Talk:Categorical distribution

message: Is the name categorical distribution a standard and official name? I only heard it in the context of BUGS. Albmont 11:11, 16 March 2007 (UTC)

message: A lot of the equations display only as text codes preceded by "Failed to parse" errors -- saw this on 2014-02-14  — Preceding unsigned comment added by 160.36.130.252 (talk) 21:50, 14 February 2014 (UTC)
thread_title:  Error in equation display 

message: "It should not be confused with the multinomial distribution."
But I've seen in several papers the usage of the term "multinomial distribution" for this distribution. For example, the Latent Dirichlet allocation paper. Are they wrong? Took (talk) 13:13, 10 July 2008 (UTC)
thread_title:  multinomial distribution 

message: This first part seems clear:
"A categorical distribution is the most general distribution whose sample space is the set {1, 2, ..., n}.  It is the generalization of the Bernoulli distribution for a categorical random variable."
In other words, while the Bernoulli is a flip of a 2-sided coin labeled {0,1}, the Categorical is the roll of an n sided die, labeled {0,1...n-1}.  
This second part must be wrong:
"Consider the extended analogy: Bernoulli random variable : Bernoulli distribution : Binomial distribution :: Categorical random variable : Categorical distribution : Multinomial distribution"
Ok, so since I know that Binomial is a sum of N Bernoulli random variables, this analogy seems to say that Multinomial is a sum of N Categorical random variables - but this is just not right. Take N=2 and n=3.  A Multinomial would count X_1 = 0, X_2 = 2 together with X_1 = 2, X_2 = 0 as giving the same sum X_1 + X_2 = 2; but a sum of two Categorical Distributions would also include X_1 = 1, X_2 = 1 (which a Multinomial would not include).  —Preceding unsigned comment added by DiagonalArg (talk • contribs) 09:28, 6 September 2008 (UTC)
thread_title:  Analogy to Multinomial Does not Hold 

message: This "categorical distribution" seems to be nothing but a standard discrete probability distribution. Does the name exist is the litterature? The analogy to multinomial does not hold. A multinomially distributed random variable is a sum of n independent random variables that each attains the unit vectors e_1,...,e_k with probabilities p_1,...p_k. Joakimekstrom March 21, 12pm EST  —Preceding undated comment added 15:50, 22 March 2009 (UTC)
replies: text: Good edits. The formulation by Bishop is also used by Mardia (1970). Joakimekstrom March 25, 5 am EST  —Preceding undated comment added 09:10, 25 March 2009 (UTC)
replies: text: Your edits made the article much cleaner. In my experience the more common use of the categorical distribution is the (equivalent) non 1-of-K encoded vector. I think it might still be worth a mention. We have found the generation could to be helpful as well. --128.187.80.2 (talk) 16:36, 25 March 2009 (UTC)
thread_title:  Original research? 

message: The article says that "if the frequency of each outcome is Ei and one begins with a uniform prior, then the posterior distribution is the function Dir(E1,...,En)." However, isn't the uniform prior Dir(1,...,1), similar to a uniform distribution being beta(1, 1)? That would make the posterior distribution Dir(E1+1,...,En+1). Ummonk (talk) 06:14, 25 April 2009 (UTC)
thread_title:  Bayesian Statistics 

message: As far as I know, in probability theory multinormal distributions are continuous. Is this word used for discrete distributions in another discipline? If so, the article should not say "In probability theory and..." Boris Tsirelson (talk) 07:13, 1 October 2010 (UTC)
replies: text: Where? I don't see "multinormal" here, except in the paragraph immediately above. Melcombe (talk) 08:37, 1 October 2010 (UTC)
replies: text: Oops... You are right. Sorry. It is "multinomial", not "multinormal". But still, the article is rather unclear. Is "categorical distribution" exactly the same as a distribution on a finite set? Or is the finite set supposed to be a product set, that is, the set of finite sequences ("vectors") of something? Boris Tsirelson (talk) 08:58, 1 October 2010 (UTC)
replies: text: Yes, it's just a general distribution on a finite set.  The intro was horribly, horribly written, as is the case with so many of the statistics articles in Wikipedia; it should be better now. (As an example of bad writing, currently the first paragraph of normal distribution says "In probability theory and statistics, the normal distribution, or Gaussian distribution, is an absolutely continuous probability distribution whose cumulants of all orders above two are zero." How in the hell is this a remotely useful intro?) Benwing (talk) 05:00, 2 October 2010 (UTC)
thread_title:  Another multinormal? 

message: Currently the infobox gives info on the cdf, mean, median, variance, and generating functions. But since the assignment of the values 1, 2, ... to the categories is totally arbitrary, there is no meaningful ordering of the variables much less any meaningful interpretation of the assigned values. So none of these infobox entries is valid; the only entries that are valid are the parameters, support, pmf, and mode. If I hear no objection I will delete the indicated invalid parts. Loraof (talk) 19:54, 26 June 2017 (UTC)
replies: text: Furthermore, the infobox gives the mean, variance, and generating functions not for the quantized categorical distribution but for the Iverson bracket, meaning that instead of treating one of the potential outcomes as, say, 3, it treats each outcome as a 0-1 variable, so we have k distributions instead of just one. This is not information about the categorical distribution and should not be in the infobox. Loraof (talk) 14:59, 27 June 2017 (UTC)
thread_title:  Invalid items in infobox 

message: As far as I know the only independant appearence of this topic is in the mentioned source, which is not an expert on probability theory. In fact is what is called a categorical distribution just a special case of the multinomial for only one draw. Madyno (talk) 15:50, 2 August 2022 (UTC)
thread_title:  Reference