# Questions tagged [joint-distribution]

Joint probability distribution of several random variables gives the probability that all of them simultaneously lie in a particular region.

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### Deriving conditional distribution using Gaussian copula

This question shows how to derive an analytical expression for the conditional distribution from a multivariate normal. I am curious how well this extends to when there's a Gaussian copula, but ...
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### Joint distribution of log hazard ratio estimates for two outcomes

I have a study where individuals are randomized to a treatment or control group, and there are two time-to-event outcomes $S_i$ and $T_i$ measured for each individual $i$. The two outcomes have some ...
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### When (if ever) is the sum of two dependent geometric RVs negative binominal?

Imagine you have two random variables $X$ and $Y$, you know $$X \sim \text{Geometric}(p) \\ X + Y \sim \text{Negative Binomial}(2, p)$$ I am interested in what if anything can be said about the ...
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### Non-parametric estimate of conditional expectation

I have a (fairly smooth) function $f$ and a sample $\{(x_i,y_i)\}_{i=1,\ldots,N}$ from the joint distribution of the random variables $X$ and $Y$. I would like to estimate the conditional expectation ...
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### Confusion about two Gaussian distributions

From here, it says that, linear combination of two Gaussian distribution, are always Gaussians. However, Let 𝑋 be standard normal and 𝜀=±1 with probability 1/2 each, independently of 𝑋. Let 𝑌=𝜀𝑋...
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### How to show two variables are asymptotically independent

Let $X_1,...,X_n$ be iid from $Exp(\theta)$ with density function $f(x) = \frac{1}{\theta}e^{-x/\theta}$. Show that $M_n = X_{n:n} - \theta \ln(n)$ and $T_n = nX_{1:n}$ are asmyptoically independent ...
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### Joint Entropy of two time series

I have two time series of same length like following: ...
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### If the joint density $f_{X_1,…,X_n}(x_1,…,x_n)$ is symmetric about the origin, does this imply that each marginal cdf $F_{X_i}(0)=1/2$?

If the joint density $f_{X_1,...,X_n}(x_1,...,x_n)$ is symmetric about the origin in the sense that for any $(x_1,...,x_n)$, it holds that $f_{X_1,...,X_n}(x_1,...,x_n)=f_{X_1,...,X_n}(-x_1,...,-x_n)$ ...
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### Combining subjoint distributions to create a larger joint distribution

I am trying to construct large joint distributions through smaller joint distributions and I'm not sure how to approach the literature. I am curious if there exists a function which can take n ...
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### Visualizing separability / independence

I’d like to visually ‘see’ the independence of random variables. I tried plotting f(x), f(y), and f(x, y) for independent and dependent pairs of variables. However, the difference is still not ...
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### How is exchangeability related to covariate shift?

I understand that exchangeability refers to the notion that the order of data in a sequence does not affect the joint distribution of that data. In a sense, the current data we possess is from the ...
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### Jensen–Shannon divergence relation between marginal and joint

I have the following distributions- Joints: $p_1$(x,y) = $\rho_1$(x) $q_1$(y|x), $p_2$(x,y) = $\rho_2$(x) $q_2$(y|x) And the marginals: $\rho_1$(x), $\rho_2$(x). Is it possible to provide any ...
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### Check whether a random sample comes from an elliptical distribution?

How can I check whether it is a reasonable assumption to say that a multivariate sample $x_1,...,x_n$ comes from an elliptical distribution, such as a normal distribution or a t-distribution? In the ...
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### Estimating parameters and simulating a multivariate time series (O-U?) process

Say I have 5 time series that may or may not be correlated with each other. I also suspect they individually may be mean reverting. I'd like to 1) be able to test the hypothesis they are ...
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### Exploiting the joint density when averaging measurements

I have two measurements of a quantity from two different sensors, each with their own variance based on the sensors' specifications, etc. From collecting a lot of training data, I have access to the ...
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### Estimating the likelihood of an observed path for a continuous state space Markov process

Problem statement Let $\mathbb{X} \subset \mathbb{R}^{k}$ and let $p:\mathbb{X}\times\mathbb{X}\rightarrow\mathbb{R}$ be a density kernel on $\mathbb{X}$. We assume the following model for the ...
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### Can I compare Mahalanobis distances from different distributions?

I have a multivariate dataset representing multiple locations, each of which has a set of reference observations and a single test observation. For each location, I would like to measure how anomalous ...
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### Calculate mutual information of twitter's users interactions

I have a research project about finding out user's interaction on Twitter. If I want to calculate the mutual information between two users A,B: I(A,B), to know the probability of A and B appearing in ...