standard bivariate normal distribution: $$\phi_2(x,y|\rho,\mu_x=0,\mu_y=0,\sigma_x=1,\sigma_y=1)=\frac{1}{2\pi\sqrt{1-\rho^2}}\exp \left(-\frac{x^2-2\rho x y ...
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1answer
26 views

Probailty of Ygreater than or equal to X^2

I want to solve the below mentioned question which involve transformation or change of variable technique
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1answer
26 views

Do outliers affect bivariate correlation? [closed]

I recently found a significant positive correlation for three variables (anxiety, depression, and Fear of Missing Out). FOMO is my variable of interest. I did a one sample t-test to measure the ...
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1answer
48 views

What is the variance of the difference of two means?

I'm trying to express $\mathrm{Var}(\mu_x - \mu_y)$ in terms of $\rho$, $\sigma_x$ and $\sigma_y$, where $\mu$ denotes the mean of the random variable. Firstly:\begin{align*} \mathrm{Var}\left(\sum_{...
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3answers
70 views

Question Regarding Zero Conditional Mean

Hi I am a beginner to econometrics! I have been dealing with bivariate regression. We use the formula $y = \beta_0 + \beta_1 x$. I am told that if $E(u\mid x) \ne 0$ then the estimate of the slope ...
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1answer
384 views

How to estimate a bivariate probit (biprobit) model in R with a different set of explanatory variables? [closed]

I'm trying to estimate a bivariate probit model (also called biprobit model) in R where the set of explanatory variables is different for both binary outcomes. Thus, my setting is: \begin{align} Y_1^*...
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2answers
57 views

Bivariate vs. multivariate analysis

I have been reading a few papers lately that has done both bivariate and multivariate analysis on their data. What I have seen most of the times is that they usually do the bivariate analysis first, ...
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289 views

MLE of Parameters of Bivariate Normal Distribution

I am working through find the maximum likelihood estimators of the bivariate normal distribution, without using matrices. I have the following density function: $f(Y_1,Y_2) = \frac{1}{2\pi\sigma_1\...
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54 views

Variance of bivariate normal distribution plus normal distribution

Problem: $W = -27 + 0.3X + 0.45Y + E$ The pair $\begin{bmatrix} X \\ Y \end{bmatrix}$ behaves like a bivariate normal with vector of averages $\begin{bmatrix} 156 \\ 86 \end{bmatrix}$ and ...
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69 views

Unexpected behavior in inhomogeneous Cross K Function (Kcross.inhom) [closed]

I am currently analyzing a point pattern in R using the "spatstat" package. I am comparing two different areas, therefore I made two plots for each area (first two plot-left-area1; second two plots-...
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2answers
96 views

I want to create a random sample of length n from a normal multivariate distribution

This may sound like a stupid question, but I have a problem in understanding this question, especially this part: "generate a random sample of length n from a normal multivariate" This is what I ...
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2answers
149 views

How to justify that $(Y_1,Y_2)$ is not bivariate normal without finding its exact distribution?

Suppose $X_1$ and $X_2$ are independent $N(0,1)$ variables. Define $$Y_1=X_1\,\text{sign}(X_2)\quad,\quad Y_2=X_2\,\text{sign}(X_1)$$ I have to show that $(Y_1,Y_2)$ is not bivariate normal ...
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55 views

Knowing correlation, bivariate normality, means and standard deviations, find values probability

After months of study I still do not get it. I apologize (see: Estimating values knowing their Pearson's r and their means and standard deviations) Imagine, for example, I have two bivariate ...
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36 views

Interpreting the coefficient of the interaction between 2 (binary) endogenous variables

I have the following outcome (second-stage) equation: $$y = \beta_0 + \beta_1w + \beta_2x + \beta_3w x + \cdots$$ $y$, $w$ and $x$ are all binary. Both $w$ and $x$ are endogenous, but I have an ...
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1answer
60 views

Solving a double integral over transformations of joint bivariate standard normal values

My problem is about calculating the covariance between transformations of two test statistics based on the correlation between these test statistics. Let $X$ and $Y$ be two test statistics whose joint ...
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11 views

multilevel discrete competing risk

Currently, i'm working my dissertation to build up the joint association in between multilevel discrete time competing risk response(Y_1tij^(r); r=event status) and another multilevel continuous ...
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1answer
146 views

Simulate Bivariate Beta Distribution , BIBETA(6, 20, 2) in R

I need to simulate bivariate beta distribution, $BIBETA(6, 20, 2)$ in r. I am looking for a package/ code that would generate bivariate beta distribution. I couldn'...
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80 views

Why is it unacceptable to use binary or count dependent variables in OLS?

