Editing Student's t-distribution (section)

====Maximum entropy distribution====
Student's {{mvar|t}}&nbsp;distribution is the [[maximum entropy probability distribution]] for a random variate ''X'' having a certain value of <math>\ \operatorname{\mathbb E}\left\{\ \ln(\nu+X^2)\ \right\}\ </math>.<ref>{{cite journal|vauthors=Park SY, Bera AK|date=2009|title=Maximum entropy autoregressive conditional heteroskedasticity model|journal=[[Journal of Econometrics]]|volume=150|issue=2|pages=219–230|doi=10.1016/j.jeconom.2008.12.014}}</ref>
{{Clarify|reason=It is not clear what is meant by "fixed" in this context. An older and more to-the-point source ( https://link.springer.com/content/pdf/10.1007/BF02481032.pdf ) demonstrates that the Student's t distribution with  {{mvar|ν}} d.o.f. is the maximum entropy solution to a specific problem, for which, in addition to one more constraint, ℰ{ ln( 1 + X²/ν)} equals some constant which is predetermined for every {{mvar|ν}}.|date=December 2020}}{{Better source needed|date=December 2020|reason=The source does not obviously state this, although it touches upon something related.}}
This follows immediately from the observation that the pdf can be written in [[exponential family]] form with <math>\nu+X^2</math> as sufficient statistic.