peakedness

A different measure of "kurtosis", that is of the "peakedness" of a distribution, is provided by using L-moments instead of the ordinary moments.

Two of these relate to the curve position (grain size and peakedness) and the other two to inclination of the limbs of the curve.

The third central moment indicates the skewness of the RTD and the fourth central moment indicates the kurtosis (the "peakedness").

The "classical" interpretation, which applies only to symmetric distributions (those whose skewness is 0), is that kurtosis measures both the "peakedness" of the distribution and the heaviness of its tail.

There are various interpretations of kurtosis, and of how particular measures should be interpreted; these are primarily peakedness (width of peak), tail weight, and lack of shoulders (distribution primarily peak and tails, not in between).

One common measure of kurtosis, originating with Karl Pearson, is based on a scaled version of the fourth moment of the data or population, but it has been argued that this measure really measures heavy tails, and not peakedness.