Talk:Independent and identically distributed random variables
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In the "Generalizations" section, I am missing pairwise/k-wise independence mentioned (i.e. any pair/k-tuple in the sequence is independent, but larger subsets are not necessarily independent). Pairwise/k-wise independence is used in theoretical CS. --David Pal
Link to German Version
Looks like this would be the corresponding article in German Wikipedia
It links to:
There in the text you will find "i.i.d. (für independent and identically distributed)".
I am leaving this in the 'talk' page, in case my edit is sloppy and removed-- but I aim to include some important information I learned today about IUDs and female anatomy, which is very mundane, but little known information: 'uterine malformation' is a common occurrence in women. We are not informed of its likelihood purchasing a potentially expensive IUD.
It is estimated that 7% of women, according to wiki's Interuterine Malformation page, (other sources will report as high as one fifth of womem) is born with this condition.
When a uterus has an unusual shape, it cannot always accommodate an IUD in such a way that it is effective. The uterus may be cleft in half, making 2 uteri. Some women have 2 cervixes, or 2 vaginas.
These unusually common malformations (they are here https://en.wikipedia.org/wiki/Uterine_malformation), absolutely must have a link in this article, for people considering the use and potential functionality of an interuterine device.
A uterus with 2 chambers cannot be sufficiently protected from pregnancy with this contraception in the same way a woman with a normal uterus would, and I had never heard of the prevalence of this condition until today. its taken me 25 years to hear about it. It would be better to consumers if this practical information were more common knowledge,
Any consumer of this product unaware of the link, or the structure of their uterus runs a risk of pregnancy and wasting money.
In short, an informational relationship between the IUD page and the Uterine Malformation page would be a very helpful one. https://en.wikipedia.org/wiki/Uterine_malformation
Not soure how to add the langunage link in this page. — Preceding unsigned comment added by 95.208.167.145 (talk) 17:59, 8 May 2013 (UTC)
How about explaining 'independent but not identically distributed' variables? The meaning of independence and identical distribution, and its implication, should be more explicitly stated... in my opinion, that is. — Preceding unsigned comment added by 182.216.110.134 (talk) 04:52, 21 April 2016 (UTC)
IID consistency
After noticing the lead contained a mixture of both, I made a bold edit in favour of IID which I personally find less visually distracting than the dots in i.i.d. when the term is dropped into every second sentence. However, IID is not exactly beautiful, either, and typographically I would advise IID (i.e. {{sc2|IID}}), except that this is apparently discouraged in the MOS. This article might the one where it makes sense to go against the recommended-style grain, though it's above my pay grade to decide this unilaterally. — MaxEnt 00:57, 20 March 2017 (UTC)
- Your decision has my support, since dropping the full stops (or periods) from initialisms (and other abbreviations) has been throughout the last century or more, and continues to be, a productive process in English writing, as seen in the following usages, for example:
- International Business Machines → I.B.M. → IBM
- Company → Co. → Co
- Proprietary Limited → Pty. Ltd. → Pty Ltd
- et caetera (or et cetera) → etc. → etc
- As an aside, it seems to me a pity that the equivalent, but more euphonious, IDI – standing, obviously, for Identically Distributed and Independent – did not become the standard usage, as advocated by one of my lecturers in my youth. Oh well, c'est la guerre! yoyo (talk) 15:16, 19 November 2017 (UTC)
Usage of the phrase "random variables"
"An element in the sequence is independent of the random variables that came before it" ... "the probability distribution for the nth random variable is a function of the previous random variable in the sequence"
Shouldn't we use "element" or value instead of the phrase "random variables"in those sentences? Each value in the sequence is a random variable? Or the whole sequence is represented by a random variable? Sarmadys (talk) 05:46, 12 June 2017 (UTC)
- There's a bigger problem. The lead asserts this:
Note that IID refers to sequences of random variables. "Independent and identically distributed" implies an element in the sequence is independent of the random variables that came before it.
- The reference given supporting the definition of IID rvv is to Professor Aaron Clauset's notes on a probability primer for a complex systems modelling course. They're fine for their stated purpose, but don't pretend to be a rigorous mathematical treatment of the underlying probability theory. Even so, nowhere in that ref is there a mention of a sequence of random variables. What is there is an indexed set of observations, the index values i coming from an initial segment of positive integers [math]1, 2, … n[/math]. And that's all that IID talks about - a set of observations, each assumed to come from the same underlying probability distribution.
- This is the first time I've seen IID defined in terms of a sequence of rvv. Arguably, one (informal) usage of the term sequence in maths is as a set indexed by the first so many (non-zero) "counting numbers", as above. But the usual connotations of the word sequence include that the ordering of the elements is essential - that's what most general readers would expect and possibly infer. However, I assert that the order of the elements is not of the essence in defining IID rvv! To say that it is essential, we need a better source. yoyo (talk) 23:29, 19 November 2017 (UTC)