5.22 FUNCTIONAL VIEW OF SKEWNESS
We can use a functional approach to show that skewness is a measure of the asymmetry of a distribution. Recall for a pdf that is symmetric about the mean, all odd central moments are zero; this occurs because 
is an odd function when n is odd, and thus its expectation is zero. When a pdf is less symmetric about its mean, odd central moments increase in value (except for the first central moment 
which is always zero). Consider the third-central moment:
(5.310) 
Figure 5.18 shows examples of 
for exponential and Rayleigh pdfs, both of which have unit variance so that 
is the same as skewness. We have also plotted the cumulative area
FIGURE 5.18 Functional view of skewness, showing FX(x), 
, and C(x). (a) Exponential with 
(). (b) Rayleigh with ().
(5.311) ...
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