Talk:Large deviations theory

Proposal: merge with Extreme Value Theory
This article is basically a reproduction of the information in the extreme value theory article, although this article does mention some connections with physics that are new to the EVT article. So, I propose that we merge this article with that one.

Paresnah 20:25, 13 March 2007 (UTC)

Response: the two topics are different
Extreme Value Theory studies the distribution of the single largest (or smallest) value encountered in a series of trials, while Large Deviations Theory essentially studies the asymptotics of the tail distribution of the *average* of such trials. These are not the same subject. The theorems are different, textbooks on either do not discuss the other, etc. 63.3.2.1 (talk) 23:58, 15 February 2009 (UTC)

Sharp?
''This bound is rather sharp, in the sense  that $$ I(x) $$ cannot be replaced with a larger number which would yield a strict inequality for all positive $$ N $$. ''

This statement is not precise. It is a function, not a number, and it makes a big different because you can always sneak in a slightly "larger" function. Well, nearly always, so you have to say what you mean by "larger": for example, say "grows faster" which would be defined to mean that the new function J(x) is related to the old by J(x)/I(x) goes to infinity as x goes to infinity. This is false though. If one merely wants to add a small number to I(x), say so, but this is rather trivial and not really worth stating. 178.38.151.183 (talk) 16:29, 29 November 2014 (UTC)


 * I think, it is about the number $$ I(x) $$, not about the function $$ I $$ (that is, $$ x \mapsto I(x) $$). "not really worth stating"? Maybe; I do not know. Boris Tsirelson (talk) 17:13, 29 November 2014 (UTC)

Approximately normally distributed
The phrase "Moreover, by the central limit theorem, we know that MN is approximately normally distributed for large N" is correct, and does not mean that this distribution converges to N(0,1); see for instance Normal distribution: "the sum of many random variables will have an approximately normal distribution"; also, "the binomial distribution is approximately normal"; etc. User:Jmbarrios understands correctly what happens, but rejects the convenient and widely used terminology. Boris Tsirelson (talk) 17:45, 30 September 2016 (UTC)