{"id":"https://openalex.org/W3123384377","doi":"https://doi.org/10.1007/s11222-021-10055-1","title":"Efficient importance sampling for large sums of independent and identically distributed random variables","display_name":"Efficient importance sampling for large sums of independent and identically distributed random variables","publication_year":2021,"publication_date":"2021-10-11","ids":{"openalex":"https://openalex.org/W3123384377","doi":"https://doi.org/10.1007/s11222-021-10055-1","mag":"3123384377"},"language":"lv","primary_location":{"id":"doi:10.1007/s11222-021-10055-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-021-10055-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-021-10055-1.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11222-021-10055-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074019505","display_name":"Nadhir Ben Rached","orcid":"https://orcid.org/0000-0003-4471-4075"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nadhir Ben Rached","raw_affiliation_strings":["Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, RWTH Aachen University, Aachen, Germany","RWTH Aachen University"],"raw_orcid":"https://orcid.org/0000-0003-4471-4075","affiliations":[{"raw_affiliation_string":"Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"RWTH Aachen University","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013203959","display_name":"Abdul-Lateef Haji-Ali","orcid":"https://orcid.org/0000-0002-6243-0335"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Abdul-Lateef Haji-Ali","raw_affiliation_strings":["School of Mathematical and Computer Sciences,  Heriot-Watt University, Edinburgh, UK","School of Mathematical and Computer Sciences; Heriot-Watt University; Edinburgh UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Computer Sciences,  Heriot-Watt University, Edinburgh, UK","institution_ids":["https://openalex.org/I32062511"]},{"raw_affiliation_string":"School of Mathematical and Computer Sciences; Heriot-Watt University; Edinburgh UK","institution_ids":["https://openalex.org/I32062511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111520064","display_name":"Gerardo Rubino","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210133778","display_name":"Centre Inria de l'Universit\u00e9 de Rennes","ror":"https://ror.org/04040yw90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210133778"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gerardo Rubino","raw_affiliation_strings":["INRIA, Rennes - Bretagne Atlantique, Rennes, France","Inria Rennes, Bretagne Atlantique, Rennes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA, Rennes - Bretagne Atlantique, Rennes, France","institution_ids":["https://openalex.org/I4210133778","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Inria Rennes, Bretagne Atlantique, Rennes, France","institution_ids":["https://openalex.org/I4210133778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004939553","display_name":"Ra\u00fal Tempone","orcid":"https://orcid.org/0000-0003-1967-4446"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE","SA"],"is_corresponding":false,"raw_author_name":"Ra\u00fal Tempone","raw_affiliation_strings":["Alexander von Humboldt Professor in Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen, Germany","Computer, Electrical and Mathematical Sciences and Engineering Division(CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia","Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alexander von Humboldt Professor in Mathematics for Uncertainty Quantification, RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"Computer, Electrical and Mathematical Sciences and Engineering Division(CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]},{"raw_affiliation_string":"Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":0.1729,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48934102,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"31","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9993000030517578,"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":0.9993000030517578,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9965999722480774,"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/T11716","display_name":"Random Matrices and Applications","score":0.987500011920929,"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/estimator","display_name":"Estimator","score":0.7928246259689331},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.7328488230705261},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6783177852630615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6655150055885315},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.6605830192565918},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6334410309791565},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.631563663482666},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.5823089480400085},{"id":"https://openalex.org/keywords/natural-exponential-family","display_name":"Natural exponential family","score":0.5671248435974121},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5111718773841858},{"id":"https://openalex.org/keywords/gamma-distribution","display_name":"Gamma