Fig. 38

\(n =\) 100; \(S_1\), \(S_2\), ..., \(S_n\) are denser near 0; Kuiper’s statistic is \(0.1893 / \sigma = 5.185\), Kolmogorov’s and Smirnov’s is \(0.1867 / \sigma = 5.112\). Figure 39 displays the ground-truth reliability diagram. The plots, whether cumulative or conventional, reveal similar information here, though the reliability diagrams with an equal number of observations per bin provide more reliable estimates than the other reliability diagrams. The cumulative plot is perhaps the easiest to interpret: the miscalibration is significant for \(0.1 \lesssim S_k \lesssim 0.23\) and \(0.27 \lesssim S_k \lesssim 0.6\), with about the correct amount of miscalibration (the amount is correct since the secant lines have the expected slopes)