November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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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
(9.299) 
Let the corresponding sample moment be
(9.300) 
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 
:
(9.301) 
which yields the following estimates:
where S2 is the sample variance. For a Gaussian ...
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