# Method of moments (probability theory)

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*See method of moments (statistics) for an account of a method of parameter estimation.*

In probability theory, the **method of moments** is a way of proving convergence in distribution by proving convergence of a sequence of moment sequences. Suppose *X* is a random variable and that all of the moments

exist. Further suppose the probability distribution of *X* is completely determined by its moments, i.e., there is no other probability distribution with the same sequence of moments
(cf. the problem of moments). If

for all values of *k*, then the sequence {*X*_{n}} converges to *X* in distribution.

The method of moments is especially useful for proving limits theorems for random matrices with independent entries, such as Wigner's semi-circle law.

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