Talk:Multivariate normal distribution

Infobox PDF requirement on covariance matrix
Previously the PDF said covariance matrix Σ had to be positive-definite. I fixed it to PSD for covariance matrix. I would also say symmetric but the article on PSD includes symmetric as part of the definition so I'll use that definition. Wqwt (talk) 20:53, 29 March 2022 (UTC)


 * Ok I misunderstood - it needs to be invertible thus positive definite to write down the PDF in that form, otherwise it is like zero variance Wqwt (talk) 21:22, 29 March 2022 (UTC)

More authoritative references?
User 174.168.4.26 has recently added three references to an SSRN preprint. The preprint is based on a student's Honors thesis (see link in section 4.3 of the preprint). There's presumably nothing wrong with the preprint but it might be preferable to cite more authoritative sources. Eldacan 08:15, 20 July 2023 (UTC)

Notation in Bivariate case
In the subsection titled "Bivariate case", the notation [XY]' is used twice. But that notation has not been previously defined and, in fact, is not used in the other sections of the article. Its meaning should be clarified. SometimesRPC 18:44, 8 January 2024 (UTC)

Formula for the limit of the isoline ellipsis' major axis in the bivariate case
The article's subsection "Bivariate case" states a formula for the limit of the major axis of isoline ellipses as $$|\rho|\rightarrow 1$$:

$$   y(x) = \sgn (\rho)\frac{\sigma_Y}{\sigma_X} (x - \mu _X) + \mu_Y. $$

and then provides a reference. However, the cited reference is just a formulation of the statement of the conditional expectation of the bivariate normal:

$$\operatorname{E}(X_1 \mid X_2=x_2) = \mu_1 + \rho \frac{\sigma_1}{\sigma_2}(x_2 - \mu_2)$$

The reference discusses this within the context of estimation, which IMO complicates the statement unnecessarily. It seems more consistent to remove the reference and cite the Wikipedia article's own section.

M hoehle (talk) 09:19, 26 January 2024 (UTC)