# Talk:Probability distribution

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 Definition:  Function of a discrete random variable yielding the probability that the variable will have a given value. [d] [e]
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## Name of article

This article seems to be a list of probability istributions, and not an article about probability distributions per se. Certainly, having such a list seems like a good thing, but I wonder if the article shouldn't be renamed. Of course, we would also want to have an article on probability distributions. Greg Woodhouse 09:53, 25 June 2007 (CDT)

## Probability vs. probability distribution

You may want to rearrange/rephrase the opening material a bit, but the article failed to distinguish between probability and probability distributions. They are not the same thing: probability distributions are functions that can be integrated (or summed) to obtain probability. Greg Woodhouse 10:32, 25 June 2007 (CDT)

## Purpose of article

1. Give an average reader a good and quick grasp of the basic idea of a probability distribution and what it's good for.
2. Give the more savvy audience a quickly grasped intro and access points into deeper ideas.
3. Provide links for further in-depth study.
4. Present the ideas in a way that doesn't scare off math-phobes. That's why I want to keep equations out until the end of the article, or keep them in separate sections, labeled "formal definitions" or similar.

Ragnar Schroder 19:17, 25 June 2007 (CDT)

## Duplicated content

I duplicated parts of this article to create the 2 new articles: continuous probability distribution and discrete probability distribution.

The duplicated contents should be removed an replaced by a summary and a link.

There's an inconsistency too, since the article [[continuous probability distribution] does not yet exist. Also some articles link to unwritten (and superfluous) articles with the same titles in plural form.

Ragnar Schroder 06:12, 26 June 2007 (CDT)

## Bayesian bias

This version came out highly biased towards the Probability as extended classical logic viewpoint. I think much of it should be moved either into the as yet unwritten probability theory article, or into a specialized one dealing with probability logic.

Ragnar Schroder 08:58, 27 June 2007 (CDT)

I think this should be an "introductory" article. Concepts unfamiliar to nonmathematicians should be reserved for an "advanced" article, or at least tucked away into an "advanced" section of this article.

Such "advanced" concepts clearly include Lebesgue integrals and measure theory - ordinary Riemann sums are known to many undergraduates, Lebesgue theory is known only to a few.

Ragnar Schroder 05:26, 15 November 2007 (CST)

It's a bit tricky to strike the right balance, but if it will be done this way then it should be clearly emphasized which part is "introductory" (less general) and which part is more "advanced" (more general, but perhaps not the most general). This article itself needs some restructuring, in a slightly earlier version there was "A gentle introduction" and then "A formal introduction", yet the later was not much more advanced then the former, so the splitting into two parts did not seem to have any purpose -- moreover "density" and "distribution" was treated synonymously which is confusing if not misleading. Perhaps the "A gentle introduction" can include the most basic definitions and a "A formal introduction" the more general measure-theoretic one. An introductory article does not mean it should have to be geared mostly towards the laymen, but rather have some balance in the presentation. In particular, those who are only acquainted with the introductory stuff but come across the article will see that there's more to it and may be enticed to find out just a bit more (well, that's quite often my experience). Hendra 06:03, 15 November 2007 (CST)
Agreed like 100%.
When we choose the Lebesgue treatment I figure there's no need to differentiate between discrete and continuous distributions. And the pdf kind of becomes unnecessay, since it doesn't even have to exist. (The current version of the article is a little inconsistent here).
But I think it's essential for newbies to have the focus on the pdf rather than the cdf, for pedagogical reasons.
All in all, it's probably best to have a clear separation between the advanced and the undergraduate approach, and stick with the latter in the introductory sections.
Ragnar Schroder 08:32, 15 November 2007 (CST)
It's not true that it will not be necessary to treat PDFs separately. Distributions which have a density (those that are absolutely continuous w.r.t to the Lebesque measure as stated in the article) are an important class of distributions -- they are in some sense "regular"-- which are significant in applications and are in general more workable specifically due to the existence of the density (e.g., the Fokker-Planck equation for the time evolution of the distibution of a Gaussian Markov process). General measures that do not have a density are more challenging. So, I think it's good that the article does mention PDFs and it should remain that way -- it just needs some restructuring and a bit more clarity. Hendra 20:07, 15 November 2007 (CST)