Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications

9.19 METHOD OF MOMENTS

The method of moments (MoM) is a parameter-estimation technique that equates sample moments, which depend on outcomes, and ensemble moments, which depend on parameters of the distribution. From Chapter 5, the mth raw moment of random variable X is

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Let the corresponding sample moment be

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For any pdf fX(x), we know that and , where are the ensemble mean and variance of the distribution. For MoM estimation, the following equations are solved for and :

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which yields the following estimates:

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where S2 is the sample variance. For a Gaussian ...