## Numerical validation

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

where 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 eventually dominates. Although almost always the same, the ML approach had slightly more error and the SPA was faster. Therefore, SPA is our method of choice.

Baggenstoss 2017-05-19