Talk:Geometric distribution

message: Shouldn't the success probability, p, be defined on the open interval (0,1)?
For p=1 few quantities are not defined, such as median, skewness or excess kurtosis.
fuzzy (talk) 08:57, 14 September 2015 (UTC)
thread_title: Definition of p

message: E(X)= \sum_{k=1}^{\infty} kpq^{k-1} = \sum_{k=1}^{\infty} k(1-q)q^{k-1} = 
 \sum_{k=1}^{\infty} kq^{k-1} - \sum_{k=1}^{\infty} kq^{k} = \sum_{k=0}^{\infty} q^{k} = \frac{1}{1-q} = \frac{1}{p} 
 –Gyorgy 11:40, Feb 02 2012 (EST)
:This is wrong: \sum_{k=1}^{\infty} kpq^{k-1} should read \sum_{k=1}^{\infty} kpq^k.131.111.184.8 (talk) 15:43, 24 May 2012 (UTC)
replies: text: Horrific idiocy on my part - it's actually correct; \sum_{k=1}^{\infty} kpq^k would be true if referring to Y.131.111.184.8 (talk) 15:49, 24 May 2012 (UTC)
thread_title: The simple proof

message: :(1 − p)/p2.
Does anyone else see a square in place of the minus sign?  –Matt 10:48, 19 Jun 2004 (UTC)
thread_title:  squares 

message: Geometric distribution is discrete, therefore it is determined by the probability mass function, not density. In MATLAB one should use stem to plot it. Consequently, the cdf of the geometric distribution is a piecewise constant right-continuous function, not piecewise linear. I may redo graphs myself next week. If someone else can do it sooner, that'd be great. PBH 17:01, 18 May 2006 (UTC)
replies: text: I'm not really that crazy about them, but unfortunately my graphic capabilities stop around here. If you can do something better, by all means replace them AdamSmithee 19:04, 18 May 2006 (UTC)
thread_title:  Graphs need to be redone 

message: This family of distributions is parameterized by just one parameter, p.  The argument n to the probability mass function is not such a parameter, i.e., we don't get a different distribution for each different value of n.  I deleted the "n" from "parameters" in the table. Michael Hardy 00:54, 31 May 2006 (UTC)
thread_title: only ONE parameter

message: this might be somewhat useful although it does not belong in the article. The process involves massaging the sum into the geometric series so it can be reduced furthur.
q=1-p
M_X(s)=E(e^{sX})=\sum_{k=1}^\infty{pq^{k-1}e^{sk}}=\sum_{m=0}^\infty{pq^{m}e^{s(m+1)}}=pe^s\sum_{m=0}^\infty{(qe^s)^m}=\frac{pe^s}{1-qe^s}
Iownatv 09:01, 20 January 2007 (UTC)
thread_title:  derivation of moment generating function 

message: Why the two subscripts in p1 and p0?  Is there a reason not to call them both just p?  It seems as if user:MarkSweep introduced them and uses one when talking about X, the number of trials needed to get one success, and the other when talking about Y, the number of failures before the first success.  But the difference between the two random variables does not correspond to any change in p.  On the contraray, in some contexts it may be important that p does not change. Michael Hardy 02:44, 6 May 2007 (UTC)
replies: text: ... and now I've changed it. Michael Hardy 02:50, 6 May 2007 (UTC)
thread_title:  What are the subscripts for? 

message: The information box is confusing. In some places it shows two versions of the geometric distribution (e.g. support, CDF). In other places it only shows only one version (mean, characteristic function). It needs to be cleaned up. My preference is to show only one version of the distribution. Steve8675309 03:17, 3 August 2007 (UTC)
thread_title: Confusing Info Box

message: Am I wrong or is the expected value / mean of a geometrically distributed random variable 1/p not (1-p)/p?  What's up with that?  —Preceding unsigned comment added by 209.244.152.96 (talk) 19:37, 14 November 2007 (UTC)
replies: text: This article assumes the distribution is over the positive numbers.  You probably learned the mean over the nonnegatives, for which the pmf is (1-p)^k p and the mean thus one less, or 1/p. Calbaer 00:47, 15 November 2007 (UTC)

text: No you guys have it backwards, for non negative numbers the mean is q/p and for positive numbers the mean is 1/p.  This article has the pmf and k defined for positive numbers so the mean should be 1/p.  I really don't feel like posting a proof in here so would someone confirm this for me.  I have the proof though (for both k defined over non-negatives and over positives) so if no one can get this straight I'll post both.  —Preceding unsigned comment added by 209.244.152.96 (talk) 18:45, 20 November 2007 (UTC)
replies: text: Okay - sorry.  I looked quickly at the article and assumed it had the correct of the two forms; the way your question was phrased, I assumed you were merely unaware of the two forms.  If you look above on the talk page, you'll see that there's much debate and confusion about the two forms, and the whole reason the wrong mean was given was the incomplete expansion from one form  to two  and back again.  The combined version was too confusing for one infobox, though it might be a good idea to have it presented with two infoboxes.  However, I'm unaware of article with two infoboxes of the same type, although there are plenty with infoboxes of two types, as discussed at Wikipedia talk:WikiProject Infoboxes#Multiple_infoboxes. Calbaer (talk) 19:30, 20 November 2007 (UTC)
thread_title: Wrong Mean

message: Is there a reason that there is no Fisher's Information in the infobox? Jamesmcmahon0 (talk) 12:30, 11 December 2013 (UTC)
thread_title:  Fisher's Information? 

message: Looking at the current location of examples on this page, it is difficult to understand the examples when the context of the example has not been explained. I think it would be easier to understand if, for example, expected mean and how to calculate it is explained and then an example is shown of that calculation. Per the Wikipedia:Manual of Style/Mathematics, this also states that an introduction should be first and I think this applies to each section within the article (definition and then examples). 
--MLicon (talk) 18:05, 13 November 2019 (UTC)
replies: text: Well, the appropriate policy here is WP:SOFIXIT.  That said, I think the way the example situations are listed along with calculations of each type for each one is kind of weird.  I'm not sure I'm completely following what you're suggesting though with respect to introduction being first, etc.  –Deacon Vorbis (carbon • videos) 18:20, 13 November 2019 (UTC)

text: Agree. This article is pretty confusing, and it also switches between the two different functions rather arbitrarily. ProcrastinatingReader (talk) 10:04, 11 June 2021 (UTC)
thread_title: Arrangement of Article