{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/combined-neyman-pearson-chi-square-an","title":"Combined Neyman-Pearson Chi-square: An Improved Approximation to the Poisson-likelihood Chi-square","arxiv_id":"1903.07185","date":"2019-03-17","proceeding":null,"authors":["Xiangpan Ji","Wenqiang Gu","Xin Qian","Hanyu Wei","Chao Zhang"],"abstract":"We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman's and Pearson's chi-squares, namely \"combined Neyman-Pearson chi-square\" ($\\chi^2_{\\mathrm{CNP}}$). Through analytical derivations and toy model simulations, we show that $\\chi^2_\\mathrm{CNP}$ leads to a significantly smaller bias on the best-fit model parameters compared to those using either Neyman's or Pearson's chi-square. When the computational cost of using the Poisson-likelihood chi-square is high, $\\chi^2_\\mathrm{CNP}$ provides a good alternative given its natural connection to the covariance matrix formalism.","url_abs":"https://arxiv.org/abs/1903.07185v3","url_pdf":"https://arxiv.org/pdf/1903.07185v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"combined-neyman-pearson-chi-square-an","repo_url":"https://github.com/Wouter-VDP/nuecc_python","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}