RunStatistics.jl

A package implementing the exact evaluation of the cumulative distribution function of the Squares test statistic $T$ as defined in

Frederik Beaujean and Allen Caldwell. A Test Statistic for Weighted Runs. doi:10.1016/j.jspi.2011.04.022 arXiv:1005.3233

This package also includes an implementation of an approximation of this cumulative for the more general case of large numbers of observations, as derived in

Frederik Beaujean and Allen Caldwell. Is the bump significant? An axion-search example doi:10.1140/epjc/s10052-018-6217-y arXiv:1710.06642

This code is based on the original implementation by Frederik Beaujean in c++ and mathematica.

Package Features

• Calculate the p-value for the Squares test statistic^[1] $T$ observed in $N$ independent trials of gaussian uncertainty
• Improved performance and readability over the original implementation thanks to Julia
• Inbuilt implementation for generating integer partitions of an integer $n$ into $k$ parts

Manual Outline

• Introduction
• • Motivation
  • The Squares test statistic
  • Interpreting the Squares statistic
  • • Approximation for large numbers of observations
• Guide
• • Installation
  • Using RunStatistics.jl
  • • Calculate $T_{obs}$
    • Calculate the p-value and evaluate the cumulative distribution function of $T$
  • Details of computation
  • • Partitions
    • Approximation for large numbers of data
    • Accuracy

Citing RunStatistic.jl

When using RunStatistics.jl for research, teaching or similar, please cite the original authors' work:

@article{beaujean2011test,
  title={A test statistic for weighted runs},
  author={Beaujean, Frederik and Caldwell, Allen},
  journal={Journal of Statistical Planning and Inference},
  volume={141},
  number={11},
  pages={3437--3446},
  year={2011},
  publisher={Elsevier}
}

@article{Beaujean2018,
  author={Beaujean, Frederik and Caldwell, Allen and Reimann, Olaf},
  title={Is the bump significant? An axion-search example},
  journal={The European Physical Journal C},
  year={2018},
  month={Sep},
  day={28},
  volume={78},
  number={9},
  pages={793},
  issn={1434-6052},
  doi={10.1140/epjc/s10052-018-6217-y},
  url={https://doi.org/10.1140/epjc/s10052-018-6217-y}
}