Method of moments (statistics)

In statistics, the method of moments is a method of estimation of population parameters. One starts with deriving equations that relate the population moments (i.e., the expected values of powers of the random variable under consideration) to the parameters of interest. Then a sample is drawn and the population moments are estimated from the sample. The equations are then solved for the parameters of interest, using the sample moments in place of the (unknown) population moments. This results in estimates of those parameters. The method of moments was introduced by Karl Pearson in 1894.

Suppose that the problem is to estimate ${\displaystyle k}$ unknown parameters ${\displaystyle \theta _{1},\theta _{2},\dots ,\theta _{k}}$ characterizing the distribution ${\displaystyle f_{W}(w;\theta )}$ of the random variable ${\displaystyle W}$. Suppose the first ${\displaystyle k}$ moments of the true distribution (the "population moments") can be expressed as functions of the ${\displaystyle \theta }$s:

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