# Talk:Probability distribution function

## Which is it?

(Note: This discussion has progressed, and many of the statement in this section no longer apply.)

This page currently redirects to probability density function, but isn't probability distribution function an alternative name for cumulative distribution function (CDF)? Also I believe that there is some convention that says pdf (lower case) stands for probability density function while PDF (upper case) stands for probability distribution function. Should this be mentioned in the relevant articles? Egriffin 12:21, 1 June 2007 (UTC)

You may well be right. I was responsible for the change in redirect, if you know better, change it back. Perhaps the text i was using was incorrect, or not consistent with general notation. And if you are sufficiently knowledgeable, please add in the difference, as it was sufficiently unclear to me for me to attempt to change the redirect. Thanks User A1 08:18, 4 June 2007 (UTC)

Indeed, there is a difference between the distribution and density functions. The distribution function is typically notated in upper case (PDF) and the density function in lower case (pdf). The page on cumulative distribution function seems to describe the PDF, and this page should redirect there rather than to probability density function. Any good text on random variables should point out the difference, in particular a well known text by A. Papoulis, Probability, Random Variables and Stochastic Processes. Section 4-2 of the fourth edition is especially illustrative. --150.135.23.29 22:30, 13 August 2007 (UTC)

The discrepancy is commented on in the article PDF (disambiguation). --Egriffin 10:30, 6 November 2007 (UTC)

## Which is it? - Mark II

The relevant pages are: PDF (disambiguation); probability distribution function; probability density function; cumulative distribution function; various versions of "pdf" (e.g. pdf, PDF, p.d.f., P.D.F., etc.); their "talk" pages (i.e. discussion pages); etc.

The problem is, the "experts" are divided on what a "probability distribution function" is, and WP is not designed to handle such a situation. Pdfpdf 12:32, 7 November 2007 (UTC)

Shall I add the following paragraph to the article? It's a bit convoluted. Do you agree with it?
Authors who consider a probability distribution function to be a cumulative distribution function often use the initialisms pdf or p.d.f. (lower case) to mean the probability density function and PDF and P.D.F. (upper case) to mean the cumulative distribution function. Authors who consider a probability distribution function to be a probability density function often use the initialism PDF to mean the probability density function and CDF to mean the cumulative distribution function.
Egriffin (talk) 23:02, 17 November 2007 (UTC)
For easy reference purposes, I'll reproduce and reformat some stuff:
Depending upon which text you consult, a probability distribution function is either:
Authors who consider a probability distribution function to be a cumulative distribution function often use the initialisms
pdf and/or p.d.f. (lower case) to mean the probability density function and (**C**)
PDF and/or P.D.F. (upper case) to mean the cumulative distribution function.
Authors who consider a probability distribution function to be a probability density function often use the initialism
PDF to mean the probability density function and (**D**)
CDF to mean the cumulative distribution function.
Do they! Oh dear, that adds confusion to the matter, doesn't it!!! (As if it wasn't confusing enough already! This is going over the top, but:
B C D
A c c x
B c x
C x
Key: c = consistent, x = inconsistent )
In other words, the statement: "Authors who consider a probability distribution function to be a probability density function often use the initialism PDF to mean the probability density function", even though true, is inconsistent with the other statements. (I know it's only annecdotal, but I used to think a probability distribution function and a probability density function were the same thing, and hence, as far as I was concerned, there was no difference between pdf and PDF.)
You asked: :Shall I add the following paragraph to the article? It's a bit convoluted. Do you agree with it?
I guess my answer is: Yes, I think "we" need to flesh out the article regardinging the "dual use" of the term, and your addition is useful, and Yes, I sort-of agree with it, but, you will also need to explain/discuss/mention/address the inconsistency.
By-the-way: What do this last group (i.e. Authors who consider a probability distribution function to be a probability density function ) have to say about "pdf"?
Pdfpdf (talk) 02:53, 18 November 2007 (UTC)
I see why you think statement D is inconsistent with A, B and C. But it's not really because PDF in statement D still stands for probability distribution function, it just denotes probability density function in that case.
Anyway, I'm not sure of my facts. I browsed through a few books on probability in the library today and I couldn't find a single use of the terms pdf, PDF or CDF. I do remember these terms were used in the statistics modules of A-level maths.
Perhaps it might be worth mentioning that probability density functions are usually lower case letters, while cumulative distribution functions are usually upper case letters.
Egriffin (talk) 00:41, 19 November 2007 (UTC)
Perhaps.
I think neither of us are sufficiently confident that there isn't some third situation lurking out there ready to confuse the issue further!
I think it's probably time to start examining and quoting specific references. And if they're not consistent with each other, then we need to address the inconsistencies. But in the meantime, do whatever you feel comfortable that you can back up.
As an aside, (even though I wrote it), when I reread: Depending upon which text you consult ... , I think it sounds pretty "wishy-washy". "In the fullness of time", I will tighten it up. (Unless "someone else" does it first!) Cheers, Pdfpdf (talk) 10:28, 19 November 2007 (UTC)

## Should redirect to Probability distribution

Differentiating between Probability distribution and Probability distribution function is artificial. For some authors the latter is a specification of the former, while other authors use the terms interchangeably. In my view the simplest and clearest solution is to make Probability distribution function redirect to Probability distribution where the new section Probability distribution#Terminology now explains that some terms are ambiguous. -- Marie Poise (talk) 14:20, 6 May 2011 (UTC)

Thanks. FYI, it's 06:36, March 23, 2014 (NTT) (Purge) where I am, so I apologise, but I'm not going to give you the answer you deserve right now. You make some good points and ask some good questions which deserve good answers. But I'm afraid it will be a little while before I compose and provide them. Cheers, Pdfpdf (talk) 14:42, 6 May 2011 (UTC)
Good heavens! Over 3 years since I wrote the above! How time flies!! Pdfpdf (talk) 14:46, 6 May 2011 (UTC)