{"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/a-robust-contaminated-discrete-weibull","title":"A robust contaminated discrete Weibull regression model for outlier-prone count data","arxiv_id":"2504.09536","date":"2025-04-13","proceeding":null,"authors":["Divan A. Burger","Janet van Niekerk","Emmanuel Lesaffre"],"abstract":"Count data often exhibit overdispersion driven by heavy tails or excess zeros, making standard models (e.g., Poisson, negative binomial) insufficient for handling outlying observations. We propose a novel contaminated discrete Weibull (cDW) framework that augments a baseline discrete Weibull (DW) distribution with a heavier-tail subcomponent. This mixture retains a single shifted-median parameter for a unified regression link while selectively assigning extreme outcomes to the heavier-tail subdistribution. The cDW distribution accommodates strictly positive data by setting the truncation limit c=1 as well as full-range counts with c=0. We develop a Bayesian regression formulation and describe posterior inference using Markov chain Monte Carlo sampling. In an application to hospital length-of-stay data (with c=1, meaning the minimum possible stay is 1), the cDW model more effectively captures extreme stays and preserves the median-based link. Simulation-based residual checks, leave-one-out cross-validation, and a Kullback-Leibler outlier assessment confirm that the cDW model provides a more robust fit than the single-component DW model, reducing the influence of outliers and improving predictive accuracy. A simulation study further demonstrates the cDW model's robustness in the presence of heavy contamination. We also discuss how a hurdle scheme can accommodate datasets with many zeros while preventing the spurious inflation of zeros in situations without genuine zero inflation.","url_abs":"https://arxiv.org/abs/2504.09536v1","url_pdf":"https://arxiv.org/pdf/2504.09536v1.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":"a-robust-contaminated-discrete-weibull","repo_url":"https://github.com/daburger1/robust-count-ctdw","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}