{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0009048227,0.0002942044,0.0003776201,0.0000317273,0.0002706278,0.0001973546,0.0003333967,0.000113562,0.0004266945],"category_scores_gemma":[0.001894998,0.0002780474,0.0002415679,0.0002235416,0.0002579037,0.00008254324,0.0002383675,0.0003609714,0.0003044179],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000022999,"about_ca_system_score_gemma":0.0002791435,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009687173,"about_ca_topic_score_gemma":0.0000486951,"domain_scores_codex":[0.9973015,0.0003251389,0.0007898078,0.0005378937,0.0005266547,0.0005189863],"domain_scores_gemma":[0.9952822,0.003289139,0.0004255541,0.0006543436,0.0001547162,0.0001939956],"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":[0.0002297634,0.0002239823,0.00005449722,0.0001446643,0.0002895925,0.0000435058,0.0005303667,0.00009574887,0.001522005,0.9904249,0.005380093,0.001060912],"study_design_scores_gemma":[0.001937322,0.000577366,0.0002336645,0.0004854394,0.0007963327,0.0000227184,0.001408416,0.3593573,0.02380166,0.6072392,0.003141499,0.0009990803],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7857649,0.000008838545,0.2080113,0.002584808,0.0003873366,0.0001526319,0.002597979,0.0000249642,0.0004672813],"genre_scores_gemma":[0.9601686,0.000006878,0.03628927,0.002476784,0.0002647128,0.000241023,0.0004687228,0.00006080003,0.00002321331],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3831857,"threshold_uncertainty_score":0.9999672,"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."}}