{"id":"W4376274338","doi":"10.1016/j.jmaa.2023.127410","title":"Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality","year":2023,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Gaussian; Bivariate analysis; Product (mathematics); Moment (physics); Mathematical proof; Inequality; Random variable; Distribution (mathematics); Gaussian random field; Mathematical analysis; Pure mathematics; Combinatorics; Gaussian process; 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":[0.005046123,0.001141449,0.001886534,0.002350919,0.0009614071,0.003217351,0.002199826,0.001530024,0.004798433],"category_scores_gemma":[0.0251625,0.0004865519,0.001624547,0.002186183,0.004020003,0.006674753,0.003056291,0.003845991,0.000673538],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002367907,"about_ca_system_score_gemma":0.001269802,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002294753,"about_ca_topic_score_gemma":0.0009943164,"domain_scores_codex":[0.9974549,0.001161652,0.00009391082,0.00038247,0.0006322749,0.0002747977],"domain_scores_gemma":[0.9848333,0.01028254,0.001318286,0.0005760478,0.00212774,0.000862104],"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":[0.0001084305,0.0000259044,0.0008157046,0.000108942,0.00004909588,0.0002584914,0.0002008668,0.008572264,0.001783294,0.9801558,0.001673709,0.006247432],"study_design_scores_gemma":[0.00002457336,0.00004562616,0.001349126,0.00003674818,0.00004211958,0.0004065536,0.0001004362,0.2152915,0.0007236439,0.779434,0.002498422,0.00004712372],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06150142,0.004872636,0.8940566,0.004681921,0.000386202,0.00004113673,0.0003620158,0.0001537954,0.03394425],"genre_scores_gemma":[0.9127826,0.005435539,0.06718931,0.00120517,0.001504179,0.0002122949,0.0004229665,0.0001747743,0.0110732],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005046123,"threshold_uncertainty_score":0.02668679,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05267255178297511,"score_gpt":0.3372759047363612,"score_spread":0.2846033529533861,"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."}}