Method of Moments (MoM)

See also: Fitting distributions to data, Fitting in ModelRisk, Analyzing and using data, Maximum Likelihood Estimates (MLEs)

The method of moments, first discussed in Pearson (1895), can be used to obtain reasonable approximations to the MLEs. The method of moments matches the equations for the mean and central moments, as necessary, of a fitted distribution to the mean and central moments of the data set. As many moments are used as there are distribution parameters. Moments are used from the lowest order first (mean, then variance, then skewness, then kurtosis) because the lower moments are the most stable.

MoM has some disadvantages: it is not available for a number of distributions, and it lacks the desirable optimality properties of maximum likelihood and least squares estimators.

The primary use of MoM is to establish starting values for MLE techniques where one is using some optimising algorithm to find the MLEs.

Examples (click to expand):

Beta distribution

Gamma distribution

 

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