distribution","score":0.5075734853744507},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"Moment-generating function","score":0.5011835098266602},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4912070631980896},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4797012507915497},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4755268394947052},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.46850043535232544},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4684097170829773},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4565623998641968},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3247513175010681},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22198468446731567},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1684706211090088},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12119054794311523},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08293482661247253}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7928246259689331},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.7328488230705261},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6783177852630615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6655150055885315},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.6605830192565918},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6334410309791565},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.631563663482666},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.5823089480400085},{"id":"https://openalex.org/C60775368","wikidata":"https://www.wikidata.org/wiki/Q17099337","display_name":"Natural exponential family","level":3,"score":0.5671248435974121},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5111718773841858},{"id":"https://openalex.org/C149717495","wikidata":"https://www.wikidata.org/wiki/Q117806","display_name":"Gamma distribution","level":2,"score":0.5075734853744507},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.5011835098266602},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4912070631980896},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4797012507915497},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4755268394947052},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.46850043535232544},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4684097170829773},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4565623998641968},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3247513175010681},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22198468446731567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1684706211090088},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12119054794311523},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08293482661247253},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","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":4,"locations":[{"id":"doi:10.1007/s11222-021-10055-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-021-10055-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-021-10055-1.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2101.09514","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.09514","pdf_url":"https://arxiv.org/pdf/2101.09514","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":null,"raw_type":"text"},{"id":"mag:3123384377","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2101.09514.pdf","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":"doi:10.48550/arxiv.2101.09514","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2101.09514","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":"doi:10.1007/s11222-021-10055-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-021-10055-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-021-10055-1.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1170852293","display_name":null,"funder_award_id":"OSR-2019-CRG8-4033","funder_id":"https://openalex.org/F4320322320","funder_display_name":"King Abdullah University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320320041","display_name":"Royal Society of Edinburgh","ror":"https://ror.org/03kx2pj14"},{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"},{"id":"https://openalex.org/F4320324232","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3123384377.pdf","grobid_xml":"https://content.openalex.org/works/W3123384377.