We now compare the methods of Sections 16.7.1 and 16.7.2
for a special case where
can be computed exactly.
Consider the trivial case where
In this case
has the Irwin-Hall distribution
In Figure 16.1, we show the
error (compared with exact Irwin-Hall distribution)
on the Y-axis for both methods for and .
The error is very small, less that .02 at and less than .004 at .
This error for a 40-dimensional PDF is very small
and for all practical purposes, can be ignored.
Notice that the error becomes smaller with increasing .
For even larger , however, the round-off error in computing Irwin-Hall
Although almost always the same, the ML approach had slightly more
error and the SPA was faster. Therefore, SPA is our method of choice.
Numerical comparison of SPA (dots) and
ML (circles) with Irwin-Hall distribution (X-axis)
for and .