{"id":"https://openalex.org/W2099499846","doi":"https://doi.org/10.1080/03610910802592812","title":"Simple and Accurate Approximations for Computing Covariance Matrices of Gamma and Weibull Order Statistics","display_name":"Simple and Accurate Approximations for Computing Covariance Matrices of Gamma and Weibull Order Statistics","publication_year":2009,"publication_date":"2009-02-06","ids":{"openalex":"https://openalex.org/W2099499846","doi":"https://doi.org/10.1080/03610910802592812","mag":"2099499846"},"language":"en","primary_location":{"id":"doi:10.1080/03610910802592812","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910802592812","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","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/A5078467361","display_name":"Scott M. Lesch","orcid":null},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]},{"id":"https://openalex.org/I4210157790","display_name":"Statistical Research (United States)","ror":"https://ror.org/058eg8775","country_code":"US","type":"company","lineage":["https://openalex.org/I4210157790"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. M. Lesch","raw_affiliation_strings":["Statistical Consulting Collaboratory, University of California","Statistical Consulting Collaboratory, University of California , Riverside, California, USA"],"affiliations":[{"raw_affiliation_string":"Statistical Consulting Collaboratory, University of California","institution_ids":["https://openalex.org/I4210157790"]},{"raw_affiliation_string":"Statistical Consulting Collaboratory, University of California , Riverside, California, USA","institution_ids":["https://openalex.org/I103635307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012280723","display_name":"Barry C. Arnold","orcid":"https://orcid.org/0000-0001-6952-2075"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]},{"id":"https://openalex.org/I2803209242","display_name":"University of California System","ror":"https://ror.org/00pjdza24","country_code":"US","type":"education","lineage":["https://openalex.org/I2803209242"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. C. Arnold","raw_affiliation_strings":["University of California","Department of Statistics, University of California, Riverside, California, USA;"],"affiliations":[{"raw_affiliation_string":"University of California","institution_ids":["https://openalex.org/I2803209242"]},{"raw_affiliation_string":"Department of Statistics, University of California, Riverside, California, USA;","institution_ids":["https://openalex.org/I103635307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034400738","display_name":"Daniel R. Jeske","orcid":"https://orcid.org/0000-0002-0214-7992"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]},{"id":"https://openalex.org/I2803209242","display_name":"University of California System","ror":"https://ror.org/00pjdza24","country_code":"US","type":"education","lineage":["https://openalex.org/I2803209242"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. R. Jeske","raw_affiliation_strings":["University of California","Department of Statistics, University of California, Riverside, California, USA;"],"affiliations":[{"raw_affiliation_string":"University of California","institution_ids":["https://openalex.org/I2803209242"]},{"raw_affiliation_string":"Department of Statistics, University of California, Riverside, California, USA;","institution_ids":["https://openalex.org/I103635307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078467361"],"corresponding_institution_ids":["https://openalex.org/I103635307","https://openalex.org/I4210157790"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.14920713,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"38","issue":"3","first_page":"590","last_page":"609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9969000220298767,"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"}},"topics":[{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9969000220298767,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.991599977016449,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.974399983882904,"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/order-statistic","display_name":"Order statistic","score":0.7402046322822571},{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":0.7101562023162842},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.7040516138076782},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6549959778785706},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5835132598876953},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5646947026252747},{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.5539657473564148},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5019519329071045},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.48324069380760193},{"id":"https://openalex.org/keywords/f-distribution","display_name":"F-distribution","score":0.414359986782074},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.2726287543773651}],"concepts":[{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.7402046322822571},{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.7101562023162842},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.7040516138076782},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6549959778785706},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5835132598876953},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5646947026252747},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.5539657473564148},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5019519329071045},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.48324069380760193},{"id":"https://openalex.org/C4162061","wikidata":"https://www.wikidata.org/wiki/Q177144","display_name":"F-distribution","level":3,"score":0.414359986782074},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2726287543773651},{"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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610910802592812","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910802592812","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1552947278","https://openalex.org/W1989165165","https://openalex.org/W1991995757","https://openalex.org/W2004736169","https://openalex.org/W2007722976","https://openalex.org/W2008086028","https://openalex.org/W2009895211","https://openalex.org/W2013155585","https://openalex.org/W2014204884","https://openalex.org/W2023014669","https://openalex.org/W2042143966","https://openalex.org/W2048742607","https://openalex.org/W2063622671","https://openalex.org/W2080860655","https://openalex.org/W2108997649","https://openalex.org/W2109533003","https://openalex.org/W2130560745","https://openalex.org/W2132891001","https://openalex.org/W2151038992","https://openalex.org/W2330147958","https://openalex.org/W2504767107","https://openalex.org/W2904627153","https://openalex.org/W4229723287","https://openalex.org/W4233409427","https://openalex.org/W4235881100","https://openalex.org/W4236493446","https://openalex.org/W4239846612","https://openalex.org/W4248517295","https://openalex.org/W4249174515","https://openalex.org/W4251613382","https://openalex.org/W4299419703"],"related_works":["https://openalex.org/W3083898685","https://openalex.org/W1973754976","https://openalex.org/W189075692","https://openalex.org/W2379986491","https://openalex.org/W4390513996","https://openalex.org/W2904683338","https://openalex.org/W2003768768","https://openalex.org/W2488265634","https://openalex.org/W2074872957","https://openalex.org/W2099499846"],"abstract_inverted_index":{"In":[0],"this":[1,124,133],"article,":[2],"we":[3],"propose":[4],"a":[5,60,117],"simple":[6],"technique":[7],"that":[8,99],"can":[9,113,135],"be":[10,114,136],"used":[11,137],"to":[12,103,138],"calculate":[13],"accurate":[14,140],"approximations":[15,102,145],"for":[16,39,49,86,116,146,156],"the":[17,28,41,46,68,82,104,157],"covariances":[18,42],"of":[19,27,33,45,107,120,149],"Weibull":[20,110],"and/or":[21],"Gamma":[22,108],"order":[23,35,47,111,150],"statistics,":[24,151],"given":[25],"knowledge":[26],"corresponding":[29],"means":[30],"and":[31,43,64,95,109,152],"variances":[32,44],"these":[34,50],"statistics.":[36],"Ratio":[37],"formulas":[38],"relating":[40],"statistics":[48,112],"two":[51],"probability":[52],"distribution":[53],"functions":[54,148],"(pdf's)":[55],"are":[56,76,128],"intuitively":[57],"derived":[58],"from":[59],"first-order":[61],"Mosteller":[62],"approximation,":[63],"then":[65],"refined":[66],"using":[67,89,123],"Blom":[69,74],"adjustment":[70],"technique.":[71],"The":[72],"necessary":[73],"coefficients":[75],"in":[77],"turn":[78],"found":[79],"by":[80],"optimizing":[81],"well-known":[83],"recursive":[84],"formula":[85],"mixed":[87],"moments":[88],"standard":[90],"nonlinear":[91],"estimation":[92],"techniques.":[93],"Analytical":[94],"simulation":[96],"results":[97],"confirm":[98],"very":[100],"good":[101],"covariance":[105],"matrices":[106],"obtained":[115],"wide":[118],"range":[119],"shape":[121],"parameters":[122],"methodology.":[125],"Four":[126],"examples":[127],"provided":[129],"which":[130],"demonstrate":[131],"how":[132],"approach":[134],"derive":[139],"o-BLU":[141],"weights,":[142],"precise":[143,153],"variance":[144],"linear":[147],"power":[154],"calculations":[155],"Gini":[158],"test":[159],"statistic.":[160]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-02-01T03:34:12.195049","created_date":"2025-10-10T00:00:00"}