Nonlinear Transformations of Random Processes by Ralph Deutsch

Author:Ralph Deutsch
Language: eng
Format: epub
Publisher: Dover Publications, Inc.
Published: 2017-11-22T05:00:00+00:00

The process of applying the Gram-Charlier expansion can be summarized in five steps.

(i)Compute the moments of the output distribution.

(ii)Find the central moments from Eq. (6-15).

(iii)Obtain the corresponding standard central moments from Eq. (6-12).

(iv)Compute the series coefficients using Eq. (6-13).

(v)Write the series representation of f(u) using Eq. (6-9).

Careful investigation of the convergence of the Gram-Charlier series has shown that if only a few terms are computed, the best grouping of terms in Eq. (6-9) is not that associated with taking terms in their natural order. Various regrouped series have been proposed, but the Edgeworth series are generally employed in most applications. The grouping proposed by Edgeworth is

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