{"id":"W3009489148","doi":"10.2139/ssrn.3547890","title":"A Counterexample to the Central Limit Theorem for Pairwise Independent Random Variables Having a Common Absolutely Continuous Arbitrary Margin","year":2020,"lang":"en","type":"article","venue":"SSRN Electronic Journal","topic":"Bayesian Methods and Mixture Models","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Kensington Health","funders":"","keywords":"Central limit theorem; Mathematics; Independent and identically distributed random variables; Pairwise independence; Random variable; Asymptotic distribution; Sequence (biology); Gaussian; Limit (mathematics); Independence (probability theory); Distribution (mathematics); Combinatorics; Infinity; Pairwise comparison; Discrete mathematics; Statistics; Mathematical analysis; Sum of normally distributed random variables; Estimator","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":[0.003782441,0.0002703171,0.0004187919,0.00006570144,0.0004358574,0.0004712015,0.00166577,0.00009771918,0.00001094903],"category_scores_gemma":[0.0001548425,0.0001858018,0.0002698169,0.0002733068,0.0000337793,0.0003396352,0.0002199963,0.001486105,0.000008345422],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003190755,"about_ca_system_score_gemma":0.001302803,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008525819,"about_ca_topic_score_gemma":0.0003621571,"domain_scores_codex":[0.9957812,0.0004123144,0.000456459,0.0004481201,0.000387431,0.002514502],"domain_scores_gemma":[0.9985878,0.0003948448,0.0002123566,0.0003888239,0.0001021591,0.0003139852],"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":[0.0005532383,0.00007623235,0.000146157,0.0000152772,0.0002078657,0.00001861911,0.003151951,0.0001250479,0.0006556105,0.8675242,0.001915119,0.1256106],"study_design_scores_gemma":[0.004773544,0.001221363,0.0003413202,0.00007923567,0.000106783,0.0007847949,0.0006412907,0.05452003,0.0004217839,0.9132742,0.02325219,0.0005834865],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.006498253,0.001750331,0.97503,0.01520408,0.0003513472,0.0007134873,0.00001063887,0.00008266107,0.0003591994],"genre_scores_gemma":[0.8960442,0.0004226805,0.09567645,0.006661867,0.0008539064,0.00005752547,0.000003439898,0.00004430299,0.0002356357],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8895459,"threshold_uncertainty_score":0.7576777,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01692197034990967,"score_gpt":0.2424999085154538,"score_spread":0.2255779381655441,"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."}}