5.23 FUNCTIONAL VIEW OF KURTOSIS
Finally, we provide a functional view of kurtosis demonstrating that it depends on the degree to which the pdf has heavy tails. The fourth-central moment is
(5.313) 
Figure 5.19 shows an example of 
for Laplace and Gaussian pdfs. We have also plotted the cumulative area
FIGURE 5.19 Functional view of kurtosis, showing FX(x), 
, and D(x). (a) Laplace with 
. (b) Gaussian with 
.
(5.314) 
as x is varied over the support of FX(x), and where 
. In both cases, the variance has been set to one so that 
is the same as the kurtosis (subtracting three gives the excess kurtosis). ...
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