{"id":"W2000209556","doi":"10.1080/02331880212859","title":"Some properties and a characterization of trivariate and multivariate binomial distributions","year":2002,"lang":"en","type":"article","venue":"Statistics","topic":"Statistical Distribution Estimation and Applications","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Negative binomial distribution; Multivariate statistics; Binomial (polynomial); Statistics; Univariate distribution; Poisson distribution; Binomial regression; Applied mathematics; Distribution (mathematics); Binomial distribution; Negative multinomial distribution; Regression analysis; Beta-binomial distribution; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006139454,0.0004656933,0.0007285661,0.003149654,0.0007146081,0.002179992,0.0009319329,0.0008836599,0.005084225],"category_scores_gemma":[0.03437972,0.0004784131,0.0008962691,0.004126013,0.002066163,0.003432178,0.001292882,0.002027368,0.001392698],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008146309,"about_ca_system_score_gemma":0.0009373535,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009335543,"about_ca_topic_score_gemma":0.0006240987,"domain_scores_codex":[0.997448,0.00102476,0.0001702182,0.0003841836,0.0007818422,0.0001910626],"domain_scores_gemma":[0.9797982,0.01391154,0.002485391,0.0008599693,0.002440674,0.0005041539],"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":[0.00003663921,0.00003745925,0.003484373,0.0001217614,0.0000322505,0.0004053292,0.0005300519,0.0143794,0.002589577,0.9375891,0.002608504,0.03818561],"study_design_scores_gemma":[0.00001631591,0.00005494528,0.003083478,0.0001072457,0.00002822752,0.001950148,0.0002361897,0.1370801,0.0009413297,0.8459842,0.01045656,0.00006118164],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02957621,0.002353415,0.9527261,0.0007690898,0.00008382404,0.00004707608,0.0002764692,0.0001417854,0.01402617],"genre_scores_gemma":[0.7331854,0.01124978,0.2406442,0.0007666854,0.0009926019,0.000603331,0.001442498,0.0003351701,0.01078037],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006139454,"threshold_uncertainty_score":0.03246891,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1048322315506107,"score_gpt":0.3087760892868808,"score_spread":0.2039438577362702,"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."}}