{"id":"W2981781402","doi":"10.1142/s2010326321500106","title":"The densities and distributions of the largest eigenvalue and the trace of a Beta–Wishart matrix","year":2019,"lang":"en","type":"article","venue":"Random Matrices Theory and Application","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"San José State University; National Science Foundation","keywords":"Wishart distribution; TRACE (psycholinguistics); Mathematics; Truncation (statistics); Eigenvalues and eigenvectors; Matrix (chemical analysis); Series (stratigraphy); BETA (programming language); Applied mathematics; Statistics; Physics; Computer science; Chemistry; Multivariate statistics","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":[0.002199616,0.0001338673,0.0003089468,0.00002544511,0.0004858897,0.00006151044,0.0002302627,0.00006373049,0.00000697224],"category_scores_gemma":[0.0001416431,0.00006309484,0.0000940995,0.0002355871,0.0005889613,0.00008075286,0.0001060955,0.0001181367,0.00000232577],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006438939,"about_ca_system_score_gemma":0.00001760352,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000307292,"about_ca_topic_score_gemma":0.00001122972,"domain_scores_codex":[0.9987977,0.0003084206,0.0004063138,0.0001843659,0.000168193,0.0001349701],"domain_scores_gemma":[0.9939452,0.005049024,0.0004396599,0.000453621,0.00008128343,0.00003123139],"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":[0.0005858808,0.00003255024,0.0006748259,0.0001660726,0.00004851028,2.006413e-8,0.0005430782,0.000004756576,0.001009695,0.9948751,0.00008069132,0.001978839],"study_design_scores_gemma":[0.01005545,0.00003898253,0.006120539,0.00007622175,0.0006952158,0.00003521514,0.002558001,0.002857071,0.003110196,0.9664239,0.007807486,0.0002217174],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9816132,0.006664736,0.007811687,0.001373709,0.00003080474,0.001857325,0.00009091641,0.00002132756,0.0005362984],"genre_scores_gemma":[0.9970302,0.002062301,0.0002204724,0.0000158244,0.00003552896,0.0001935859,0.00000434279,0.00001121453,0.0004265584],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02845117,"threshold_uncertainty_score":0.3737119,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005168907723794841,"score_gpt":0.2577927617026899,"score_spread":0.252623853978895,"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."}}