Talk:Large deviations theory

Statistics Mid‑importance

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Mathematics Mid‑priority

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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)[reply]

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)[reply]

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 $N$ .^{[dubious – discuss]}

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)[reply]

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)[reply]

Approximately normally distributed

The phrase "Moreover, by the central limit theorem, we know that M_N 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#Central limit theorem: "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)[reply]