{"id":"W2108293464","doi":"10.1016/s1007-5704(03)00037-6","title":"Fractional Poisson Process","year":2003,"lang":"en","type":"article","venue":"Communications in Nonlinear Science and Numerical Simulation","topic":"Fractional Differential Equations Solutions","field":"Mathematics","cited_by":298,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Compound Poisson process; Poisson distribution; Mathematics; Applied mathematics; Generalization; Compound Poisson distribution; Fractional calculus; Exponential function; Phase-type distribution; Exponential distribution; Markov process; Counting process; Poisson process; Mathematical analysis; Poisson regression; Statistics","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":[0.000856324,0.0005931586,0.0009770734,0.001717186,0.001150833,0.002548566,0.0008359469,0.002010285,0.01680982],"category_scores_gemma":[0.004773079,0.000276695,0.0009060481,0.001313782,0.001524172,0.002236342,0.0015046,0.001542769,0.00204123],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001260561,"about_ca_system_score_gemma":0.0007235066,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001035094,"about_ca_topic_score_gemma":0.0003623596,"domain_scores_codex":[0.9995095,0.00009907611,0.00002689383,0.00009755859,0.0001990406,0.00006796775],"domain_scores_gemma":[0.9989864,0.0002967951,0.0001348309,0.0001847585,0.0002674915,0.0001297032],"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":[0.0000263604,0.00001567631,0.0001255171,0.00002844482,0.00000987328,0.000126203,0.00005734155,0.004337166,0.001221911,0.9857086,0.002228059,0.006114787],"study_design_scores_gemma":[0.00002252275,0.00002568091,0.0003723269,0.00002576977,0.0000253792,0.0005078241,0.00007582684,0.109098,0.001995481,0.864958,0.02286165,0.00003167324],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1025992,0.00521326,0.6084269,0.01033305,0.007165178,0.0001115105,0.0005510032,0.000745197,0.2648547],"genre_scores_gemma":[0.8519027,0.003379823,0.02186143,0.00103888,0.002069494,0.00007916288,0.0003384623,0.0001564174,0.1191737],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01680982,"threshold_uncertainty_score":0.05623448,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1221629333010942,"score_gpt":0.4397849128229801,"score_spread":0.317621979521886,"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."}}