Figure 3

Functional boxplot and ranking. (a) Functional boxplot of the MAX data set (top) and MAX mortality curves (bottom) color-coded according to their ranking, as shown in the MAX column of (b). In the boxplot, Toscana is the median (black continuous line); Lombardia, Valle d’Aosta and Liguria are identified as outliers (red dashed lines); and the 50% innermost “box” (grey area) include the curves for Trento/Bolzano, Emilia-Romagna, Marche, Friuli Venezia Giulia, Veneto, Toscana, Molise, Abruzzo, Sardegna, Umbria, and Basilicata. Note that the “box” is skewed upwardly. (b) Rankings of the ISTAT (left), MAX (center) and DPC (right) mortality curves. The median regions are in bold, gray rectangles mark the 50% innermost boxes, and pale red rectangles mark outliers (no region is labeled as an outlier in the ISTAT data set; see Methods). The dots representing each region are color-coded (from intense red, through gray, to intense blue) according to their signed depth values (see Methods). In all three data sets, Lombardia’s curve is the most extreme at the very top of the ranking and, in contrast, Veneto’s curve is deep in the bulk close to the median (Toscana for ISTAT and MAX, Friuli Venezia Giulia for DPC). Segments joining the regions across the three rankings show how the top portion remains rather stable, while the mid- and bottom portions contain several crossings. Regions at the top are those characterized by “exponential” epidemics (Group 1), while regions in the middle and at the bottom are those with “flat(tened)” epidemics (Group2), whose curves can more easily switch in their depth ranks.