{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.02797185,0.001640816,0.004397711,0.003603552,0.00347676,0.007142184,0.00748069,0.00727954,0.01131974],"category_scores_gemma":[0.1092629,0.001561527,0.004377701,0.004218874,0.01376508,0.01674645,0.01381912,0.01322194,0.001929123],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002507503,"about_ca_system_score_gemma":0.002243085,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001225307,"about_ca_topic_score_gemma":0.0006811809,"domain_scores_codex":[0.9841816,0.006460769,0.0005548124,0.003372212,0.004438148,0.0009924952],"domain_scores_gemma":[0.9072394,0.0767747,0.003955439,0.006014369,0.004175524,0.001840585],"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":[0.0000550808,0.00001993616,0.0002503558,0.0000588459,0.00004237206,0.0001154898,0.0001118783,0.001727524,0.0001793452,0.9915974,0.00214341,0.003698306],"study_design_scores_gemma":[0.00004596819,0.0000194224,0.0001387398,0.00002872005,0.00001941266,0.0002912975,0.00002070981,0.02442175,0.0001901451,0.9733565,0.001444952,0.00002257149],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02633666,0.00110278,0.9386124,0.01172522,0.0005392719,0.0000845301,0.0003013814,0.0004400263,0.02085773],"genre_scores_gemma":[0.6761326,0.002274275,0.2834143,0.01151614,0.003916055,0.001228967,0.0007385218,0.000999262,0.0197798],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02797185,"threshold_uncertainty_score":0.147931,"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."}}