information:extraction
Other well-known distributions

Several well-known, unimodal, and symmetric distributions from different parametric families are compared here. Each has a mean and skewness of zero. The parameters have been chosen to result in a variance equal to 1 in each case. The images on the right show curves for the following seven densities, on a linear scale and logarithmic scale:

Note that in these cases the platykurtic densities have bounded support, whereas the densities with positive or zero excess kurtosis are supported on the whole real line.

One cannot infer that high or low kurtosis distributions have the characteristics indicated by these examples. There exist platykurtic densities with infinite support,

and there exist leptokurtic densities with finite support.

Also, there exist platykurtic densities with infinite peakedness,

and there exist leptokurtic densities that appear flat-topped,