Cramér's Theorem

Cramér's theorem may also refer to another result of the same mathematician concerning the partial sums of a sequence of independent, identically distributed random variables, say X1, X2, X3, …. It is well known, by the law of large numbers, that in this case the sequence

converges in probability to the mean of the probability distribution of Xk. Cramér's theorem in this sense states that the probabilities of "large deviations" away from the mean in this sequence decay exponentially with the rate given by the Cramér function, which is the Legendre transform of the cumulant-generating function of Xk.

Read more about Cramér's TheoremSlutsky's Theorem

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Famous quotes containing the word theorem:

    To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.
    Albert Camus (1913–1960)