Talk:Degenerate distribution

message: I am not convinced by the argument above, and I think the article needs more discussion about degenerate distributions and point probabilities from a discrete and continuous perspective.  I could easily imagine somebody saying that a die (dice) with a probability mass function 
:Prob(X=x)={1 \over 6} \text{ for }x=1,2,3,4,5,6
could be written using Kronecker deltas as 
:Prob(X=n)={\delta_{x1} + \delta_{x2} + \delta_{x3} + \delta_{x4} + \delta_{x5} + \delta_{x6} \over 6} 
so in a sense might be considered as if it had a density
:p(x)={\delta(x-1)+ \delta(x-2)+ \delta(x-3)+ \delta(x-4)+ \delta(x-5)+ \delta(x-6) \over 6} 
to the extent that any Dirac delta densities are meaningful. They could then extend this to the case where the die was fixed to produce a single result with probability 1. --Rumping (talk) 17:32, 3 March 2008 (UTC)
replies: text: Yes, I believe that is entirely correct within the context of the theory of distributions. 207.62.177.230 (talk) 19:14, 7 April 2008 (UTC)
thread_title: Continuous v. discrete

message: Why are the skewness and excess kurtosis given as zero?  For skewness, the 3rd central moment is zero and the variance is zero.  So the skewness seems to be undefined.  And since the 4th central moment is also zero, the kurtosis seems to be undefined.  While intuitively it makes sense to define the skewness as zero, I am not sure the same can be said for the excess kurtosis, which reduces to an undefined amount minus 3. Rlendog (talk) 21:05, 18 August 2009 (UTC)
replies: text: The change to "undefined" just made seems best. An approach arguing via families of distribution that can be made to approach a degenerate distribution profuces different answers for different families, for example the uniform and normal distributions would both give a skewness of zero but different kurtoses, while using a Gamma distribution concentrating towards zero using the scale parameter would give skewness and kurtosis depending on the shape parameter assumed. Melcombe (talk) 10:10, 18 December 2009 (UTC)
thread_title: Skewness & excess kurtosis

message: IMHO this merge occurred in an incorrect direction. It would be better to explain degenerate distribution as the distribution of the (only possible) constant random variable with a given value, rather that redirect the title constant random variable to an article about its distribution. Incnis Mrsi (talk) 09:31, 8 March 2012 (UTC)
thread_title:  "Degenerate distribution" or "constant random variable"? 

message: This article is accurate only for univariate (discrete or continuous) probability distributions.  The title should be changed as indicated (I do not know how to make such an edit, or I would have done so.)  The article is only correct for the univariate case; however, "distribution" (or "probability distribution") is not limited to that case (e.g., see Wikipedia article "Probability distribution"). A degenerate distribution in the general case (i.e., as per the current title) is a distribution in a space (discrete or continuous) with support only on a space of lower dimension.  David Shalloway (talk) 13:07, 26 May 2017 (UTC)
replies: text: Thanks for the suggestion. I've expanded the article so that it accurately reflects the title "Degenerate distribution", by clarifying the lead and adding a section on higher dimensions. Loraof (talk) 18:07, 20 August 2017 (UTC)
thread_title:  Inaccurate title; change to "Degenerate distribution (univariate)" 

message: Our two references give different definitions. I don't know which is more accepted. I have modified the first couple sentences to reflect this. But if the first reference is the accepted definition then we should change the whole article! Eric Kvaalen (talk) 13:57, 8 August 2021 (UTC)
thread_title: Maybe almost the whole article is inaccurate