{"id":"https://openalex.org/W2002409735","doi":"https://doi.org/10.1017/s096354831400011x","title":"The Largest Missing Value in a Sample of Geometric Random Variables","display_name":"The Largest Missing Value in a Sample of Geometric Random Variables","publication_year":2014,"publication_date":"2014-05-22","ids":{"openalex":"https://openalex.org/W2002409735","doi":"https://doi.org/10.1017/s096354831400011x","mag":"2002409735"},"language":"en","primary_location":{"id":"doi:10.1017/s096354831400011x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831400011x","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"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/A5044912186","display_name":"Margaret Archibald","orcid":"https://orcid.org/0000-0001-5635-6733"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"MARGARET ARCHIBALD","raw_affiliation_strings":["The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, PO Wits, 2050 Johannesburg, South Africa (e-mail:","university of the Witwatersrand"],"affiliations":[{"raw_affiliation_string":"The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, PO Wits, 2050 Johannesburg, South Africa (e-mail:","institution_ids":["https://openalex.org/I192619145"]},{"raw_affiliation_string":"university of the Witwatersrand","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036711367","display_name":"Arnold Knopfmacher","orcid":"https://orcid.org/0000-0003-1962-043X"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"ARNOLD KNOPFMACHER","raw_affiliation_strings":["The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, PO Wits, 2050 Johannesburg, South Africa (e-mail:","university of the Witwatersrand"],"affiliations":[{"raw_affiliation_string":"The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, PO Wits, 2050 Johannesburg, South Africa (e-mail:","institution_ids":["https://openalex.org/I192619145"]},{"raw_affiliation_string":"university of the Witwatersrand","institution_ids":["https://openalex.org/I192619145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044912186"],"corresponding_institution_ids":["https://openalex.org/I192619145"],"apc_list":null,"apc_paid":null,"fwci":0.2911,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.53758463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"5","first_page":"670","last_page":"685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10317","display_name":"Advanced Database Systems and Queries","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.7862957715988159},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.6907235383987427},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.6819220781326294},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.6128906011581421},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5884273052215576},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5747435092926025},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5551714897155762},{"id":"https://openalex.org/keywords/mean-value","display_name":"Mean value","score":0.4660080075263977},{"id":"https://openalex.org/keywords/expected-value","display_name":"Expected value","score":0.46242088079452515},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.42181670665740967},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4140075743198395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12877240777015686},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07597526907920837}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7862957715988159},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.6907235383987427},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6819220781326294},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.6128906011581421},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5884273052215576},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5747435092926025},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5551714897155762},{"id":"https://openalex.org/C2988626262","wikidata":"https://www.wikidata.org/wiki/Q2796622","display_name":"Mean value","level":2,"score":0.4660080075263977},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.46242088079452515},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.42181670665740967},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4140075743198395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12877240777015686},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07597526907920837},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s096354831400011x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354831400011x","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1488981024","https://openalex.org/W1552339458","https://openalex.org/W1583824100","https://openalex.org/W1597723816","https://openalex.org/W1918497102","https://openalex.org/W1967105343","https://openalex.org/W1973606520","https://openalex.org/W1987135975","https://openalex.org/W2025051251","https://openalex.org/W2030350455","https://openalex.org/W2033890710","https://openalex.org/W2046365524","https://openalex.org/W2079997965","https://openalex.org/W2127105762","https://openalex.org/W2500470525","https://openalex.org/W2739678403","https://openalex.org/W4300597689","https://openalex.org/W7066900558"],"related_works":["https://openalex.org/W2038157384","https://openalex.org/W2585279543","https://openalex.org/W57364028","https://openalex.org/W3043435145","https://openalex.org/W2545761980","https://openalex.org/W2047057931","https://openalex.org/W170825502","https://openalex.org/W4285709129","https://openalex.org/W2049621396","https://openalex.org/W2354392213"],"abstract_inverted_index":{"We":[0,54,83],"consider":[1,56],"samples":[2,57,108],"of":[3,26,90,116,129],"n":[4,91],"geometric":[5],"random":[6,29],"variables":[7,92],"with":[8,58,109,134],"parameter":[9],"0":[10],"<":[11,13],"p":[12,117,139],"1,":[14],"and":[15,47,66,77,124],"study":[16],"the":[17,23,33,40,45,59,62,67,80,85,94,100,103,127,130],"largest":[18,63,68,105],"missing":[19,64],"value,":[20],"that":[21,35,61,87,126],"is,":[22],"highest":[24],"value":[25,65,69,106],"such":[27],"a":[28,88],"variable,":[30],"less":[31],"than":[32],"maximum,":[34],"does":[36,71],"not":[37],"appear":[38,72],"in":[39,107],"sample.":[41],"Asymptotic":[42],"expressions":[43],"for":[44,49,102,138],"mean":[46,101],"variance":[48],"this":[50,79,110],"quantity":[51],"are":[52],"presented.":[53],"also":[55],"property":[60],"which":[70],"differ":[73],"by":[74],"exactly":[75],"one,":[76],"call":[78],"LMV":[81,95],"property.":[82,111],"find":[84],"probability":[86],"sample":[89],"has":[93,120],"property,":[96],"as":[97,99],"well":[98],"average":[104],"The":[112],"simpler":[113],"special":[114],"case":[115],"=":[118,140],"1/2":[119,141],"previously":[121,136],"been":[122],"studied,":[123],"verifying":[125],"results":[128],"present":[131],"paper":[132],"coincide":[133],"those":[135],"found":[137],"leads":[142],"to":[143],"some":[144],"interesting":[145],"identities.":[146]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}