Fig. 16

Monarch (or milkweed) butterfly (Danaus plexippus), with scores being the negative log-likelihoods; \(n =\) 1300; Kuiper’s statistic is \(0.01144 / \sigma = 2.856\), Kolmogorov’s and Smirnov’s is \(0.01144 / \sigma = 2.856\). The deviation of the subpopulation below the full population that occurs for scores greater than 1.5 is apparent only in the cumulative plot or in the (very noisy) reliability diagrams whose bins are roughly equispaced along the scores. The scalar summary statistics detect somewhat significant deviation, but not as much as would be possible if the Kolmogorov-Smirnov and Kuiper metrics were to take fully into account the steep drop that occurs in the plot of cumulative differences