{"id":"W2808441222","doi":"10.48550/arxiv.1805.02803","title":"Convergence rates in the law of large numbers and new kinds of convergence of random variables","year":2018,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Probability and Risk Models","field":"Decision Sciences","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Concordia University","funders":"Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China","keywords":"Independent and identically distributed random variables; Law of large numbers; Convergence (economics); Convergence of random variables; Proofs of convergence of random variables; Mathematics; Random variable; Convergence tests; Normal convergence; Applied mathematics; Rate of convergence; Statistics; Sum of normally distributed random variables; Computer science; Key (lock); Economics","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":[],"consensus_categories":[],"category_scores_codex":[0.003813215,0.0002131542,0.0007374244,0.000209604,0.00007097889,0.00002340143,0.001811672,0.0002769178,0.0003593506],"category_scores_gemma":[0.0006428576,0.0001566982,0.00020437,0.0008939118,0.001167172,0.0002630853,0.0008781907,0.0002858148,0.000009625472],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002391602,"about_ca_system_score_gemma":0.0003345446,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004074278,"about_ca_topic_score_gemma":0.001439568,"domain_scores_codex":[0.9973454,0.0006122295,0.0007321403,0.0007264756,0.0003464773,0.0002372338],"domain_scores_gemma":[0.9958026,0.001684276,0.0008418802,0.00111413,0.0004650986,0.00009197356],"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":[0.001126653,0.0003973499,0.2157791,0.0003035581,0.0001467287,0.00002541732,0.006209824,0.03550684,0.0004683018,0.7388572,0.001091501,0.00008764266],"study_design_scores_gemma":[0.002647529,0.0001268012,0.008045118,0.0002609799,0.0001303871,0.000002161184,0.002181504,0.05230629,0.004875256,0.9285128,0.0005820495,0.0003291826],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9592299,0.0002054997,0.03614743,0.0000684097,0.0003158751,0.0003769884,0.0001060246,0.000008169919,0.003541666],"genre_scores_gemma":[0.9988084,0.000479614,0.0002730897,0.00004858148,0.0000179162,4.288617e-7,0.000003581984,0.000005715176,0.0003626249],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2077339,"threshold_uncertainty_score":0.6389966,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1892772345629229,"score_gpt":0.2852863344633817,"score_spread":0.0960090999004588,"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."}}