{"id":"W3123559192","doi":"10.1016/j.cam.2021.113418","title":"Expressions for joint moments of elliptical distributions","year":2021,"lang":"en","type":"article","venue":"Journal of Computational and Applied Mathematics","topic":"Statistical Distribution Estimation and Applications","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"National Natural Science Foundation of China","keywords":"Mathematics; Lemma (botany); Elliptical distribution; Laplace transform; Random variable; Moment-generating function; Joint probability distribution; Moment (physics); Multivariate statistics; Joint (building); Product (mathematics); Mathematical analysis; Function (biology); Applied mathematics; Multivariate normal distribution; 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":[0.0002326267,0.00009611869,0.0003231474,0.00004754832,0.0001035878,0.00002344633,0.00006866051,0.00004688865,0.000070341],"category_scores_gemma":[0.0007097608,0.000080332,0.0001027993,0.0001362034,0.0000929314,0.00004132461,0.0000341633,0.0000904696,0.000002355149],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002230021,"about_ca_system_score_gemma":0.0001086291,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.704233e-8,"about_ca_topic_score_gemma":6.352206e-8,"domain_scores_codex":[0.9987029,0.00001196797,0.0008033994,0.0000886192,0.0002923273,0.0001007719],"domain_scores_gemma":[0.9973176,0.001341086,0.0004753544,0.00009021798,0.000663324,0.0001124171],"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":[0.000008788805,0.0005214248,0.000001863112,0.0001957139,0.00004839734,8.033253e-7,0.00009258347,0.0003856045,0.003264615,0.9927365,0.002153218,0.0005904688],"study_design_scores_gemma":[0.0006870493,0.00003215821,0.0003009162,0.00008887256,0.0001019846,0.00006120576,0.0002794308,0.01181772,0.005111225,0.9809996,0.0004382504,0.00008155034],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02391399,0.00002600702,0.9742512,0.0006644421,0.00003340833,0.0001571918,0.0003216911,0.000009299159,0.0006227778],"genre_scores_gemma":[0.4149109,0.000005378482,0.5849057,0.00002656138,0.00003486284,0.00001543067,0.00004931444,0.000007144515,0.00004475321],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3909969,"threshold_uncertainty_score":0.3275844,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08468057928293632,"score_gpt":0.3577001634417104,"score_spread":0.273019584158774,"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."}}