  The so-called 'energy test' is a frequentist technique used in experimental
particle physics to decide whether two samples are drawn from the same
distribution. Its usage requires a good understanding of the distribution of
the test statistic, T, under the null hypothesis. We propose a technique which
allows the extreme tails of the T-distribution to be determined more
efficiently than possible with present methods. This allows quick evaluation of
(for example) 5-sigma confidence intervals that otherwise would have required
prohibitively costly computation times or approximations to have been made.
Furthermore, we comment on other ways that T computations could be sped up
using established results from the statistics community. Beyond two-sample
testing, the proposed biased bootstrap method may provide benefit anywhere
extreme values are currently obtained with bootstrap sampling.
