= Cramér's theorem
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{wiki=Cramér's_theorem_(large_deviations)}
= Cramér theorem
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{synonym}
For <independent and identically distributed random variables> with a <moment-generating function> finite on an open <interval> containing zero, the <sample mean>[empirical mean] satisfies a <large deviation principle> with <Rate function> given by the <Legendre transform of a cumulant-generating function>. The exponential-moment hypothesis is part of this theorem; mere integrability does not guarantee this full large-deviation principle.
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