{"id":"W2058825489","doi":"10.1016/j.amc.2010.08.040","title":"A class of bivariate negative binomial distributions with different index parameters in the marginals","year":2010,"lang":"en","type":"article","venue":"Applied Mathematics and Computation","topic":"Statistical Distribution Estimation and Applications","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Bivariate analysis; Negative binomial distribution; Mathematics; Marginal distribution; Binomial distribution; Joint probability distribution; Beta-binomial distribution; Statistics; Multinomial distribution; Poisson distribution; Bivariate data; Continuity correction; Applied mathematics; Random variable","routes":{"ca_aff":true,"ca_fund":false,"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":[],"consensus_categories":[],"category_scores_codex":[0.0002295539,0.00013457,0.0002195786,0.00006146692,0.0001000243,0.00005018425,0.0001101608,0.00005774486,0.00001353633],"category_scores_gemma":[0.0001347864,0.00008664086,0.00002590398,0.0002608293,0.0001753267,0.0000333789,0.00002417556,0.0001895518,0.000002687881],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001374443,"about_ca_system_score_gemma":0.00002208903,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001511706,"about_ca_topic_score_gemma":0.00004728544,"domain_scores_codex":[0.9991128,0.00002012295,0.0003669666,0.0001539035,0.0002132733,0.0001328694],"domain_scores_gemma":[0.9981221,0.001358674,0.0002304492,0.000171499,0.00007363752,0.00004366041],"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":[0.0000151913,0.0003000611,0.00005349965,0.00006633374,0.00001397246,3.927697e-7,0.0008350852,0.00007595088,0.0004320067,0.9966184,0.00007574609,0.001513382],"study_design_scores_gemma":[0.0008395137,0.00004546434,0.01404911,0.00003073744,0.00005682373,0.000008886902,0.0009824937,0.06470402,0.000750653,0.9183714,0.00001813311,0.0001427035],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4644652,6.275156e-7,0.5341013,0.0003411038,0.000009964955,0.0003749913,0.00005689987,0.00001579799,0.0006341013],"genre_scores_gemma":[0.9166867,0.000001345753,0.08303718,0.00003537993,0.000008326198,0.0001657505,0.000053665,0.000008412683,0.000003248854],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.4522215,"threshold_uncertainty_score":0.3533112,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0358866703828388,"score_gpt":0.3100295659361819,"score_spread":0.2741428955533431,"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."}}