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W5385147","https://openalex.org/W34142743","https://openalex.org/W242065599","https://openalex.org/W604181985","https://openalex.org/W1522045078","https://openalex.org/W1998311240","https://openalex.org/W2077846544","https://openalex.org/W2099881771","https://openalex.org/W2100512474","https://openalex.org/W2101111766","https://openalex.org/W2127095832","https://openalex.org/W2142011291","https://openalex.org/W2145736413","https://openalex.org/W2147656391","https://openalex.org/W2154158634","https://openalex.org/W2157882677","https://openalex.org/W2158429877","https://openalex.org/W2261416239","https://openalex.org/W2275145915","https://openalex.org/W2276496321","https://openalex.org/W2428781461","https://openalex.org/W2556190538","https://openalex.org/W2613400311","https://openalex.org/W2780698077","https://openalex.org/W2952596376","https://openalex.org/W2953774778","https://openalex.org/W2963732797","https://openalex.org/W2963929939","https://openalex.org/W3009963299","https://openalex.org/W3102573515","https://openalex.org/W3155455898","https://openalex.org/W4211042066"],"related_works":["https://openalex.org/W2489225089","https://openalex.org/W3136232832","https://openalex.org/W2012815150","https://openalex.org/W1555033159","https://openalex.org/W2746996149","https://openalex.org/W2338962180","https://openalex.org/W2188190578","https://openalex.org/W2084838236","https://openalex.org/W3123669981","https://openalex.org/W2127090196","https://openalex.org/W65642992","https://openalex.org/W2159403046","https://openalex.org/W1993028513","https://openalex.org/W1888362598","https://openalex.org/W2944383996","https://openalex.org/W2077690391","https://openalex.org/W2415140658","https://openalex.org/W2769916088","https://openalex.org/W2922494004","https://openalex.org/W2196722904"],"abstract_inverted_index":{"Abstract":[0],"We":[1,57],"discuss":[2],"estimating":[3],"the":[4,7,62,106,109,125,158,164,168,174,248,259,280,284,288,291,296,301,327,335,338,348],"probability":[5,188],"that":[6,148,317],"sum":[8],"of":[9,108,112,138,154,246,267,277,283,290,337,350],"nonnegative":[10],"independent":[11],"and":[12,121,132,156,232,313],"identically":[13],"distributed":[14],"random":[15],"variables":[16],"falls":[17],"below":[18],"a":[19,83,318,343],"given":[20],"threshold,":[21],"i.e.,":[22],"$$\\mathbb":[23],"{P}(\\sum":[24],"_{i=1}^{N}{X_i}":[25],"\\le":[26],"\\gamma":[27],")$$":[28],"<mml:math":[29,73,114,199,210,223,234,270,357],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[30,74,115,200,211,224,235,271,358],"<mml:mrow>":[31,36,201,212,225,236],"<mml:mi>P</mml:mi>":[32],"<mml:mo>(</mml:mo>":[33],"<mml:msubsup>":[34],"<mml:mo>\u2211</mml:mo>":[35],"<mml:mi>i</mml:mi>":[37,45,118],"<mml:mo>=</mml:mo>":[38],"<mml:mn>1</mml:mn>":[39,229],"</mml:mrow>":[40,50,205,218,230,240],"<mml:mi>N</mml:mi>":[41],"</mml:msubsup>":[42],"<mml:msub>":[43,116],"<mml:mi>X</mml:mi>":[44,117],"</mml:msub>":[46,119],"<mml:mo>\u2264</mml:mo>":[47],"<mml:mi>\u03b3</mml:mi>":[48,75,272,359],"<mml:mo>)</mml:mo>":[49],"</mml:math>":[51,76,120,206,219,231,241,273,360],",":[52,207,220,279],"via":[53],"importance":[54],"sampling":[55,123],"(IS).":[56],"are":[58,192],"particularly":[59],"interested":[60],"in":[61,90,157,258,341,347],"rare":[63,159,260],"event":[64,160,261],"regime":[65,262,349],"when":[66],"N":[67,278,352],"is":[68,77,82,129,141],"large":[69,275,351],"and/or":[70,274,353],"$$\\gamma":[71,268,355],"$$":[72,269,356],"small.":[78],"The":[79,136,182],"exponential":[80,169,292,328],"twisting":[81,170,293,329],"popular":[84],"technique":[85,171],"for":[86,151,221],"similar":[87],"problems":[88],"that,":[89],"most":[91],"cases,":[92],"compares":[93],"favorably":[94],"to":[95,142,208,264],"other":[96],"estimators.":[97],"However,":[98],"it":[99],"has":[100],"some":[101],"limitations:":[102],"(i)":[103],"It":[104],"assumes":[105],"knowledge":[107],"moment-generating":[110],"function":[111],"$$X_i$$":[113],"(ii)":[122],"under":[124],"new":[126],"IS":[127,146,250,320,330],"PDF":[128,147,251,305,321],"not":[130,178],"straightforward":[131],"might":[133],"be":[134],"expensive.":[135],"aim":[137],"this":[139,244],"work":[140],"propose":[143],"an":[144],"alternative":[145],"approximately":[149],"yields,":[150],"certain":[152],"classes":[153],"distributions":[155,186],"regime,":[161],"at":[162,173,306],"least":[163],"same":[165,175,281],"performance":[166,282],"as":[167,195],"and,":[172],"time,":[176],"does":[177],"introduce":[179],"serious":[180],"limitations.":[181],"first":[183],"class":[184,245],"includes":[185],"whose":[187,304],"density":[189],"functions":[190],"(PDFs)":[191],"asymptotically":[193],"equivalent,":[194],"$$x":[196],"\\rightarrow":[197],"0$$":[198],"<mml:mi>x</mml:mi>":[202,215],"<mml:mo>\u2192</mml:mo>":[203],"<mml:mn>0</mml:mn>":[204,239],"$$bx^{p}$$":[209],"<mml:mi>b</mml:mi>":[213,237],"<mml:msup>":[214],"<mml:mi>p</mml:mi>":[216,226],"</mml:msup>":[217],"$$p&gt;-1$$":[222],"<mml:mo>&gt;</mml:mo>":[227,238],"<mml:mo>-</mml:mo>":[228],"$$b&gt;0$$":[233],".":[242,361],"For":[243],"distributions,":[247],"Gamma":[249,319],"with":[252,322],"appropriately":[253],"chosen":[254],"parameters":[255,324],"retrieves":[256],"approximately,":[257],"corresponding":[263],"small":[265,354],"values":[266,276],"estimator":[285,340],"based":[286],"on":[287],"use":[289],"technique.":[294],"In":[295],"second":[297],"class,":[298],"we":[299,314],"consider":[300],"Log-normal":[302],"setting,":[303],"zero":[307],"vanishes":[308],"faster":[309],"than":[310],"any":[311],"polynomial,":[312],"show":[315],"numerically":[316],"optimized":[323],"clearly":[325],"outperforms":[326],"PDF.":[331],"Numerical":[332],"experiments":[333],"validate":[334],"efficiency":[336],"proposed":[339],"delivering":[342],"highly":[344],"accurate":[345],"estimate":[346]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2022-07-25T00:00:00"}