{"id":"https://openalex.org/W1966280901","doi":"https://doi.org/10.1198/tast.2009.08104","title":"Revisiting the Classical Occupancy Problem","display_name":"Revisiting the Classical Occupancy Problem","publication_year":2009,"publication_date":"2009-10-28","ids":{"openalex":"https://openalex.org/W1966280901","doi":"https://doi.org/10.1198/tast.2009.08104","mag":"1966280901"},"language":"en","primary_location":{"id":"doi:10.1198/tast.2009.08104","doi":"https://doi.org/10.1198/tast.2009.08104","is_oa":false,"landing_page_url":"https://doi.org/10.1198/tast.2009.08104","pdf_url":null,"source":{"id":"https://openalex.org/S4179095","display_name":"The American Statistician","issn_l":"0003-1305","issn":["0003-1305","1537-2731"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Statistician","raw_type":"journal-article"},"volume":null,"type":"article","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/A5072229296","display_name":"Patricia Pepple Williamson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I184840846","display_name":"Virginia Commonwealth University","ror":"https://ror.org/02nkdxk79","country_code":"US","type":"education","lineage":["https://openalex.org/I184840846"]},{"id":"https://openalex.org/I58956616","display_name":"Case Western Reserve University","ror":"https://ror.org/051fd9666","country_code":"US","type":"education","lineage":["https://openalex.org/I58956616"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patricia Pepple Williamson","raw_affiliation_strings":["Patricia Pepple Williamson is Instructor, Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 . Darcy P. Mays is Associate Professor and Chair, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083 . Ghidewon Abay Asmerom is Associate Professor and Assistant Chair, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 . Yingying Yang is Graduate, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083. The authors thank Wojbor Woyczynski, Case Western Reserve University, for his helpful comments. The authors also thank the referee, associate editor, and editor for the very thorough and helpful review that contributed to substantial improvement of the article"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Patricia Pepple Williamson is Instructor, Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 . Darcy P. Mays is Associate Professor and Chair, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083 . Ghidewon Abay Asmerom is Associate Professor and Assistant Chair, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 . Yingying Yang is Graduate, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083. The authors thank Wojbor Woyczynski, Case Western Reserve University, for his helpful comments. The authors also thank the referee, associate editor, and editor for the very thorough and helpful review that contributed to substantial improvement of the article","institution_ids":["https://openalex.org/I184840846","https://openalex.org/I58956616"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079936664","display_name":"Darcy P. Mays","orcid":"https://orcid.org/0000-0001-6309-0611","observed_orcids":["https://orcid.org/0000-0001-6309-0611"]},"institutions":[{"id":"https://openalex.org/I184840846","display_name":"Virginia Commonwealth University","ror":"https://ror.org/02nkdxk79","country_code":"US","type":"education","lineage":["https://openalex.org/I184840846"]},{"id":"https://openalex.org/I58956616","display_name":"Case Western Reserve University","ror":"https://ror.org/051fd9666","country_code":"US","type":"education","lineage":["https://openalex.org/I58956616"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Darcy P. Mays","raw_affiliation_strings":["Patricia Pepple Williamson is Instructor, Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 . Darcy P. Mays is Associate Professor and Chair, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083 . Ghidewon Abay Asmerom is Associate Professor and Assistant Chair, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 . Yingying Yang is Graduate, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083. The authors thank Wojbor Woyczynski, Case Western Reserve University, for his helpful comments. The authors also thank the referee, associate editor, and editor for the very thorough and helpful review that contributed to substantial improvement of the article"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Patricia Pepple Williamson is Instructor, Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 . Darcy P. Mays is Associate Professor and Chair, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083 . Ghidewon Abay Asmerom is Associate Professor and Assistant Chair, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 . Yingying Yang is Graduate, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083. The authors thank Wojbor Woyczynski, Case Western Reserve University, for his helpful