A new statistical distribution, PEVD, precisely fits the distributions of simulated profile similarity scores: An example of fitting a simulated score distribution of 1e6 scores with Gumbel extreme value distribution (EVD) and with PEVD. The distribution's tail is shown in a logarithmic scale. Inset: full plot in a linear scale. Below: Histograms of the chi-square-goodness-of-fit P-values for multiple individual distributions. P-values for EVD are mostly low; P-value histogram for PEVD is close to the ideally expected uniform distribution.