Talk:Dirichlet distribution

From Wikipedia, the free encyclopedia

Mathematics Portal

This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.

Mathematics rating:

Start Class

Mid Priority

Field: Probability and statistics

Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments.
Please add to or update the comments to suggest improvements to the article.
Needs references. Geometry guy 15:56, 10 June 2007 (UTC)

Should that be a Dirac delta, not a Kronecker delta? If it were Kronecker, then distribution would be everywhere finite, but nonzero only on a set of measure zero.

According to David J.C. MacKay and Linda C. Bauman Peto "A Hierarchical Dirichlet Language Model" it should be a Dirac delta function.

It is clearly a Dirac delta since it has to be defined over real numbers, and not integers.

[edit] Question regarding chained Dirichlet distributions

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)

[edit] Dummy questions

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)

I think, the sum which is 1 in the second paragraph should sum over all Alphas not over all x. Munibert 16:29, 15 March 2007 (UTC) Am I right or wrong?

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)

Can someone please explain what this distribution reflects? For the normal distribution, the authors go into lengths to cite examples what kinds of everyday values follow a normal distribution... cannot someone add an example like this for the dirichlet distribution? --Maximilianh 05:18, 4 June 2006 (UTC)

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)

Why is this distribution called a continuous distribution, when the cumulative distribution is not continuous? It should be neither continuous nor discrete. Albmont 18:58, 16 October 2006 (UTC)

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)

What does this mean? "The characteristic function χ ensures that the density is zero unless..." The page doesn't define a characteristic function. I'm going to change it to say that the sum over the x's is defined as 1, which is what I think it means... MisterSheik 20:05, 26 February 2007 (UTC)

I just stumbled over the very first figure in this article, showing the probability densities. 1. I think it would be useful to explain $α$ a bit more, like: $\alpha=(\alpha_x, \alpha_y, \alpha_z)=(6,2,2), (3,7,5), \ldots$ 2. I think the last two choices for $α$ got twisted; from the pictures the order should be $(2,3,4),(6,2,6)$ rather t $(6,2,6),(2,3,4)$ (at least if my clock moves according to the standard). —Preceding unsigned comment added by 87.113.20.9 (talk) 10:25, 25 January 2008 (UTC)

Last sentence says The variance around this mean varies inversely with α₀. Seems contradictory to : $\mathrm{Var}[X_i] = \frac{\alpha_i (\alpha_0-\alpha_i)}{\alpha_0^2 (\alpha_0+1)}$ . —Preceding unsigned comment added by 217.133.67.206 (talk) 15:05, 4 April 2008 (UTC)