Method of moments (statistics)

In statistics, the method of moments is a method of estimation of population parameters.
Method.
Suppose that the problem is to estimate formula_1 unknown parameters formula_2 describing the distribution formula_3 of the random variable formula_4. Suppose the first formula_1 moments of the true distribution (the "population moments") can be expressed as functions of the formula_6s:
Suppose a sample of size formula_8 is drawn, and it leads to the values formula_9. For formula_10, let 
be the "j"-th sample moment, an estimate of formula_12. The method of moments estimator for formula_13 denoted by formula_14 is defined as the solution (if there is one) to the equations: 
Reasons to use it.
The method of moments is simple and gets consistent estimators (under very weak assumptions). However, these estimators are often biased.