{"id":"W3137498593","doi":"10.1007/s00184-023-00897-2","title":"A refined continuity correction for the negative binomial distribution and asymptotics of the median","year":2023,"lang":"en","type":"article","venue":"Metrika","topic":"Statistical Methods and Bayesian Inference","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"Fonds Québécois de la Recherche sur la Nature et les Technologies; Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada; Centre de Recherches Mathématiques","keywords":"Mathematics; Negative binomial distribution; Binomial distribution; Continuity correction; Binomial (polynomial); Estimator; Distribution (mathematics); Limit (mathematics); Upper and lower bounds; Random variable; Combinatorics; Statistics; Beta-binomial distribution; Mathematical analysis; Poisson distribution","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.0008185234,0.00006688808,0.0001527585,0.00002995122,0.0001348785,0.0000190854,0.00009902407,0.00005022499,0.00001074864],"category_scores_gemma":[0.0196476,0.00003512145,0.00005154105,0.0005344351,0.0001400361,0.00001964834,0.0000508821,0.00008993426,0.000001503803],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002566186,"about_ca_system_score_gemma":0.0000267186,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003696367,"about_ca_topic_score_gemma":0.00006123937,"domain_scores_codex":[0.9993375,0.0001181291,0.0001867294,0.0001025461,0.0001349933,0.000120091],"domain_scores_gemma":[0.9902683,0.009317448,0.000122752,0.0001556576,0.0001100859,0.00002569603],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001505149,0.00006292293,0.003332353,0.000132468,0.00009390893,6.270688e-7,0.0009329188,0.000001460768,0.0007175662,0.5903492,0.02414279,0.3800833],"study_design_scores_gemma":[0.000732871,0.0001445885,0.1067,0.00005547009,0.0001613984,0.000002391407,0.0003993778,0.01598712,0.01072413,0.8630565,0.001926328,0.0001097744],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03190604,0.00001148647,0.9647809,0.001203648,0.0009970772,0.0005191249,0.0003555031,0.00003717465,0.0001890716],"genre_scores_gemma":[0.9503867,0.00002123901,0.04902369,0.00003512975,0.0001249035,0.00005187223,0.00001024535,0.0000108115,0.0003353767],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9184807,"threshold_uncertainty_score":0.9886103,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05968265485861679,"score_gpt":0.358064667786666,"score_spread":0.2983820129280492,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}