Talk:Complex normal distribution

Wiki Education Foundation-supported course assignment
This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Mowen17. Peer reviewers: Mowen17.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 18:13, 16 January 2022 (UTC)

Field of parameters
The parameter matrices are complex, the article should mention this in the text.

Definition of characteristic function for arbitrary complex distribution?
The section Characteristic function in its entirety is as follows:

"The characteristic function of complex normal distribution is given by



\varphi(w) = \exp\!\big\{i\operatorname{Re}(\overline{w}'\mu) - \tfrac{1}{4}\big(\overline{w}'\Gamma w + \operatorname{Re}(\overline{w}'C\overline{w})\big)\big\}, $$

where the argument $$w$$ is an n-dimensional complex vector."

The linked article "Characteristic function" contains no information about how to define the characteristic function for an arbitrary complex probability distribution.

I hope someone knowledgeable about this subject can include a definition, because otherwise the entire meaning of this section is unclear. 2601:200:C000:1A0:BC00:5039:DB55:E9EC (talk) 20:23, 29 July 2022 (UTC)