Peak shape models statistical moments

The alternative is the use of a descriptive mathematical model without any relation with the solution of the transport equation. On the analog of the characterization of statistical probability density functions a peak shape f(t) can be characterized by moments, defined by ... 

Modeling of an analytical signal by a mathematical function enables one to obtain parameters, such as statistical moments, to characterize the peak shape of the signal. 

Several of the standard statistical distributions are described by Hahn Shapiro (Statistical Models in Engineering, 1967) with mention of their applicability. The most useful models are the Gamma (or Erlang) and the Gaussian and some of their minor modifications. As an illustration of something different the Weibull distribution is touched on in problem P5.02.18. These distributions usually are representable by only a few parameters that define the asymmetry, the peak and the shape in the vicinity of the peak. The moments are such parameters. 

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