{"id":"W2071433805","doi":"10.1016/j.jmva.2014.04.023","title":"A note on the computation of sharp numerical bounds for the distribution of the sum, product or ratio of dependent risks","year":2014,"lang":"en","type":"article","venue":"Journal of Multivariate Analysis","topic":"Probability and Risk Models","field":"Decision Sciences","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University; McGill University; Université Laval; Actua","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Cumulative distribution function; Product (mathematics); Random variable; Computation; Function (biology); Measure (data warehouse); Joint probability distribution; Applied mathematics; Distribution (mathematics); Probability density function; Value (mathematics); Numerical analysis; Distribution function; Upper and lower bounds; Expected value; Mathematical optimization; Statistics; Mathematical analysis; Algorithm; Computer science","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":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.009666755,0.0001054876,0.000548547,0.0001375297,0.0002197559,0.00005825835,0.0008552645,0.00005352525,0.00003210439],"category_scores_gemma":[0.01009364,0.00003558166,0.0007551617,0.001303142,0.0001841173,0.0001508534,0.00008026611,0.0001981116,9.254073e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005005142,"about_ca_system_score_gemma":0.0001457633,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003053882,"about_ca_topic_score_gemma":0.0001280527,"domain_scores_codex":[0.9960138,0.0009194771,0.00138338,0.0001866402,0.001377122,0.0001195896],"domain_scores_gemma":[0.9902605,0.005130486,0.002527186,0.000536375,0.001508956,0.0000364993],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.001394559,0.000575466,0.009907941,0.00002001212,0.001307412,2.912522e-7,0.002194719,0.9514323,0.003172252,0.004065852,0.0003462913,0.02558289],"study_design_scores_gemma":[0.0005790036,0.0002544978,0.1402155,0.00003162354,0.001092234,0.000002256209,0.0002566948,0.8351499,0.007705357,0.01441585,0.0002371268,0.00006002409],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3320986,0.00003843154,0.6640024,0.003482654,0.0001114062,0.0002061411,0.00004596337,0.000001178778,0.00001323645],"genre_scores_gemma":[0.9990087,0.00001312964,0.000821465,0.00003830915,0.00006888981,0.000003759888,0.000002469788,0.000003592578,0.00003971972],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6669101,"threshold_uncertainty_score":0.9982448,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1407077876085044,"score_gpt":0.4150531966224966,"score_spread":0.2743454090139923,"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."}}