{"id":"https://openalex.org/W7097869971","doi":null,"title":"Institute of Statistics Mimeo Series No. 1466 September 1984RANDOM HYPERPLANE INTERSECTING A FIXED LINE IN Rn AND THE CAUCIIY DISTRIBUTIO~","display_name":"Institute of Statistics Mimeo Series No. 1466 September 1984RANDOM HYPERPLANE INTERSECTING A FIXED LINE IN Rn AND THE CAUCIIY DISTRIBUTIO~","publication_year":null,"publication_date":null,"ids":{"openalex":"https://openalex.org/W7097869971"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.6594","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.6594","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.ncsu.edu/library/mimeo.archive/ISMS_1984_1466.pdf","raw_type":"text"},"parent_works":[],"lineage":["https://openalex.org/W7097869971"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ibrahim A","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ibrahim A","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Ibrahim A","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ibrahim A","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.5127000212669373,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.5127000212669373,"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"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.42820000648498535,"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":0.022700000554323196,"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/cauchy-distribution","display_name":"Cauchy distribution","score":0.9110000133514404},{"id":"https://openalex.org/keywords/random-hyperplanes","display_name":"random hyperplanes","score":0.824999988079071}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7864999771118164},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7817999720573425},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5382000207901001},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.5177000164985657},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5170999765396118},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4796999990940094},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4632999897003174},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4020000100135803},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34700000286102295},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3398999869823456},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29809999465942383},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2646999955177307}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.6594","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.6594","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stat.ncsu.edu/library/mimeo.archive/ISMS_1984_1466.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2044342573","https://openalex.org/W2524249436","https://openalex.org/W2080528280","https://openalex.org/W1964705506","https://openalex.org/W2783830670","https://openalex.org/W786851397","https://openalex.org/W2024226895","https://openalex.org/W2334950951","https://openalex.org/W1968510219","https://openalex.org/W2002361938"],"abstract_inverted_index":{"of":[0,70,72,139],"independent":[1],"Cauchy":[2,5,132],"random":[3],"variables":[4],"distribution;":[6],"product":[7],"and":[8,31,46,75,133],"quotient":[9],"Let":[10,35,64],"L":[11],"be":[12,37,67],"a":[13,38,48,104],"fixed":[14],"line":[15],"in":[16,40],"R":[17,29,41],"n":[18,30,42,45,125],"given":[19,49],"by":[20,51],"the":[21,52,68,122],"equation":[22,53],"L(t)":[23,65],"B":[24],"+":[25,126],"tV,":[26],"B,V":[27],"E":[28,33,59,89],"t":[32],"R.":[34],"P(c)":[36],"hyperplane":[39],"Consider":[43],"X":[44,77,120,129],"assume":[47],"n-l":[50,96],"c.P":[54],"=":[55,108],"0,":[56],"where":[57,128],"c":[58,66,85,87],"Sand":[60],"c.V":[61],"#":[62,92],"o.":[63],"point":[69],"intersection":[71],"Land":[73],"P(c),":[74],"define":[76],"(P(c))":[78],"Sgn":[79],"(t)":[80],"II":[81],"L(t)-":[82],"L(0)":[83],"II.":[84],"1":[86],"{c":[88],"Sn-":[90],"Ic.v":[91],"o}":[93],"to":[94],"R,":[95],"S":[97,107],"\u2022":[98],"v":[99,109],"as":[100,103],"aX":[101],"n_ln":[102],"map":[105],"from":[106],"uniform":[110],"distribution":[111],"over":[112],"We":[113],"show":[114],"that":[115],"for":[116],"every":[117],"n>":[118],"2,":[119],"has":[121],"same":[123],"distribution-":[124],"b,":[127],"is":[130],"standard":[131],"a,b":[134],"are":[135,142],"constants.":[136],"Some":[137],"consequences":[138],"this":[140],"result":[141],"discussed.":[143],"1.":[144]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2025-10-27T00:00:00"}