comments. The authors also thank the referee, associate editor, and editor for the very thorough and helpful review that contributed to substantial improvement of the article","institution_ids":["https://openalex.org/I184840846","https://openalex.org/I58956616"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037016565","display_name":"Ghidewon Abay\u2010Asmerom","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I184840846","display_name":"Virginia Commonwealth University","ror":"https://ror.org/02nkdxk79","country_code":"US","type":"education","lineage":["https://openalex.org/I184840846"]},{"id":"https://openalex.org/I58956616","display_name":"Case Western Reserve University","ror":"https://ror.org/051fd9666","country_code":"US","type":"education","lineage":["https://openalex.org/I58956616"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ghidewon Abay Asmerom","raw_affiliation_strings":["Patricia Pepple Williamson is Instructor, Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 . Darcy P. Mays is Associate Professor and Chair, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083 . Ghidewon Abay Asmerom is Associate Professor and Assistant Chair, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 . Yingying Yang is Graduate, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083. The authors thank Wojbor Woyczynski, Case Western Reserve University, for his helpful comments. The authors also thank the referee, associate editor, and editor for the very thorough and helpful review that contributed to substantial improvement of the article"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Patricia Pepple Williamson is Instructor, Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 . Darcy P. Mays is Associate Professor and Chair, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083 . Ghidewon Abay Asmerom is Associate Professor and Assistant Chair, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 . Yingying Yang is Graduate, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083. The authors thank Wojbor Woyczynski, Case Western Reserve University, for his helpful comments. The authors also thank the referee, associate editor, and editor for the very thorough and helpful review that contributed to substantial improvement of the article","institution_ids":["https://openalex.org/I184840846","https://openalex.org/I58956616"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059333469","display_name":"Yingying Yang","orcid":"https://orcid.org/0000-0002-7653-0601","observed_orcids":["https://orcid.org/0000-0002-7653-0601"]},"institutions":[{"id":"https://openalex.org/I184840846","display_name":"Virginia Commonwealth University","ror":"https://ror.org/02nkdxk79","country_code":"US","type":"education","lineage":["https://openalex.org/I184840846"]},{"id":"https://openalex.org/I58956616","display_name":"Case Western Reserve University","ror":"https://ror.org/051fd9666","country_code":"US","type":"education","lineage":["https://openalex.org/I58956616"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yingying Yang","raw_affiliation_strings":["Patricia Pepple Williamson is Instructor, Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 . Darcy P. Mays is Associate Professor and Chair, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083 . Ghidewon Abay Asmerom is Associate Professor and Assistant Chair, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 . Yingying Yang is Graduate, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083. The authors thank Wojbor Woyczynski, Case Western Reserve University, for his helpful comments. The authors also thank the referee, associate editor, and editor for the very thorough and helpful review that contributed to substantial improvement of the article"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Patricia Pepple Williamson is Instructor, Department of Statistics, Case Western Reserve University, Cleveland, OH 44106-7054 . Darcy P. Mays is Associate Professor and Chair, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083 . Ghidewon Abay Asmerom is Associate Professor and Assistant Chair, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284-2014 . Yingying Yang is Graduate, Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284-3083. The authors thank Wojbor Woyczynski, Case Western Reserve University, for his helpful comments. The authors also thank the referee, associate editor, and editor for the very thorough and helpful review that contributed to substantial improvement of the article","institution_ids":["https://openalex.org/I184840846","https://openalex.org/I58956616"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3867,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.82991256,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"63","issue":"4","first_page":"356","last_page":"360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.9599999785423279,"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":0.9599999785423279,"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":0.039400000125169754,"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":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/occupancy-problem","display_name":"occupancy