{"id":"W3124785140","doi":"10.1016/j.jmva.2013.03.002","title":"On the moments of ratios of quadratic forms in normal random variables","year":2013,"lang":"en","type":"article","venue":"Journal of Multivariate Analysis","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Social Sciences and Humanities Research Council of Canada","keywords":"Mathematics; Positive-definite matrix; Quadratic equation; Matrix (chemical analysis); Combinatorics; Series (stratigraphy); Quadratic form (statistics); Random variable; Pure mathematics; Mathematical analysis; Statistics; Geometry","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":[0.009307964,0.001665181,0.002195319,0.004716077,0.0006910438,0.003016802,0.002650537,0.001630222,0.004709286],"category_scores_gemma":[0.04767201,0.001211885,0.001406285,0.002427628,0.005881323,0.007197229,0.002709158,0.003088698,0.0006467988],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001553368,"about_ca_system_score_gemma":0.001014017,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001427469,"about_ca_topic_score_gemma":0.001254039,"domain_scores_codex":[0.9967354,0.001841628,0.0001629076,0.0003500917,0.0005697353,0.0003401636],"domain_scores_gemma":[0.9578023,0.03367741,0.002818994,0.001612247,0.002236911,0.001852204],"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":[0.0002024311,0.00005119833,0.001450167,0.0001417633,0.00006162924,0.0002718382,0.000323301,0.03169978,0.002915356,0.951173,0.001559287,0.01015024],"study_design_scores_gemma":[0.00003596711,0.00008188353,0.002381523,0.0000892408,0.00004386723,0.0003715283,0.0001133627,0.3162403,0.001004201,0.6782379,0.001289034,0.0001111808],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2642772,0.004341428,0.7134674,0.002868986,0.0004482352,0.00009998027,0.0004230563,0.0003950331,0.01367867],"genre_scores_gemma":[0.9383725,0.004470655,0.04603367,0.0005148129,0.001974874,0.0001466089,0.0005031998,0.0003997684,0.007583935],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009307964,"threshold_uncertainty_score":0.04922581,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007566050622800883,"score_gpt":0.2383921580205893,"score_spread":0.2308261073977884,"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."}}