{"id":"W4386885312","doi":"10.1016/j.jmva.2023.105240","title":"Stochastic representations and probabilistic characteristics of multivariate skew-elliptical distributions","year":2023,"lang":"en","type":"article","venue":"Journal of Multivariate Analysis","topic":"Statistical Distribution Estimation and Applications","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"National Natural Science Foundation of China; Qufu Normal University","keywords":"Mathematics; Skew; Multivariate statistics; Probabilistic logic; Elliptical distribution; Class (philosophy); Transformation (genetics); Quadratic equation; Applied mathematics; Skew normal distribution; Multivariate normal distribution; Mathematical analysis; Distribution (mathematics); Statistics; Geometry","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":[0.0007280185,0.0001729178,0.0006737577,0.0004617476,0.0001792488,0.00005052652,0.0001844349,0.00009461644,0.0001631079],"category_scores_gemma":[0.008129348,0.0001476642,0.0003023371,0.001984485,0.0002050819,0.0001262983,0.00007242816,0.0002311306,0.00001821932],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006312632,"about_ca_system_score_gemma":0.00008345216,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003419974,"about_ca_topic_score_gemma":0.000007697072,"domain_scores_codex":[0.9976259,0.0001643749,0.001325116,0.0002183983,0.00043274,0.0002335053],"domain_scores_gemma":[0.9950857,0.002582245,0.0009323104,0.0003052747,0.0008692503,0.0002252402],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00007049531,0.0007062408,0.001063136,0.0001150312,0.001889131,0.00001701796,0.0005834729,0.002776077,0.002528053,0.9880167,0.0006144913,0.001620159],"study_design_scores_gemma":[0.00121808,0.00009505606,0.4074234,0.00008787186,0.005793976,0.00002318779,0.0002477157,0.4140741,0.0001162595,0.1704804,0.0001495847,0.0002904026],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1251823,0.000008504579,0.8730291,0.0006837017,0.00006115389,0.000190411,0.0007375959,0.00004120786,0.00006605083],"genre_scores_gemma":[0.9805883,0.0000147551,0.01894274,0.00001021335,0.00005909282,0.00001906131,0.0002132942,0.00001417024,0.0001383601],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.855406,"threshold_uncertainty_score":0.9732175,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06179435899054962,"score_gpt":0.3869300360306945,"score_spread":0.3251356770401448,"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."}}