{"id":"W4402616598","doi":"10.1017/s1748499524000198","title":"Generalized Poisson random variable: its distributional properties and actuarial applications","year":2024,"lang":"en","type":"article","venue":"Annals of Actuarial Science","topic":"Statistical Distribution Estimation and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Prince Edward Island; Western University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Poisson distribution; Mathematics; Negative binomial distribution; Random variable; Binomial (polynomial); Conditional probability distribution; Applied mathematics; Zero-inflated model; Transformation (genetics); Compound Poisson distribution; Distribution (mathematics); Binomial distribution; Conditional expectation; Econometrics; Poisson regression; 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":[],"consensus_categories":[],"category_scores_codex":[0.0008338123,0.0001319968,0.0002049078,0.00009188737,0.0003835777,0.0002171532,0.0002622681,0.00006347003,0.000333755],"category_scores_gemma":[0.001919239,0.0001042597,0.00004932316,0.0008274834,0.0006019486,0.0003601374,0.00008417019,0.0001041201,0.00003227036],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002876977,"about_ca_system_score_gemma":0.0003772918,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002545831,"about_ca_topic_score_gemma":0.000001034115,"domain_scores_codex":[0.9984853,0.00003861963,0.0003851336,0.0003495569,0.0004746472,0.0002667698],"domain_scores_gemma":[0.9985954,0.0005130034,0.00009085562,0.0002041552,0.0004282345,0.0001683383],"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":[0.0000472767,0.00005451954,0.000002584031,0.00006290274,0.00001513006,2.841008e-7,0.00008197373,0.000007977594,0.01693537,0.9774095,0.002917414,0.002465112],"study_design_scores_gemma":[0.001248829,0.0000934811,0.0008429164,0.000161875,0.0001038213,0.00001726281,0.00005493103,0.05483858,0.04893715,0.8533465,0.039927,0.0004276098],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03662128,0.0003583685,0.9510887,0.006128842,0.0003293746,0.001084867,0.001346455,0.0002283528,0.002813733],"genre_scores_gemma":[0.9925923,0.00004844072,0.00663606,0.0001035134,0.0001951031,0.0001790817,0.00006804145,0.000008572644,0.0001688461],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9559711,"threshold_uncertainty_score":0.4251589,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1854241248568868,"score_gpt":0.4042898357007662,"score_spread":0.2188657108438795,"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."}}