Talk:Cumulative distribution function
This page had a redirect from distribution function, which I've now made into its own article describing a related but distinct concept in physics. I'll try to modify the pages pointing here through that redirect so that the net change in the wikipedia is minimal.SMesser 16:12, 24 Feb 2005 (UTC)
Cumulative density function
I originally created the redirect cumulative density function in March to point to this article. Why? A simple google test for cumulative density function shows 41,000 hits while cumulative distribution function shows 327,000 hits. Michael Hardy's contention is that "cumulative density" is patent nonsense (see deletion log) and a redirect shouldn't exist.
Regardless of the correctness of "cumulative density", there still is a significant usage of it in reference to this article and its content. "Cumulative density function" is even used in a doctoral thesis. Hardly patent nonsense.
Even if "cumulative density function" is incorrect, someone still may look for it, find nothing, and create an article paralleling this article. If you don't buy the "it's not patent nonsense, or even just nonsense" then I invoke (from WP:R#When should we delete a redirect?) that it increases accidental linking and therefore should not be deleted.
Michael, if you have a problem with the correctness of "cumulative density" then by all means add a section here or change the redirect to an article and explain it there. Either way, cumulative density function needs to be a valid link. Cburnett 14:42, 14 December 2005 (UTC)
=== How is this a debate?
The word "cumulative distribution function" is used in many elementary books. It is a pretty stupid term, but we are stuck with it. The best we can do is acknoledge that the term is out there, that is should simply be "distribution function" and that its definition MUST be with <= or elase many tables, software routines, etc will be incorrectly used.
Doesn't make sense
"Note that in the definition above, the "less or equal" sign, '≤' could be replaced with "strictly less" '<'. This would yield a different function, but either of the two functions can be readily derived from the other. The only thing to remember is to stick to either definition as mixing them will lead to incorrect results. In English-speaking countries the convention that uses the weak inequality (≤) rather than the strict inequality (<) is nearly always used."
Surely it doesn't matter at all! Since the probability of one single value is 0, hence the two interval boundaries can be included or excluded.
- If you're only interested in integrals. Shinobu 22:50, 7 June 2006 (UTC)
- The convention in the entire world is to use '≤' and it matters HUGELY for the binomial, poisson, negative binomial, etc. To use anything else and to rely upon the formulas in any text would lead substantial errors, say when one is using a table of the binomial distribution. Jmsteele 01:18, 21 October 2006 (UTC)
- I'm not sure about that. The definition: F(x) = P(X <= x)
- Because P(X <= x) = P(X < x) + P(X = x), F(x) = P(X < x) + P(X = x)
- Now for normal functions (the kind of functions you mention) P(X = x) = 0.
- Of course, there are things like deltafunctions, but that's not what you're talking about. Shinobu 16:27, 27 October 2006 (UTC)
F(x) vs Phi(x)
I completely disagree with "It is conventional to use a capital F for a cumulative distribution function, in contrast to the lower-case f used for probability density functions and probability mass functions." From all the literature I have read, is the cumulative distribution function and is used for probability density/mass functions. Where's the reference to make such a bold claim that F and f are convention? See the probit article which uses for the inverse to cdf. -- Thoreaulylazy 19:13, 3 October 2006 (UTC)
- There is no such convention - you can pick any symbol you like, of course. It is common practice to use the capital for the cdf, because it's the primitive of the df. I've seen phi in quantum mechanical books, but I've also seen f and rho. Shinobu 22:58, 3 October 2006 (UTC)