{"id":"W3158535647","doi":"10.1016/j.spl.2021.109132","title":"On the number of trials needed to obtain <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e22\" altimg=\"si8.svg\"><mml:mi>k</mml:mi></mml:math> consecutive successes","year":2021,"lang":"en","type":"article","venue":"Statistics & Probability Letters","topic":"Statistical Mechanics and Entropy","field":"Physics and Astronomy","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Bernoulli distribution; Bernoulli trial; Probability distribution; Moment-generating function; Factorial; Combinatorics; Moment (physics); Sequence (biology); Function (biology); Random variable; Discrete mathematics; Statistics; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.01875738,0.001523587,0.00270799,0.001715073,0.0008369097,0.002065567,0.002645409,0.002903682,0.05074524],"category_scores_gemma":[0.147435,0.0008418394,0.001164908,0.001192587,0.001172324,0.002739366,0.002029797,0.003070391,0.01260887],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001898798,"about_ca_system_score_gemma":0.004359249,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002847803,"about_ca_topic_score_gemma":0.007132624,"domain_scores_codex":[0.9894271,0.003397823,0.001324798,0.001793523,0.003409219,0.000647506],"domain_scores_gemma":[0.8776197,0.09659517,0.003463715,0.01007441,0.009695858,0.00255111],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.05191202,0.002606288,0.02100126,0.001779811,0.001091231,0.0002262499,0.0005405526,0.07946018,0.0279785,0.04000101,0.0646125,0.7087905],"study_design_scores_gemma":[0.009615851,0.01373429,0.08222904,0.001432707,0.001307131,0.0009883265,0.0009047818,0.6406602,0.04214276,0.1662517,0.04000099,0.0007323031],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.3919992,0.003187547,0.4357981,0.008734069,0.00442789,0.01494644,0.02261093,0.01098859,0.1073073],"genre_scores_gemma":[0.7050992,0.001497657,0.2077969,0.001891257,0.0004967593,0.01053841,0.01166575,0.001742376,0.05927167],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.05074524,"threshold_uncertainty_score":0.1697598,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02427314597884781,"score_gpt":0.2780916704555688,"score_spread":0.253818524476721,"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."}}