Talk:Elliptical distribution

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Is this statement always true?[edit]

I am not sure the following statement is always true:

"Elliptical distributions are important in portfolio theory because if the returns on all assets available for portfolio formation are jointly elliptically distributed then all portfolios can be characterized completely by their mean and variance..."

I think a multivariate Cauchy distribution is elliptical, but mean and variance would necessarily be undefined. Rlendog (talk) 19:53, 14 December 2010 (UTC)

This statement is wrong since Levy-Stable distributions are elliptical and only the Gaussian (special case) has a variance. Limit-theorem (talk) 00:44, 8 August 2014 (UTC)

(davidma) I agree with the above. You can have many different elliptical distributions with the same mean and variance. — Preceding unsigned comment added by (talk) 04:57, 15 July 2011 (UTC)
The quote from the article missed out the bit "two portfolios with identical mean and variance of portfolio return have identical distributions of portfolio return", which may have some effect (but the meaning isn't defined). Still, it looks as if there should be a change from "variance" to "scale paramerter" at least, and presumably there should also be something like "... for a given characteristic generator...". Has anyone looked at the two references for this paragraph to see what is going on there? Melcombe (talk) 09:07, 15 July 2011 (UTC)
This article needs some work. Most article define the spherical distribution first, with the elliptical as a special case, and the characteristic generator has to have properties clearly discussed here. I will work on it soon. Limit-theorem (talk) 00:43, 8 August 2014 (UTC)

Constraints on g[edit]

I don't have the paper cited available right now, but it seems strange to me that in the definition g should be constrained to the domain of non-negative reals. In the case of a normal distribution, the domain for exp() is actually constrained to the nonpositive reals. Can anyone verify that this is correct/incorrect?