{"id":"W4321226224","doi":"10.1002/sta4.550","title":"A slew of mixture relationships involving discrete and continuous generalized hypergeometric distributions and their special cases","year":2023,"lang":"en","type":"article","venue":"Stat","topic":"Statistical Distribution Estimation and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Hypergeometric distribution; Mathematics; Negative binomial distribution; Poisson distribution; Hypergeometric function; Infinite divisibility; Logarithm; Gauss; Logarithmic distribution; Context (archaeology); Binomial (polynomial); Applied mathematics; Pure mathematics; Mathematical analysis; Statistics; Physics","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":[0.0002182824,0.0001097324,0.0002067396,0.0001259551,0.0002609849,0.00003501043,0.00005057218,0.00005670888,0.0000807337],"category_scores_gemma":[0.003229496,0.00009045435,0.00003543977,0.0008002504,0.0001580851,0.00006539778,0.00005479382,0.0001105899,0.000007380879],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002054508,"about_ca_system_score_gemma":0.00001903669,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001664519,"about_ca_topic_score_gemma":0.00003117853,"domain_scores_codex":[0.9992039,0.00007668474,0.0002848581,0.0001682805,0.0001095977,0.000156724],"domain_scores_gemma":[0.9977595,0.001786123,0.0001030332,0.0001474959,0.000103932,0.00009993918],"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":[0.000009646566,0.00003517931,0.002106407,0.00006804882,0.00002494957,0.000003279736,0.0004349504,0.000001880005,0.0004281721,0.9821703,0.01252398,0.002193145],"study_design_scores_gemma":[0.001402263,0.00009006813,0.1305736,0.00009969288,0.0001531308,0.0000638735,0.002202293,0.01028037,0.0007997269,0.8423445,0.01153707,0.000453407],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7858732,0.0002506942,0.2059847,0.0009422757,0.00007193045,0.0003765755,0.005825468,0.0001482519,0.0005269023],"genre_scores_gemma":[0.993766,0.0001292499,0.005121531,0.00001414627,0.00007186197,0.00004099326,0.0005756167,0.00001119779,0.0002694812],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2078927,"threshold_uncertainty_score":0.3866242,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0950344683284487,"score_gpt":0.337063390908503,"score_spread":0.2420289225800543,"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."}}