I know this is a basic question but I really want to make sure I fully understand the reason's why this is the case. If possible, can someone help explain to me as simply as possible why it is bad to ...
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29 views

bivariate regression calculation?

I have been trying to follow the example available in this link about bivariate regression, page 4: http://core.ecu.edu/psyc/wuenschk/MV/IntroMV.pdf The univariate regression is easy to follow, the ...
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40 views

Bivariate probit : is there a heteroscedastic version of the model?

I know there exists a version of the simple probit model which is robust to heteroscedasticity (the heteroscedastic probit model). Is there an equivalent for the bivariate probit model? Is there a way ...
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2answers
85 views

Bivariate/multivariate models for multinomial response variables

I need to fit two categorical (potentially correlated) response variables (each has three classes) on a set of explanatory variables, while considering for the response variables' correlation. What ...
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43 views

Getting marginal distributions from a bivariate probability distribution function [duplicate]

I understand the basic principles of bivariate distributions and their marginal counterparts. I am stuck on a slightly more sophisticated question however. Given the following bivariate distribution: ...
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1answer
430 views

What is histogram classifier and how to use it? [closed]

This question is about the assignment on my ML course.. I have been given two continuous data in a normal distribution and predict the values of both for class labels(m/f) in 2 steps: build a ...
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1answer
49 views

Is it right to model a binary response variable on a set of variables, where one of the explanatory variables is assumed dependent on the others?

I am modeling the binary variable Y on a set of variables, say the vector X, using logistic regression. Then, I want to model another binary variable, Z, again on vector X plus Y. Is this ...
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319 views

cov(x,x*y) Covariance of two normally distributed variables

I have been trying to find an expression for the covariance of two normally distributed variables X and Y if cov(x,y)=c then cov(x,xy)=? I would greatly appreciate any help. Probably it must be ...
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40 views

Finding the overlap of two Bivariate Non Parametric models using R

I need a few suggestions on some methods to try or to be pointed in the right direction. I will start off describing the big picture. I have little stats background. I come from physics and astronomy. ...
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153 views

An example of a bivariate pdf, where marginals are triangular distributions

What could be a form of $$f_{X,Y}(x,y)$$ where $f_X(x)$ and $f_Y(x)$ both have the form of a triangular distribution with support $(0,1)$, but with different parameters that governs location of mode? ...
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138 views

Why does test on Pearson correlation require bivariate normality?

For a pair of random variables $X$ and $Y$, we can compute their Pearson correlation coefficient $r$ and conduct hypothesis testing on the null hypothesis $H_{0}:r=0$ with the $t$ statistic $t=r\sqrt{...
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1answer
102 views

Covariance of 2 dimensional bivariate normal distribution

I'm forgetting my basics, so I must be being a silly sausage, but consider $$X\sim N(0,1)$$ $$Y\sim N(0,1)$$ if $f(x,y)$ is the join probability of these 2 variables, then the 3D plot looks like ...
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1answer
271 views

Derivative of bivariate normal CDF with common mean parameters

I am trying to calculate a derivative of the form $\frac{d}{dz}\Phi_2(\mu_1(z),\mu_2(z),\rho)$ where $\Phi_2$ is the standard bivariate normal CDF. I am thinking it might be an application of a ...
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1answer
102 views

Joint distribution of $(\bar{X},\bar{X^2})$?

I have found in this Pdf, theorem 2, that asymptotically: $(\frac{\sum X_i}{N}, \frac{\sum X_i^{2}}{N})$ converges in distribution to a bivariate random variable with mean $(\mu_1,\mu_2)$ and ...
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2answers
374 views

What is the expected value of $X$ given $X<Y$, where $X,Y\sim\mathcal{N}(\mu,\sigma^2)$? [duplicate]

What is $\mathbb{E}[X|X<Y]$ if $X,Y\overset{iid}{\sim}\mathcal{N}(\mu,\sigma^2)$? I have found that $\mathbb{E}[X|X<Y]=\int_{-\infty}^{\infty} -\log(\Phi(\frac{x-\mu}{\sigma}))x\phi(\frac{x-\mu}...
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1answer
292 views

Given bivariate data (X, Y), how to determine a cut-off of X that meets some condition of Y?

