{"id":"W4385260299","doi":"10.3390/mca28040085","title":"Moments of the Negative Multinomial Distribution","year":2023,"lang":"en","type":"article","venue":"Mathematical and Computational Applications","topic":"Statistical Distribution Estimation and Applications","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Multinomial distribution; Negative multinomial distribution; Distribution (mathematics); Mathematics; Statistics; Negative binomial distribution; Beta-binomial distribution; Poisson distribution; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002700135,0.0005058672,0.0006904547,0.001730051,0.0004858986,0.001462018,0.0008262678,0.0004741817,0.004637939],"category_scores_gemma":[0.0199944,0.0002585847,0.0005467143,0.001198394,0.002106666,0.002391832,0.0009976755,0.001250057,0.00114711],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006918095,"about_ca_system_score_gemma":0.0008738842,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001208453,"about_ca_topic_score_gemma":0.00111104,"domain_scores_codex":[0.9987838,0.0004112412,0.00006482681,0.0001946358,0.0003699486,0.0001756831],"domain_scores_gemma":[0.9924607,0.005070095,0.0007532337,0.000486072,0.00102885,0.0002011089],"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":[0.0001007582,0.0000348645,0.00389173,0.0002461772,0.00003187664,0.0005740354,0.0003629027,0.04103991,0.004184301,0.8885203,0.005449668,0.05556342],"study_design_scores_gemma":[0.00002120537,0.00004807694,0.003738239,0.0001644707,0.00002985393,0.001336112,0.0001657849,0.317698,0.002093202,0.6639917,0.01063173,0.00008157848],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.04327443,0.001509782,0.9447144,0.0004647466,0.0001757476,0.00004397647,0.0003020806,0.0002611942,0.009253724],"genre_scores_gemma":[0.8208895,0.0043907,0.1593217,0.0005458624,0.0007875884,0.0002788934,0.0008556229,0.0003316843,0.01259835],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.004637939,"threshold_uncertainty_score":0.01551539,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04970134594663277,"score_gpt":0.3432340746326143,"score_spread":0.2935327286859815,"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."}}