{"id":"https://openalex.org/W1985231478","doi":"https://doi.org/10.1109/tit.2013.2241174","title":"Chaotic Method for Generating $q$-Gaussian Random Variables","display_name":"Chaotic Method for Generating $q$-Gaussian Random Variables","publication_year":2013,"publication_date":"2013-01-17","ids":{"openalex":"https://openalex.org/W1985231478","doi":"https://doi.org/10.1109/tit.2013.2241174","mag":"1985231478"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2241174","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2241174","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1205.1690","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001619132","display_name":"Ken Umeno","orcid":"https://orcid.org/0000-0002-9162-1261"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ken Umeno","raw_affiliation_strings":["Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan","Dept. of Appl. Math. & Phys., Kyoto Univ., Kyoto, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]},{"raw_affiliation_string":"Dept. of Appl. Math. & Phys., Kyoto Univ., Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101531043","display_name":"Akihiro Sato","orcid":"https://orcid.org/0000-0001-7410-6324"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Aki-Hiro Sato","raw_affiliation_strings":["Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan","Dept. of Appl. Math. & Phys., Kyoto Univ., Kyoto, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]},{"raw_affiliation_string":"Dept. of Appl. Math. & Phys., Kyoto Univ., Kyoto, Japan","institution_ids":["https://openalex.org/I22299242"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I22299242"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14218382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"5","first_page":"3199","last_page":"3209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.968500018119812,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.7507967352867126},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.680957555770874},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6338366270065308},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.517131507396698},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5131464600563049},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4721631705760956},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.4715597331523895},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.44320690631866455},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.40619611740112305},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33831897377967834},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3312832713127136},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.27227672934532166},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25564301013946533},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15928778052330017},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1290881335735321},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1050390899181366}],"concepts":[{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.7507967352867126},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.680957555770874},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6338366270065308},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.517131507396698},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5131464600563049},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4721631705760956},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.4715597331523895},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.44320690631866455},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.40619611740112305},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33831897377967834},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3312832713127136},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27227672934532166},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25564301013946533},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15928778052330017},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1290881335735321},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1050390899181366},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2013.2241174","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2241174","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1205.1690","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.1690","pdf_url":"https://arxiv.org/pdf/1205.1690","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1985231478","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1205.1690","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.760.2861","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.760.2861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1205.1690.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1205.1690","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1205.1690","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1205.1690","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.1690","pdf_url":"https://arxiv.org/pdf/1205.1690","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5944823943","display_name":"\u4e71\u6570\u306e\u7406\u8ad6\u3068\u64ec\u4f3c\u4e71\u6570\u691c\u5b9a","funder_award_id":"24540153","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1985231478.pdf","grobid_xml":"https://content.openalex.org/works/W1985231478.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W234899517","https://openalex.org/W1528589873","https://openalex.org/W1598573928","https://openalex.org/W1776349877","https://openalex.org/W1972501654","https://openalex.org/W1973429805","https://openalex.org/W1979593580","https://openalex.org/W1982073844","https://openalex.org/W1991843946","https://openalex.org/W1999029409","https://openalex.org/W2010213277","https://openalex.org/W2057037947","https://openalex.org/W2059374347","https://openalex.org/W2074466695","https://openalex.org/W2087349373","https://openalex.org/W2095669515","https://openalex.org/W2096509667","https://openalex.org/W2113961056","https://openalex.org/W2152100192","https://openalex.org/W2482944896","https://openalex.org/W4231687540","https://openalex.org/W6631861121"],"related_works":["https://openalex.org/W2949450384","https://openalex.org/W2952469878","https://openalex.org/W2129977757","https://openalex.org/W2122886989","https://openalex.org/W3010646696","https://openalex.org/W2344262842","https://openalex.org/W2053157356","https://openalex.org/W3087675345","https://openalex.org/W1489542724","https://openalex.org/W2032217995","https://openalex.org/W2094255923","https://openalex.org/W2090992490","https://openalex.org/W1992076274","https://openalex.org/W2078766198","https://openalex.org/W2987815332","https://openalex.org/W2091783809","https://openalex.org/W2118126685","https://openalex.org/W284989950","https://openalex.org/W2131611181","https://openalex.org/W2057200620"],"abstract_inverted_index":{"<?Pub":[0],"Dtl=\"\"?>":[1],"This":[2],"study":[3],"proposes":[4],"a":[5,20],"pseudorandom":[6],"number":[7,74],"generator":[8,75],"of":[9,22,48,79,120],"<formula":[10,23,29,67,80,95,121,129,150,158],"formulatype=\"inline\"":[11,24,30,68,81,96,122,130,151,159],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12,25,31,69,82,97,123,131,152,160],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[13,26,32,70,83,132,161],"Notation=\"TeX\">$q$</tex>":[14],"</formula>":[15,134,163],"-Gaussian":[16,72,101],"random":[17,73],"variables":[18],"for":[19,76,118,149],"range":[21],"Notation=\"TeX\">$q$</tex></formula>":[27,71,84,100,126,155],"values,":[28],"Notation=\"TeX\">$-\\infty":[33],"&lt;":[34,36],"q":[35],"3$</tex></formula>":[37],",":[38],"based":[39,58],"on":[40,51,59],"deterministic":[41],"chaotic":[42,49],"map":[43,56],"dynamics.":[44],"Our":[45],"method":[46,107],"consists":[47],"maps":[50],"the":[52,60,66,109,140],"unit":[53],"circle":[54],"and":[55,85,90],"dynamics":[57],"piecewise":[61],"linear":[62],"map.":[63],"We":[64],"perform":[65],"several":[77],"values":[78,119],"conduct":[86],"both":[87],"Kolmogorov\u2013Smirnov":[88],"(KS)":[89],"Anderson\u2013Darling":[91],"(AD)":[92],"tests.":[93],"The":[94],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[98,124,153],"<tex":[99,125,154],"samples":[102],"generated":[103],"by":[104],"our":[105],"proposed":[106],"pass":[108,139],"KS":[110],"test":[111,142],"at":[112,143],"more":[113,144],"than":[114,145],"5%":[115,146],"significance":[116,147],"level":[117,148],"ranging":[127,156],"from":[128,157],"Notation=\"TeX\">$-{1.0}$</tex>":[133],"to":[135,164],"2.7,":[136],"while":[137],"they":[138],"AD":[141],"Notation=\"TeX\">$-{1}$</tex>":[162],"2.4.":[165]},"counts_by_year":[],"updated_date":"2026-07-09T07:52:08.696243","created_date":"2025-10-10T00:00:00"}
