Second factorial moment

For comparison, we have calculated the statistical parameter n (second order factorial moment) for the PDF shown in Fig. 2 and Fig. 3. The scattering geometries are the same but the number of samples is higher (10 series of 10 positions). The results are shown in Fig. 4 and Fig. 5. In general, n is noisier and its relative errors are much higher than those of P(/cross = 0). For both scattering systems, the second moment of the co-polarized scattered intensity,... 

Exercise. It is also possible to deduce from (6.4) equations for the second moments. The most condensed way of expressing the result is in terms of the factorial cumulants (1.3.13) ... 

In the same way one finds by laborious algebra an equation for the second moments , which simplifies when expressed in the factorial cumulants... 

The factorial methods in this chapter are also called second-order transformations, because only two moments, mean and covariance, are needed to describe the Gaussian distribution of the variables. Other second-order transformations are FA, independent component analysis (ICA), and multivariate curve resolution (MCR). 

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