The Moment Notation

In this convention, mean size values are defined through the moments of different types of distributions (e.g., number, length, surface, or volume distribution). For distributions in histogram form, the k complete moment M of a density distribution is defined as  

Depending on the numbers chosen for the subscripts k and r, different mean values may be defined. These two systems can be related to each other for arithmetic mean values only since there is no definition of geometric mean values in the moment notation. Their relations can be summarized in the following table for the mean values commonly used. 

Name Moment-Ratio System Moment System 

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