{"id":"https://openalex.org/W59634454","doi":"https://doi.org/10.1007/978-1-4757-3843-8_20","title":"The Law of Large Numbers and the Central Limit Theorem","display_name":"The Law of Large Numbers and the Central Limit Theorem","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W59634454","doi":"https://doi.org/10.1007/978-1-4757-3843-8_20","mag":"59634454"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4757-3843-8_20","doi":"https://doi.org/10.1007/978-1-4757-3843-8_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4757-3843-8_20","pdf_url":null,"source":{"id":"https://openalex.org/S4210168872","display_name":"Textbooks in mathematical sciences","issn_l":"1431-9381","issn":["1431-9381"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Textbooks in mathematical sciences","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2476550113","display_name":"Activity-Based Statistics"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029643986","display_name":"Richard L. Scheaffer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard L. Scheaffer","raw_affiliation_strings":["University of Florida, USA","[University of Florida]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida, USA","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"[University of Florida]","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111565339","display_name":"Ann E. Watkins","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I127339247","display_name":"California State University System","ror":"https://ror.org/020qm1538","country_code":"US","type":"education","lineage":["https://openalex.org/I127339247"]},{"id":"https://openalex.org/I157638225","display_name":"California State University, Northridge","ror":"https://ror.org/005f5hv41","country_code":"US","type":"education","lineage":["https://openalex.org/I157638225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ann Watkins","raw_affiliation_strings":["California State University, Northridge, USA","CALIFORNIA STATE UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California State University, Northridge, USA","institution_ids":["https://openalex.org/I157638225"]},{"raw_affiliation_string":"CALIFORNIA STATE UNIVERSITY","institution_ids":["https://openalex.org/I127339247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083405793","display_name":"Mrudulla Gnanadesikan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I32907511","display_name":"Fairleigh Dickinson University","ror":"https://ror.org/04wkzvc75","country_code":"US","type":"education","lineage":["https://openalex.org/I32907511"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mrudulla Gnanadesikan","raw_affiliation_strings":["Fairleigh Dickinson University, USA","Fairleigh-Dickinson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fairleigh Dickinson University, USA","institution_ids":["https://openalex.org/I32907511"]},{"raw_affiliation_string":"Fairleigh-Dickinson University","institution_ids":["https://openalex.org/I32907511"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070174468","display_name":"Jeffrey A. Witmer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I70571728","display_name":"Oberlin College","ror":"https://ror.org/05ac26z88","country_code":"US","type":"education","lineage":["https://openalex.org/I70571728"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeffrey A. Witmer","raw_affiliation_strings":["Oberlin College, USA","Oberlin College >  >  >  >"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oberlin College, USA","institution_ids":["https://openalex.org/I70571728"]},{"raw_affiliation_string":"Oberlin College >  >  >  >","institution_ids":["https://openalex.org/I70571728"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7489,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.90263368,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"92","last_page":"96"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11875","display_name":"Statistics Education and Methodologies","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"law of large numbers","score":0.9990000128746033},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"central limit theorem","score":1.0},{"id":"https://openalex.org/keywords/sampling-variability","display_name":"sampling variability","score":0.7680000066757202},{"id":"https://openalex.org/keywords/sample-proportion","display_name":"sample proportion","score":0.7639999985694885},{"id":"https://openalex.org/keywords/coin-toss","display_name":"coin tossing","score":0.5580000281333923},{"id":"https://openalex.org/keywords/polling-accuracy","display_name":"polling accuracy","score":0.3630000054836273},{"id":"https://openalex.org/keywords/large-samples","display_name":"large samples","score":0.40700000524520874}],"concepts":[{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.7082431316375732},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4776802659034729},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4736151397228241},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4523223638534546},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.43584197759628296},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.41142675280570984},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3957408666610718},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.23939469456672668},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.2130405604839325},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.16934213042259216},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14622515439987183},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13638201355934143},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4757-3843-8_20","doi":"https://doi.org/10.1007/978-1-4757-3843-8_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4757-3843-8_20","pdf_url":null,"source":{"id":"https://openalex.org/S4210168872","display_name":"Textbooks in mathematical sciences","issn_l":"1431-9381","issn":["1431-9381"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Textbooks in mathematical sciences","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Peace, justice, and strong institutions","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/16"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2798819106","https://openalex.org/W2897876927","https://openalex.org/W3092094169","https://openalex.org/W2189170925","https://openalex.org/W1165020812","https://openalex.org/W2411429408","https://openalex.org/W2995391497","https://openalex.org/W2285927776","https://openalex.org/W2353396818","https://openalex.org/W2377661431"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2025-10-10T00:00:00"}
