Exponential distribution of large excess death rates in Europe during the COVID-19 outbreak in the spring of 2020

Martin-Olalla, J. M.

Excess death rates E during the spring of 2020 are computed in N=340 level 3 European territorial units for statistics ---NUTS3 in Netherlands (44), Belgium (40), France (96), Spain (50) and Italy (110)--- from 2020 provisional week deaths, the population numbers for 2020, and observations in previous years (reference or baseline), all of them obtained from Eurostat web page. The distribution of excess death rates is found to follow an exponential law with empirical complementary cumulative distribution function Y following logY=a+b(E-Eave)/s. In the middle of the distribution b1=-1.356{+/-} 0.009; R2=0.998 are found and for the largest m=46 excess death rates b1=-0.645{+/-} 0.018; R2=0.992 is observed. This result suggests that abnormally large excess death rates may develop in statistical regions independently of what happens in the outside. Distribution of excess death rates are also analyzed on a country basis. A two-sample Kolmogorov-Smirnov test does not reject the null hypothesis "normal values of E for country i and country j come from the same parent distribution" for any pairing. This is an evidence of a common background in the outcomes. In other words statistical differences among countries can be characterized by averages and standard deviations only. Average death rates, sample standard deviations, excess death tolls are: Netherlands 407x10-6,387x 10-6,8104; Belgium 667x10-6,364x 10-6,8436; France 228x 10-6,377x10-6,21780 (overseas departments not included); Spain 1059x 10-6,1149x10-6,48931 (Canary Islands not included); Italy 791x 10-6,1140x 10-6,49184; and 610x 10-6,877x 10-6,136435 for the combined distribution. A Kolmogorov-Smirnov test rejects (p<0.001$) the null hypothesis "normal scores of E come from a Gaussian distribution" only for Italian data and the whole set of excess death rates.