Comparison

A good check on the analysis is to compare the two methods just presented in Sections 8.2 and 8.1.2.

We tried the case of $N=100$, $M=3$, $t_1=3$, $t_2=7$. Samples of input data vector ${\bf x}$ were generated using $N$ independent uniformly distributed RVs (in the range 0 to 1), then scaled by a random scale factor in the range 0 to 10. Note that the PDF used for data generation is not important because we are comparing two PDF approximations for the same input feature vector. The PDF of ${\bf z}$ was computed using the methods of Sections 8.2 and 8.1.2. The results are shown in Figure 8.1. The two methods agreed very closely - within a maximum error of .059 in log space.

Figure 8.1: Comparison of Saddlepoint Approximation (Section 8.2) with integral solution (Section 8.1.2). Largest difference was .059