The method of moments is a very simple idea. Suppose that we observe from a distribution , where is the vector of parameter which may be *d* dimensional. The idea of this method is to match the empirical moments estimated from data with theoretical moments calculated using the distribution .

Obviously, the theoretical moments will need to exist, and one needs a minimum of *d* moments to obtain *d* equations to be able to estimate all the components of the parameter vector . An example of a distribution for which this method does not work is the Cauchy distribution since it has infinite theoretical moments.

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