Talk:Dirichlet distribution

message: Since the article states that the Dirichlet distribution is a maximum entropy distribution, could someone more knowledgeable than me add the relevant constraints to the article?
See https://www.sciencedirect.com/science/article/pii/S0047259X05001004. Thanks! 2A02:1811:3707:B900:C4B:98F2:7DE6:7518 (talk) 18:45, 28 May 2020 (UTC)
thread_title: Maximum Entropy

message: If I draw a probability distribution X\sim Dir(\alpha), and then another distribution Y\sim Dir(rX) for some constant r, is the marginal distribution of Y Dirichlet? A5 15:12, 20 April 2006 (UTC)
thread_title:  Question regarding chained Dirichlet distributions 

message: Where it writes: "The Dirichlet distribution is conjugate to the multinomial distribution in the following sense: if", should the "X~Mult(X)" be "X~Mult(alpha)"? The notation Mult(X) doesn't make sense to me since X is a random variable, not a parameter. Chongman 01:28, 19 April 2007 (UTC)
replies: text: Since, I now realise that the Alphas stand for events (from N) and the x are the probabilities I was wrong. But why does one use this terminology which seems to reverse the usage from multinominal distributions? Munibert 16:35, 15 March 2007 (UTC)

text: The "cutting up strings" text recently added provides a minimal example of where this distribution would come up.  Having others would be good, of course.  BSVulturis 20:47, 12 March 2007 (UTC)

text: It's now defined without the dirac delta function that was there before.  Someone will have to check, but I think it's now defined over a set that we integrate and whose integral is continous.  MisterSheik 21:36, 27 February 2007 (UTC)
thread_title:  Dummy questions 

message: Can please somebody explain me what it is? Diego Torquemada (talk) 07:08, 23 April 2008 (UTC)
thread_title:  Uniform Dirichlet Distribution 

message: The first equation doesn't make sense. The product ranges from i=1 to i=K, which implies that there is an x[K] in the product. However, the left hand side makes it clear that x[K] is not present in the function. It's hard to have any confidence in the article as a whole when the defining equation is inconsistent: could someone who understands this please fix it?
213.162.107.11 (talk) 07:30, 12 June 2009 (UTC)
replies: text: @Schmock for 2 vars (x) and (1-x) makes sense. Notice the left hand side of the Beta distribution funciton just shows x so it is all Kosher. Now in the dirichlet definition you have x_1 ... x_{K-1} in the LHS and x_K appears on the right hand side. This equation is syntactically wrong and doesn't make sense to the user until they read the following paragraph.
With the proposed change I made, equations stands on its own and we clarify that we are over a symplex and x_1 ... x_K must sum to 1. 
--74.13.201.69 (talk) 19:52, 5 December 2009 (UTC)
thread_title:  First equation appears wrong 

message: The agreed-upon math style is to not use math tags around things like K-dimensional vector. It's harder to read in certain browsers.
Crasshopper (talk) 00:48, 23 January 2011 (UTC)
thread_title:  math style 

message: So. I think the assumptions in the Wiki page are not correct. I believe that the provided PDF is only valid when equal scaling is applied to all shape parameters, i.e. a_1= a_2=\cdots=a_k. In the case where you want to introduce biasing in your distribution towards different variables, then you will need to use a scaled PDF. See Compositional Data Analysis: Theory and Applications (Section 10.2) for more information.  — Preceding unsigned comment added by Datahipster (talk • contribs) 22:42, 26 November 2011 (UTC)
thread_title:  Scaled Dirichlet distribution 

message: Should the support really be x1 ... xK, and not to xK-1? It makes more sense for xK to be understood and implied as 1-(x1+...+xK-1), just as in the special case of the beta distribution.
It is stated that each x_i must lie in (0,1) for x to be in the support. However, the support is, by definition, a closed set, so, for example, x = (0,1,0) should be in the support, right? Anyway, even some definition of "support" allows for this use, it is inconsistent with the infobox, which may be confusing to nonmathematicians like me. Franknarf11 (talk) 06:23, 3 October 2013 (UTC)
thread_title:  Support 

message: In the right panel, in "support", it says: Σxi = 1. Shouldn't be Σxi < 1? At least this is how appears in the Mathematica help  — Preceding unsigned comment added by Olimak9000 (talk • contribs) 17:17, 6 January 2014 (UTC)
thread_title:  error in right panel 

message: How is the new plot better than the old one?
New: https://en.wikipedia.org/wiki/Dirichlet_distribution#/media/File:Dirichleit_Probability_Distribution_for_Different_Alpha.png 
Old: https://en.wikipedia.org/w/index.php?title=Dirichlet_distribution&oldid=782668807#/media/File:Dirichlet-3d-panel.png
GrantZ (talk) 09:17, 28 July 2017 (UTC)
thread_title:  PDF plot 

message: The box says: "with α_0 defined as for variance, above". But I can't find such definition. --89.204.135.44 (talk) 18:09, 13 May 2019 (UTC)
thread_title:  alpha_0 

message: Recently a new graphic was proposed: https://upload.wikimedia.org/wikipedia/commons/2/2f/Page1-1125px-Dirichlet.png with the author claiming the original one is incorrect: https://upload.wikimedia.org/wikipedia/commons/7/74/Dirichlet.pdf
In my opinion, the labeling on the proposed one is confusing. E.g. in the top right, x1 refers to the single dimension that has its axis shown in the graph. However, the placement of "x1" would suggest it is a label for the bottom horizontal axis.
Second, the new axis does not provide any additional information. The graphic only projects the axis labels of the old graphic onto a line in the middle. This only obscures parts of the plot.
Lastly, the quality of the graphic is below the standard, especially he visible remains of the old oxis that appearently have only been whited. Also the axis labels do not use proper subscripts.
I suppose the main confusion here is that the plot does not have orthogonal dimensions, like a normal 2d plot, but axis that have a 120° angle between them. The ticks on the x2 and x3 axis indicate this. I do agree that this is very subtle, but definitely not wrong in the original plot. As an improvement, I would suggest to add small grid lines to the orgiginal plot. 141.76.60.253 (talk) 15:51, 3 May 2023 (UTC)
thread_title:  PDF plot