{"id":"https://openalex.org/W4233659442","doi":"https://doi.org/10.1007/978-3-642-04898-2_167","title":"Chebyshev\u2019s Inequality","display_name":"Chebyshev\u2019s Inequality","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W4233659442","doi":"https://doi.org/10.1007/978-3-642-04898-2_167"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-04898-2_167","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-04898-2_167","pdf_url":null,"source":{"id":"https://openalex.org/S4306513849","display_name":"International Encyclopedia of Statistical Science","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Encyclopedia of Statistical Science","raw_type":"book-chapter"},"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/A5090566468","display_name":"Gerold Alsmeyer","orcid":"https://orcid.org/0000-0001-7843-4130"},"institutions":[{"id":"https://openalex.org/I4210123467","display_name":"Institut f\u00fcr Angewandte Statistik","ror":"https://ror.org/03abd2075","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210123467"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Gerold Alsmeyer","raw_affiliation_strings":["Institut f\u00fcr Mathematische Statistik, Einsteinstra\u00dfe 62, D-48149, M\u00fcnster, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematische Statistik, Einsteinstra\u00dfe 62, D-48149, M\u00fcnster, Germany","institution_ids":["https://openalex.org/I4210123467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090566468"],"corresponding_institution_ids":["https://openalex.org/I4210123467"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.57269155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"239","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9434000253677368,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9434000253677368,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/chebyshev-filter","display_name":"Chebyshev filter","score":0.667996346950531},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6020517349243164},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.523112952709198},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.4535757303237915},{"id":"https://openalex.org/keywords/chebyshevs-inequality","display_name":"Chebyshev's inequality","score":0.41677555441856384},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4021747410297394},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.3560376763343811},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.33112144470214844},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32938921451568604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24087539315223694},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.14928919076919556},{"id":"https://openalex.org/keywords/kantorovich-inequality","display_name":"Kantorovich inequality","score":0.13431236147880554}],"concepts":[{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.667996346950531},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6020517349243164},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.523112952709198},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.4535757303237915},{"id":"https://openalex.org/C71564387","wikidata":"https://www.wikidata.org/wiki/Q249514","display_name":"Chebyshev's inequality","level":5,"score":0.41677555441856384},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4021747410297394},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3560376763343811},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33112144470214844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32938921451568604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24087539315223694},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.14928919076919556},{"id":"https://openalex.org/C206399364","wikidata":"https://www.wikidata.org/wiki/Q3154001","display_name":"Kantorovich inequality","level":4,"score":0.13431236147880554}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-04898-2_167","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-04898-2_167","pdf_url":null,"source":{"id":"https://openalex.org/S4306513849","display_name":"International Encyclopedia of Statistical Science","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Encyclopedia of Statistical Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2382532955","https://openalex.org/W2106962382","https://openalex.org/W2541927208","https://openalex.org/W2368445280","https://openalex.org/W2056379897","https://openalex.org/W2074316639","https://openalex.org/W2365714836","https://openalex.org/W2969580250","https://openalex.org/W4213342932","https://openalex.org/W1481531974"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
