In my recent blog on this theme I stated:
These early instruments needed a very robust and simple calculation mode, the ‘2nd Cumulant’ method, for evaluation because the calculation power of the then available computers were still very limited. Still today this simplified calculation method is positioned in the related ISO 13321 framework. It generates as results a mean particle diameter and a value for the width of an assumed Gaussian distribution only.
Regarding this rather abreviated definition of the results given by 2nd Cumulant method I was asked to correct it to a precise one.
As 2nd Cumulant is a typical series expansion it is not resulting in any, whatever shaped curve but in a series of moments. As the name indicates only the first and second moment of this series are evaluted. The first moment gives the value for the mean diameter and the second moment gives the width . These two values are the only result of the 2nd Cumulant method. Today nearly all instruments also do graphical reports and only for this they show an assumed Gaussian distribution based on the two values given by the first two moments of the series expansion.
This means that scientifically and mathematically correct the result of a 2nd Cumulant evaluation is only the mean diameter and the width. The presented graph as a Gaussian distribution is correctly not the result but only one possibility to ease understanding to visual skilled creatures as we are.