Introducing novel order statistic tests based on spacings and their applications to Neutrino experiments

The use of spacings between ordered real-valued numbers is very useful in many areas of science. In particular, either unnaturally small or large spacings can be a signal of an interesting effect.
We introduce new statistical tests based on the observed spacings of ordered data. These statistics are sensitive to detect non-uniformity in random samples, or short-lived features in event time series. Under some conditions, these new test can outperform existing ones, such as the well known Kolmogorov-Smirnov or Anderson-Darling tests, in particular when the number of samples is small and differences occur over a small quantile of the null hypothesis distribution.
These features allow our tests to be effective in detecting signal lines in low background experiments or when looking for highly peaked signals in experiments with substantial background.
A detailed description of the test statistics is provided including examples and proposed applications in the analysis of neutrino experiments, such as an online monitoring system for supernova early detection or as background validation for double beta decay experiments.