{"id":"W4417101080","doi":"10.5539/ijsp.v13n2p66","title":"An Alternative Proof for the Difference of Two Non-central Chi-square Quadratic Polynomials to be Non-central Chi-square","year":2024,"lang":"","type":"article","venue":"International Journal of Statistics and Probability","topic":"Statistical Distribution Estimation and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Quadratic equation; Characterization (materials science); Polynomial; Multivariate statistics; Random variable; Orthogonal polynomials","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.01273817,0.001021422,0.001312965,0.002000237,0.001312295,0.002034079,0.002700858,0.002006181,0.01769237],"category_scores_gemma":[0.072281,0.0005327442,0.001711285,0.002161914,0.005291858,0.006579541,0.004653477,0.006904708,0.00211872],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001308925,"about_ca_system_score_gemma":0.003056142,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001451893,"about_ca_topic_score_gemma":0.001306696,"domain_scores_codex":[0.9929191,0.002083943,0.0003870489,0.001606329,0.002146122,0.0008574558],"domain_scores_gemma":[0.9165978,0.05590333,0.004167667,0.005435278,0.01566981,0.002226109],"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":[0.0002677268,0.0001381171,0.004777987,0.0003380101,0.00009536331,0.001240448,0.0009996821,0.004382082,0.006649121,0.9561058,0.006932469,0.01807336],"study_design_scores_gemma":[0.0002331933,0.0004192287,0.006024048,0.00010068,0.00008007746,0.003273254,0.0005804718,0.06673206,0.004487175,0.9011891,0.01676227,0.0001184001],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03217799,0.0005989114,0.9500653,0.003011295,0.0006537347,0.0001094384,0.0005258399,0.0002700203,0.01258748],"genre_scores_gemma":[0.7409167,0.0007596324,0.2413933,0.005023343,0.00197238,0.0004459159,0.0008105966,0.000210056,0.00846812],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01769237,"threshold_uncertainty_score":0.06736666,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05627128371100137,"score_gpt":0.3860690462067291,"score_spread":0.3297977624957277,"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."}}