{"id":"https://openalex.org/W4297347584","doi":"https://doi.org/10.3390/a15100350","title":"Estimating Tail Probabilities of Random Sums of Phase-Type Scale Mixture Random Variables","display_name":"Estimating Tail Probabilities of Random Sums of Phase-Type Scale Mixture Random Variables","publication_year":2022,"publication_date":"2022-09-27","ids":{"openalex":"https://openalex.org/W4297347584","doi":"https://doi.org/10.3390/a15100350"},"language":"en","primary_location":{"id":"doi:10.3390/a15100350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15100350","pdf_url":"https://www.mdpi.com/1999-4893/15/10/350/pdf?version=1666700272","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/15/10/350/pdf?version=1666700272","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112865442","display_name":"Hui Yao","orcid":null},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Hui Yao","raw_affiliation_strings":["School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089135298","display_name":"Thomas Taimre","orcid":"https://orcid.org/0000-0003-4470-7668"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Thomas Taimre","raw_affiliation_strings":["School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112865442"],"corresponding_institution_ids":["https://openalex.org/I165143802"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.3274,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61827036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"15","issue":"10","first_page":"350","last_page":"350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9951000213623047,"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/random-variable","display_name":"Random variable","score":0.5964512825012207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5948454737663269},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5918506383895874},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"Moment-generating function","score":0.5238832831382751},{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.5010178089141846},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4961124360561371},{"id":"https://openalex.org/keywords/heavy-tailed-distribution","display_name":"Heavy-tailed distribution","score":0.4798519015312195},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4387509226799011},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42678558826446533},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4246140122413635},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3877277076244354},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.37737709283828735},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.28555813431739807}],"concepts":[{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5964512825012207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5948454737663269},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5918506383895874},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.5238832831382751},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.5010178089141846},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4961124360561371},{"id":"https://openalex.org/C1602530","wikidata":"https://www.wikidata.org/wiki/Q1472677","display_name":"Heavy-tailed distribution","level":3,"score":0.4798519015312195},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4387509226799011},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42678558826446533},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4246140122413635},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3877277076244354},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37737709283828735},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.28555813431739807},{"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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a15100350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15100350","pdf_url":"https://www.mdpi.com/1999-4893/15/10/350/pdf?version=1666700272","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a1358678fe414c72816e36672bd5a925","is_oa":true,"landing_page_url":"https://doaj.org/article/a1358678fe414c72816e36672bd5a925","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 15, Iss 10, p 350 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/15/10/350/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a15100350","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 15; Issue 10; Pages: 350","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a15100350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15100350","pdf_url":"https://www.mdpi.com/1999-4893/15/10/350/pdf?version=1666700272","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4297347584.pdf","grobid_xml":"https://content.openalex.org/works/W4297347584.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W5385147","https://openalex.org/W1514890731","https://openalex.org/W1550502786","https://openalex.org/W1570713732","https://openalex.org/W1977691343","https://openalex.org/W2019055161","https://openalex.org/W2019623327","https://openalex.org/W2059423650","https://openalex.org/W2077846544","https://openalex.org/W2132474128","https://openalex.org/W2144755793","https://openalex.org/W2149405017","https://openalex.org/W2171557682","https://openalex.org/W2613795777","https://openalex.org/W2963736472","https://openalex.org/W3102259966","https://openalex.org/W4232729308","https://openalex.org/W6634057643"],"related_works":["https://openalex.org/W2168519368","https://openalex.org/W2049434049","https://openalex.org/W2566241227","https://openalex.org/W4382601967","https://openalex.org/W4224311898","https://openalex.org/W2096321176","https://openalex.org/W2997019937","https://openalex.org/W2948303187","https://openalex.org/W2950559747","https://openalex.org/W2182862251"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,94,97,102,118,165,168,180,184],"problem":[3],"of":[4,8,11,14,18,31,63,96,120,123,128,146,149,152,167,175,183],"estimating":[5,54,143],"tail":[6,144],"probabilities":[7,145],"random":[9,22,37,42,147],"sums":[10,148],"scale":[12,121,150],"mixture":[13,122,151],"phase-type":[15,41,124,153],"distributions\u2014a":[16],"class":[17,119,174],"distributions":[19,64,154],"corresponding":[20],"to":[21,110],"variables":[23],"which":[24,155],"can":[25,69],"be":[26,70,83],"represented":[27],"as":[28],"a":[29,32,40,172],"product":[30],"non-negative":[33],"but":[34,106],"otherwise":[35],"arbitrary":[36],"variable":[38],"with":[39],"variable.":[43],"Our":[44],"motivation":[45],"arises":[46],"from":[47],"applications":[48],"in":[49,72,85],"risk,":[50],"queueing":[51],"problems":[52],"for":[53,117,142,171],"ruin":[55],"probabilities,":[56],"and":[57,68,159,178],"waiting":[58],"time":[59],"distributions,":[60,177],"respectively.":[61],"Mixtures":[62],"are":[65,108,113,131],"flexible":[66],"models":[67],"exploited":[71],"modelling":[73],"non-life":[74],"insurance":[75],"loss":[76],"amounts.":[77],"Classical":[78],"rare-event":[79],"simulation":[80,140],"algorithms":[81],"cannot":[82],"implemented":[84],"this":[86,129],"setting":[87],"because":[88],"these":[89,107,135],"methods":[90,141,186],"typically":[91],"rely":[92],"on":[93],"availability":[95],"cumulative":[98],"distribution":[99],"function":[100],"or":[101,112],"moment":[103],"generating":[104],"function,":[105],"difficult":[109],"compute":[111],"not":[114],"even":[115],"available":[116],"distributions.":[125],"The":[126],"contributions":[127],"paper":[130],"that":[132],"we":[133],"address":[134],"issues":[136],"by":[137],"proposing":[138],"alternative":[139],"combine":[156],"importance":[157],"sampling":[158],"conditional":[160],"Monte":[161],"Carlo":[162],"methods,":[163],"showing":[164],"efficiency":[166],"proposed":[169],"estimators":[170],"wide":[173],"scaling":[176],"validating":[179],"empirical":[181],"performance":[182],"suggested":[185],"via":[187],"numerical":[188],"experimentation.":[189]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}