Cramér's Theorem ·
The Rate Function
un
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.com · P(S̄ₙ ≈ x) ≍ e
−nI(x)
· large deviations of the sample mean
Samples n
1
Rate I(x)
0.00
phase
—
Sample-mean histogram
Rate function I(x)
Tilt / Legendre λ(k)
True mean μ · I(μ)=0
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.com · Cramér's Theorem and the Rate Function: Large Deviations of Sample Means