Statistical Moments, Skew And Excess - Agilent Technologies 8453 Operator's Manual

Statistical Moments, Skew and Excess

Statistical moments are calculated as an alternative to describe asymmetric
peak shapes. There is a infinite number of peak moments, but only the first
five are used in connection with chromatographic peaks. These are called 0
Moment, 1
The 0
The 1
center of gravity of the peak. It is different from the chromatographic
retention time measured at peak maximum unless the peak is symmetrical.
The 2
It is the sum of the variance contributed by different parts of the instrument
system.
The 3
departure of the peak shape from the Gaussian standard. The skew given
additionally in the Performance & Extended report is its dimensionless form.
A symmetrically peak has a skew of zero. Tailing peaks have positive skew and
their 1. Moment is greater than the retention time. Fronting peaks have
negative skew and their 1. Moment is less than the retention time.
The 4
peak along a vertical axis, and how this compares to a Gaussian standard for
which the 4. Moment is zero. It can be visualized by moving in or pulling apart
the sides of a Gaussian peak while maintaining constant area. If the peak is
compressed or squashed down in comparison, its excess is negative. If it is
taller, its excess is positive. Also the excess is given in the Performance &
Extended report in its dimensionless form.
Understanding Your Agilent ChemStation
st th
Moment, ... 4
th
Moment represents the peak area.
st
Moment is the mean retention time, or retention time measured at the
nd
Moment is the peak variance which is a measure of lateral spreading.
rd
Moment describes the vertical symmetry or skew. It is a measure of the
th
Moment or excess is a measure of the compression or stretching of the
Moment.
Evaluating System Suitability
Performance Test Definitions
11
th
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