I have two distributions, $X$ and $Y$ (shown on the horizontal X axis and vertical Y axis, respectively, see image), that represent different ways of scoring some complex system. For a subset of ...
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1answer
160 views

Numerical computation of the means and covariance in a truncated bivariate normal distribution

How can I compute the means and covariance of a truncated bivariate normal distribution? I am particularly worried about the case when the truncation occurs very far from the mean. Is there a robust ...
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1answer
104 views

Creating a bivariate distribution with one customized marginal distribution

I am looking at modelling a bivariate distribution with observed data from distributions that look like this: Variable 1's distribution looks like a gamma distribution and variable 2's distribution ...
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1answer
618 views

Copula for non-standard distributions in R

I'm trying to model a bivariate distribution using copulas in R. See image below for the pairs plot of the data. Variable 1 can be modeled nicely using a gamma distribution, but variable 2 fails ...
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1answer
96 views

finding Pr(X+Y > 500) given the following joint probability density function

I am reviewing for a probability and statistics class. I am stuck on a problem despite repeated attempts. (THIS IS NOT HOMEWORK!) The questions is: Consider an electronic system with two components. ...
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1answer
86 views

Finding probability of bivariate random variable from joint probability density function

I have a Bivariate continuous random variable (X,Y) with joint probability density function $ f_{X,Y}(x,y) = \{{6(y^2-x^2)}$ for $ 0 < x < y < 1$ (0 otherwise) I want to work out $P(X + Y &...
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2answers
263 views

Bivariate normal distribution , link $\Bbb E(Y\mid X=x)$ and $\Bbb E(X\mid Y=y)$ [duplicate]

Note: I edited this question on 1/1/2018 because of the comments on the original question. So some comments relate to the earlier version. It is closed as duplicaten but I dusagree with that For a ...
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1answer
346 views

How to generate random samples from Gumbel’s bivariate exponential distribution?

The earliest and the simplest known bivariate exponential distribution, introduced by Gumbel (1960), has joint survivor function and joint probability density function given by: \begin{equation}\...
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30 views

Explicit closed form of $\mathbb{E}[v_1^iv_2^j]$ from bivariate normal distribution

Suppose I have a bivariate normal distribution $V=\begin{bmatrix} v_1 \\ v_2 \\ \end{bmatrix} \mathtt{\sim}\left( \begin{bmatrix} 0 \\ 0 \\ \end{bmatrix}, \begin{bmatrix} 1 & ...
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0answers
23 views

Bivariate Probability Distribution

How can I prove $F$ is a bivariate distribution function where $F(x_1,x_2)=F_1(x_1)F_2(x_2)[1-t(1-F_1(x_1))(1-F_2(x_2))]$ $F_1$ and $F_2$ are univariate distribution functions. And $-1\leq t\leq1$ $...
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1answer
202 views

Calculate $E[XY]$ for $(X,Y)\sim N(\mu_{1},\mu_{2},\sigma_{1}^{2},\sigma_{2}^{2}, \rho)$

I need to calculate $E[XY]$ for $(X,Y) \sim N(\mu_{1},\mu_{2},\sigma_{1}^{2}, \sigma_{2}^{2}, \rho)$ by using integration and then determine the correlation coefficient afterwards. Now, when $X \sim ...
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0answers
437 views

Bivariate Beta distribution

I am analyzing two dimensional data. After analyzing each dimension with the help of the fitdistrplus and logspline packages, they both fit the Beta distribution. Is it possible to analyze the two ...
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2answers
73 views

Bivariate distribution for log returns of stocks

I'm aware that the log returns of securities are often considered to follow Levy alpha-stable, or truncated Levy Flight distributions, and sometimes t-distributions or normal mixtures too. What about ...
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1answer
30 views

Survival model for two survival times

I have two time to event data measured on same individual.they time to diagnose and time to first treatment from diagnosis . i have fitted two cox models separately for two survival times. Now I want ...