problem","score":0.9440000057220459},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-second-kind","display_name":"Stirling numbers of the second kind","score":0.9449999928474426},{"id":"https://openalex.org/keywords/asymptotic-results","display_name":"asymptotic results","score":0.7609999775886536},{"id":"https://openalex.org/keywords/combinatorial-enumeration","display_name":"combinatorial enumeration","score":0.8360000252723694},{"id":"https://openalex.org/keywords/probability-education","display_name":"probability education","score":0.6150000095367432}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6361681222915649},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.6256914138793945},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5842892527580261},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5328401327133179},{"id":"https://openalex.org/C187825244","wikidata":"https://www.wikidata.org/wiki/Q372071","display_name":"Probability-generating function","level":4,"score":0.48692286014556885},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4451757073402405},{"id":"https://openalex.org/C160331591","wikidata":"https://www.wikidata.org/wiki/Q7075743","display_name":"Occupancy","level":2,"score":0.4362225830554962},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.3602578043937683},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3514571189880371},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07712528109550476},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1198/tast.2009.08104","doi":"https://doi.org/10.1198/tast.2009.08104","is_oa":false,"landing_page_url":"https://doi.org/10.1198/tast.2009.08104","pdf_url":null,"source":{"id":"https://openalex.org/S4179095","display_name":"The American Statistician","issn_l":"0003-1305","issn":["0003-1305","1537-2731"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-b","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Statistician","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:bes:amstat:v:63:i:4:y:2009:p:356-360","doi":null,"is_oa":false,"landing_page_url":"http://pubs.amstat.org/doi/abs/10.1198/tast.2009.08104","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Quality education","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/4"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1983710187","https://openalex.org/W1996441202","https://openalex.org/W2037581451","https://openalex.org/W2079633783","https://openalex.org/W2081059960","https://openalex.org/W2096768134","https://openalex.org/W2124181495","https://openalex.org/W2138217409","https://openalex.org/W2321328275","https://openalex.org/W2340364767","https://openalex.org/W3026721701"],"related_works":["https://openalex.org/W2194653021","https://openalex.org/W1992891197","https://openalex.org/W2077866208","https://openalex.org/W2115150096","https://openalex.org/W4416932225","https://openalex.org/W1601003675","https://openalex.org/W2059467574","https://openalex.org/W4406411469","https://openalex.org/W2995214147","https://openalex.org/W2327358451"],"abstract_inverted_index":{"This":[0,49],"article":[1],"is":[2,53,76,98],"offered":[3],"as":[4],"an":[5,30],"example":[6],"of":[7,21,59,72,87,94,105,116,129,136],"a":[8,19,39,134],"probability":[9,34,92],"problem,":[10,139],"simple":[11],"to":[12,17,55,67,79,85],"state,":[13],"but":[14],"rich":[15],"enough":[16],"permit":[18],"variety":[20],"explorations":[22],"by":[23,64,82],"students":[24],"with":[25],"adequate":[26],"analytical":[27],"skills":[28],"in":[29,33],"introductory":[31],"course":[32],"and":[35,107,120],"statistics.":[36],"It":[37],"involves":[38,112],"discrete":[40],"random":[41,50,96,131],"variable":[42,51,97],"originating":[43],"from":[44],"the":[45,73,88,113,117,137],"classical":[46],"occupancy":[47],"problem.":[48],"X":[52],"defined":[54],"be":[56,80],"how":[57],"many":[58],"N":[60,74],"elements":[61,75],"are":[62,124,140],"selected":[63],"or":[65,83],"assigned":[66,84],"K":[68,89],"individuals":[69],"when":[70],"each":[71],"equally":[77],"likely":[78],"chosen":[81],"any":[86],"individuals.":[90],"The":[91,110],"distribution":[93,111],"this":[95,130],"derived":[99],"utilizing":[100],"various":[101],"counting":[102],"rules,":[103],"properties":[104],"probability,":[106],"observing":[108],"trends.":[109],"Stirling":[114],"numbers":[115],"second":[118],"kind":[119],"some":[121],"asymptotic":[122],"results":[123],"given.":[125],"Several":[126],"interesting":[127],"applications":[128],"variable,":[132],"including":[133],"variant":[135],"birthday":[138],"described.":[141]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}