{"id":"W54143233","doi":"","title":"MONOTONICITY OF RATIOS INVOLVING INCOMPLETE GAMMA FUNCTIONS WITH ACTUARIAL APPLICATIONS","year":2008,"lang":"en","type":"article","venue":"","topic":"Risk and Portfolio Optimization","field":"Decision Sciences","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University; York University","funders":"","keywords":"Monotonic function; Mathematics; Probabilistic logic; Mathematical economics; Gamma function; Calculus (dental); Applied mathematics; Conditional probability; Econometrics; Pure mathematics; Statistics; Mathematical analysis; Medicine","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":[0.0004137282,0.00009281242,0.0001925568,0.0002042917,0.0003287978,0.00004471262,0.0002790881,0.0000504642,0.0005407702],"category_scores_gemma":[0.000179747,0.00006138455,0.00005856993,0.0009660185,0.0001439511,0.0003695615,0.0000455453,0.00007255466,0.00012044],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001693511,"about_ca_system_score_gemma":0.0001630964,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001724959,"about_ca_topic_score_gemma":0.0001983662,"domain_scores_codex":[0.998408,0.00006202668,0.0004910018,0.0002732609,0.0006389259,0.000126738],"domain_scores_gemma":[0.9983262,0.0003753514,0.0002539493,0.0005013029,0.0004680007,0.00007515454],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.0004581017,0.0006595465,0.7388816,0.000006951628,0.0001266873,0.000008418647,0.003797987,0.1028801,0.004582589,0.05720825,0.04772851,0.04366131],"study_design_scores_gemma":[0.004626111,0.0009434749,0.3973265,0.000026257,0.0001424459,0.0001607199,0.005111662,0.2029411,0.01292793,0.0250314,0.3494026,0.001359688],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2212002,0.0000214044,0.7473637,0.0002049239,0.00007752558,0.000410574,0.00001303342,0.0000549002,0.03065374],"genre_scores_gemma":[0.9804716,0.0000849103,0.01635488,0.00007147103,0.00008531471,0.00006006648,0.00001578576,0.000007177181,0.002848809],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7592714,"threshold_uncertainty_score":0.5921054,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08991675392504822,"score_gpt":0.3238771379795721,"score_spread":0.2339603840545239,"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."}}