{"id":"https://openalex.org/W2040713331","doi":"https://doi.org/10.1088/0026-1394/44/2/003","title":"Trapezoidal and triangular distributions for Type B evaluation of standard uncertainty","display_name":"Trapezoidal and triangular distributions for Type B evaluation of standard uncertainty","publication_year":2007,"publication_date":"2007-02-26","ids":{"openalex":"https://openalex.org/W2040713331","doi":"https://doi.org/10.1088/0026-1394/44/2/003","mag":"2040713331"},"language":"en","primary_location":{"id":"doi:10.1088/0026-1394/44/2/003","doi":"https://doi.org/10.1088/0026-1394/44/2/003","is_oa":false,"landing_page_url":"https://doi.org/10.1088/0026-1394/44/2/003","pdf_url":null,"source":{"id":"https://openalex.org/S7291761","display_name":"Metrologia","issn_l":"0026-1394","issn":["0026-1394","1681-7575"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Metrologia","raw_type":"journal-article"},"volume":null,"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/A5061215075","display_name":"Raghu N. Kacker","orcid":"https://orcid.org/0000-0002-7666-3391","observed_orcids":["https://orcid.org/0000-0002-7666-3391"]},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"government","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raghu N Kacker","raw_affiliation_strings":["Mathematical and Computational Science Division , National Institute of Standards and Technology , Gaithersburg, MD, 20899, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical and Computational Science Division , National Institute of Standards and Technology , Gaithersburg, MD, 20899, USA","institution_ids":["https://openalex.org/I1321296531"]}]},{"author_position":"last","author":{"id":null,"display_name":"James F Lawrence","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"government","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]},{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James F Lawrence","raw_affiliation_strings":["Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA","Mathematical and Computational Science Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA","institution_ids":["https://openalex.org/I162714631"]},{"raw_affiliation_string":"Mathematical and Computational Science Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA","institution_ids":["https://openalex.org/I1321296531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3325,"currency":"USD","value_usd":3325},"apc_paid":null,"fwci":4.0741,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.9412224,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"44","issue":"2","first_page":"117","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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":0.0038999998942017555,"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/T13500","display_name":"Probability and Statistical Research","score":0.002400000113993883,"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/trapezoidal-distribution","display_name":"trapezoidal distribution","score":0.9879999756813049},{"id":"https://openalex.org/keywords/triangular-distribution","display_name":"triangular distribution","score":0.9990000128746033},{"id":"https://openalex.org/keywords/uniform-distribution","display_name":"uniform distribution","score":0.9490000009536743},{"id":"https://openalex.org/keywords/type-b-evaluation","display_name":"type B evaluation","score":0.796999990940094},{"id":"https://openalex.org/keywords/standard-uncertainty","display_name":"standard uncertainty","score":0.9670000076293945},{"id":"https://openalex.org/keywords/skewed-distributions","display_name":"skewed distributions","score":0.8659999966621399},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"moment generating function","score":0.8619999885559082},{"id":"https://openalex.org/keywords/moments","display_name":"moments","score":0.6660000085830688},{"id":"https://openalex.org/keywords/bias-correction","display_name":"bias correction","score":0.6200000047683716},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.6039999723434448},{"id":"https://openalex.org/keywords/guide-to-the-expression-of-uncertainty-in-measurement","display_name":"Guide to the Expression of Uncertainty in Measurement","score":0.8610000014305115}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6517106294631958},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4001334607601166},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.38974863290786743},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36783382296562195},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33969390392303467},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33544033765792847},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.09315791726112366},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.03747105598449707},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1088/0026-1394/44/2/003","doi":"https://doi.org/10.1088/0026-1394/44/2/003","is_oa":false,"landing_page_url":"https://doi.org/10.1088/0026-1394/44/2/003","pdf_url":null,"source":{"id":"https://openalex.org/S7291761","display_name":"Metrologia","issn_l":"0026-1394","issn":["0026-1394","1681-7575"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Metrologia","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W149807329","https://openalex.org/W1632540354","https://openalex.org/W1970591590","https://openalex.org/W2025318362","https://openalex.org/W2031377355","https://openalex.org/W2065329544","https://openalex.org/W2137480309","https://openalex.org/W2170608154","https://openalex.org/W2533252699","https://openalex.org/W2795968596","https://openalex.org/W4232792366"],"related_works":["https://openalex.org/W2016811712","https://openalex.org/W2769115647","https://openalex.org/W4401094110","https://openalex.org/W2040850483","https://openalex.org/W2041431899","https://openalex.org/W2084139610","https://openalex.org/W2591137717","https://openalex.org/W4242766052","https://openalex.org/W1993515911","https://openalex.org/W2129941024"],"abstract_inverted_index":{"The":[0,34],"Guide":[1],"to":[2,31],"the":[3,12,58,65,76,104,110,124,161,166],"Expression":[4],"of":[5,60,75,89,103,119,123,156],"Uncertainty":[6],"in":[7,145,153,159],"Measurement":[8],"(GUM),":[9],"published":[10],"by":[11,25],"International":[13],"Organization":[14],"for":[15,149],"Standardization":[16],"(ISO),":[17],"recognizes":[18],"Type":[19,137],"B":[20,138],"state-of-knowledge":[21],"probability":[22,38,66],"distributions":[23,39,99],"specified":[24],"scientific":[26],"judgment":[27],"as":[28],"valid":[29],"means":[30],"quantify":[32],"uncertainty.":[33],"ISO-GUM":[35],"discusses":[36],"symmetric":[37],"only.":[40],"Sometimes":[41],"an":[42],"asymmetric":[43,55,139],"distribution":[44,51,70,141],"is":[45],"needed.":[46],"We":[47,63,93],"describe":[48,64],"a":[49,90,131,136,147,154],"trapezoidal":[50,91,105,125,140],"which":[52],"may":[53,142],"be":[54,143],"depending":[56],"on":[57],"settings":[59],"its":[61],"parameters.":[62],"density":[67],"function,":[68,80],"cumulative":[69],"function":[71,74],"(cdf),":[72],"inverse":[73],"cdf,":[77],"moment":[78,111],"generating":[79,112],"moments":[81],"about":[82],"origin":[83],"(zero),":[84],"expected":[85,115],"value":[86],"and":[87,97,117,158],"variance":[88],"distribution.":[92,106,126],"show":[94],"that":[95],"triangular":[96],"rectangular":[98],"are":[100],"special":[101,121],"cases":[102,122],"Then":[107],"we":[108,128],"derive":[109],"functions,":[113],"moments,":[114],"values":[116],"variances":[118],"various":[120],"Finally,":[127],"illustrate":[129],"through":[130],"real":[132],"life":[133],"example":[134],"how":[135],"useful":[144],"quantifying":[146,160],"correction":[148],"bias":[150],"(systematic":[151],"error)":[152],"result":[155],"measurement":[157],"standard":[162],"uncertainty":[163],"associated":[164],"with":[165],"correction.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-09-29T14:09:16.559479","created_date":"2016-06-24T00:00:00"}