Talk:Independent and identically distributed random variables: Difference between revisions
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→IID consistency: - support the usage "IID" |
→Usage of the phrase "random variables": - IID rvv are NOT an (ordered) sequence |
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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? [[User:Sarmadys|Sarmadys]] ([[User talk:Sarmadys|talk]]) 05:46, 12 June 2017 (UTC)
:There's a bigger problem. The lead asserts this:
<blockquote>
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.
</blockquote>
: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. [[User:Yahya Abdal-Aziz|yoyo]] ([[User talk:Yahya Abdal-Aziz|talk]]) 23:29, 19 November 2017 (UTC)
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