Lecture 3: Cramer's theorem
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چکیده
We have established in the previous lecture that under some assumptions on the Moment Generating Function (MGF) M(θ), an i.i.d. sequence of random variables Xi, 1 ≤ i ≤ n with mean μ satisfies P(Sn ≥ a) ≤ exp(−nI(a)), ; −1 where Sn = n Xi, and I(a) £ supθ(θa− log M(θ)) is the Legendre 1≤i≤n transform. The function I(a) is also commonly called the rate function in the theory of Large Deviations. The bound implies
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تاریخ انتشار 2013