|WikiProject Statistics||(Rated Start-class, Low-importance)|
Is this statement always true?
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)
- 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)
Constraints on g
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?