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Questions tagged [elliptical-distribution]

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Covariance of two spherical variables

I have encountered a problem here. Suppose $x_1,x_2,x_3\in\mathbb{R}^p$ are three independent r.v. following $N(0,I_p)$, then I want to derive the value of $$E\bigg\{\big(\frac{\beta^T(x_1-x_2)}{||x_1-...
Gareth's user avatar
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2 votes
1 answer
55 views

Distribution of absolute value of Elliptically Symmetric Random Variable

I am studying Elliptically Symmetric Distributions and someone recommended me Symmetric Multivariate and Related Distributions by Fang (1990), which is the book I am reading for that purpose. I know ...
Clemente Ferrer's user avatar
1 vote
0 answers
61 views

Does a whitening transformation of the prior affect the performance of elliptical slice sampling?

I have been using elliptical slice sampling (ESS) with much success lately and I have a question I can't seem to figure out myself. Does a whitening transformation of the prior affect ESS performance? ...
marnix's user avatar
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1 vote
0 answers
119 views

Contour lines for multivariate Laplace distribution

In the p-variate normal distribution ($\mathbf{N_p(\mu,\Sigma)}$), the solid ellipsoid of x values satisfying $(\mathbf{x-\mu)'\Sigma^{-1}(\mathbf{x}-\mu)}\leq \chi^2_p(\alpha)$ has probability $1-\...
Helder Alves Arruda's user avatar
1 vote
0 answers
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Proof involving elliptically symmetric distributions in regression analysis

Let me start by setting the scene and stating the theorem. I just want some pointers on how to follow the proof. Let $y$ be an observable, $n$-dimensional random vector and $f$ be a known, Borel ...
Stéphane's user avatar
  • 258
5 votes
1 answer
119 views

Joint distribution of two t-distributions with different degrees of freedom

Let $x$ and $y$ be 2 random variables with t-distributions with mean = 0 but different degrees of freedom. Can their joint distribution be elliptical?
dayum's user avatar
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2 votes
0 answers
131 views

Estimation of common variance in elliptical distribution

Suppose you observe a random $p$-vector $X$ which follows an elliptical distribution with mean zero, covariance $\sigma^2 I$ and (unknown) distribution function $g$. Given a single observation of $X$...
shabbychef's user avatar
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1 vote
1 answer
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Difference between bivariate exponential family and bivariate elliptical family

I'm studying the elliptical family and I'd like to know the principal differences between the bivariate exponential and elliptical family.
Wagner Jorge's user avatar
1 vote
0 answers
74 views

What are elliptical errors?

When can we have elliptical errors in linear regression?
Timothy Aiyepola's user avatar
2 votes
0 answers
246 views

generate multivariate cauchy random variable

How can we generate multivariate random variable in matlab? Will the set of t distribution with 1 degree of freedom will give multivairate cauchy noise, How to generate?
undefined's user avatar
  • 463
2 votes
0 answers
67 views

Distribution of a linear combination of the components of an elliptically distributed random vector

What is the distribution of a linear combination of the components of an elliptically distributed random vector? Is the linear combination an elliptically distributed random variable?
bob sherman's user avatar
10 votes
2 answers
992 views

Distribution of the Rayleigh quotient

For a research project I need to find the expected value of the generalized Rayleigh quotient: $$E\,[w^T A w \ / \ w^T B w].$$ Here A and B are positive definite deterministic p x p covariance ...
Stats's user avatar
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10 votes
3 answers
7k views

Multivariate Laplace distribution

I find it strange, but I can't find what multivariate Laplace distribution looks like. What is its pdf? I googled for a while but couldn't find a good description. I wasn't paying attention to ...
user34790's user avatar
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