{"id":"https://openalex.org/W99212099","doi":null,"title":"Estimating statistical characteristics under interval uncertainty and constraints: Mean, variance, covariance, and correlation","display_name":"Estimating statistical characteristics under interval uncertainty and constraints: Mean, variance, covariance, and correlation","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W99212099","mag":"99212099"},"language":"en","primary_location":{"id":"pmh:oai:digitalcommons.utep.edu:open_etd-3318","doi":null,"is_oa":true,"landing_page_url":"https://digitalcommons.utep.edu/open_etd/2319","pdf_url":"https://digitalcommons.utep.edu/open_etd/2319","source":{"id":"https://openalex.org/S4377196403","display_name":"scholarworks - UTEP (The University of Texas at El Paso)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I164936912","host_organization_name":"The University of Texas at El Paso","host_organization_lineage":["https://openalex.org/I164936912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Open Access Theses & Dissertations","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://digitalcommons.utep.edu/open_etd/2319","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044599707","display_name":"Ali Jalal-Kamali","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ali Jalal-Kamali","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5044599707"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00756776,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.002300000051036477,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.0020000000949949026,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/interval-uncertainty","display_name":"interval uncertainty","score":0.9120000004768372},{"id":"https://openalex.org/keywords/measurement-error-bounds","display_name":"measurement error bounds","score":0.7760000228881836},{"id":"https://openalex.org/keywords/sample-mean","display_name":"sample mean","score":0.5410000085830688},{"id":"https://openalex.org/keywords/sample-variance","display_name":"sample variance","score":0.9959999918937683},{"id":"https://openalex.org/keywords/covariance","display_name":"covariance","score":0.781000018119812},{"id":"https://openalex.org/keywords/correlation","display_name":"correlation","score":0.878000020980835},{"id":"https://openalex.org/keywords/np-hardness","display_name":"NP-hardness","score":0.8230000138282776},{"id":"https://openalex.org/keywords/interval-valued-data","display_name":"interval data","score":0.3160000145435333}],"concepts":[{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6821812391281128},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6786360740661621},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5710518956184387},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.5569185018539429},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4940217137336731},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.44198864698410034},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4065009355545044},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.092630535364151},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08567896485328674},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:digitalcommons.utep.edu:open_etd-3318","doi":null,"is_oa":true,"landing_page_url":"https://digitalcommons.utep.edu/open_etd/2319","pdf_url":"https://digitalcommons.utep.edu/open_etd/2319","source":{"id":"https://openalex.org/S4377196403","display_name":"scholarworks - UTEP (The University of Texas at El Paso)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I164936912","host_organization_name":"The University of Texas at El Paso","host_organization_lineage":["https://openalex.org/I164936912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Open Access Theses & Dissertations","raw_type":"text"},{"id":"pmh:oai:digitalcommons.utep.edu:dissertations-7273","doi":null,"is_oa":false,"landing_page_url":"https://digitalcommons.utep.edu/dissertations/AAI1513642","pdf_url":null,"source":{"id":"https://openalex.org/S4377196403","display_name":"scholarworks - UTEP (The University of Texas at El Paso)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I164936912","host_organization_name":"The University of Texas at El Paso","host_organization_lineage":["https://openalex.org/I164936912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ETD Collection for University of Texas, El Paso","raw_type":"text"},{"id":"pmh:oai:scholarworks.utep.edu:dissertations-7273","doi":null,"is_oa":false,"landing_page_url":"https://scholarworks.utep.edu/dissertations/AAI1513642","pdf_url":null,"source":{"id":"https://openalex.org/S4377196403","display_name":"scholarworks - UTEP (The University of Texas at El Paso)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I164936912","host_organization_name":"The University of Texas at El Paso","host_organization_lineage":["https://openalex.org/I164936912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ETD Collection for University of Texas, El Paso","raw_type":"text"},{"id":"pmh:oai:scholarworks.utep.edu:open_etd-3318","doi":null,"is_oa":false,"landing_page_url":"https://scholarworks.utep.edu/open_etd/2319","pdf_url":null,"source":{"id":"https://openalex.org/S4377196403","display_name":"scholarworks - UTEP (The University of Texas at El Paso)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I164936912","host_organization_name":"The University of Texas at El Paso","host_organization_lineage":["https://openalex.org/I164936912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Open Access Theses & Dissertations","raw_type":"text"},{"id":"mag:99212099","doi":null,"is_oa":false,"landing_page_url":"https://digitalcommons.utep.edu/open_etd/2319/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:digitalcommons.utep.edu:open_etd-3318","doi":null,"is_oa":true,"landing_page_url":"https://digitalcommons.utep.edu/open_etd/2319","pdf_url":"https://digitalcommons.utep.edu/open_etd/2319","source":{"id":"https://openalex.org/S4377196403","display_name":"scholarworks - UTEP (The University of Texas at El Paso)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I164936912","host_organization_name":"The University of Texas at El Paso","host_organization_lineage":["https://openalex.org/I164936912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Open Access Theses & Dissertations","raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W99212099.pdf","grobid_xml":"https://content.openalex.org/works/W99212099.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W296311487","https://openalex.org/W1507872748","https://openalex.org/W1537323566","https://openalex.org/W1592387255","https://openalex.org/W1968447210","https://openalex.org/W2000292097","https://openalex.org/W2020583713","https://openalex.org/W2021902442","https://openalex.org/W2024367676","https://openalex.org/W2037918059","https://openalex.org/W2111428526","https://openalex.org/W2121804746","https://openalex.org/W2129527059","https://openalex.org/W2169855231","https://openalex.org/W2754154881","https://openalex.org/W4254572943"],"related_works":["https://openalex.org/W157306916","https://openalex.org/W1540801505","https://openalex.org/W2169855231","https://openalex.org/W1511735263","https://openalex.org/W2021902442","https://openalex.org/W7019362061","https://openalex.org/W7100772810","https://openalex.org/W1599300978","https://openalex.org/W2115726592","https://openalex.org/W7095845540"],"abstract_inverted_index":{"In":[0,116],"many":[1],"practical":[2],"situations,":[3],"we":[4,15,27,101,120],"have":[5,102,121],"a":[6,11,20,29,52,72],"sample":[7,38,174,176],"of":[8,10,19,31,47,59,173,187,190,211],"objects":[9,65],"given":[12],"type.":[13],"When":[14,36],"measure":[16],"the":[17,37,43,48,56,64,97,104,108,122,126,137,144,164,185],"values":[18,32,49,85,159,172,189],"certain":[21],"quantity":[22,61],"x":[23],"for":[24,55,62,221],"these":[25,191],"objects,":[26],"get":[28],"sequence":[30],"x1,":[33],"\u2026,":[34],"xn.":[35],"is":[39,51,92,107,180,198,214],"large":[40],"enough,":[41],"then":[42],"arithmetic":[44],"mean":[45],"E":[46],"xi":[50,86,141,146,160,162,194],"good":[53,73],"approximation":[54,74],"average":[57],"value":[58,140],"this":[60,67,114,117,212],"all":[63],"from":[66,88,163],"class.":[68],"Other":[69],"expressions":[70],"provide":[71],"to":[75,143,170,183,215,232],"statistical":[76],"characteristics":[77,192],"such":[78,202,226],"as":[79],"variance,":[80,177],"covariance,":[81],"and":[82,90,230],"correlation.":[83],"The":[84,208],"come":[87],"measurements,":[89],"measurement":[91,105,123],"never":[93],"absolutely":[94],"accurate.":[95],"Often,":[96],"only":[98],"information":[99],"that":[100,136,200],"about":[103],"error":[106],"upper":[109],"bound":[110],"\u0394":[111,133,152,156],"i":[112,129,134],"on":[113],"error.":[115],"case,":[118],"once":[119],"result":[124],"x\u02dci,":[125],"condition":[127],":x\u02dc":[128],"\u2013":[130,151],"xi:":[131],"\u2264":[132],"implies":[135],"actual":[138],"(unknown)":[139],"belongs":[142],"interval":[145],"[special":[147],"characters":[148],"omitted]":[149],"[x\u02dci":[150],"i,":[153],"x\u02dci":[154],"+":[155],"i].":[157],"Different":[158],"\u2208":[161,195],"corresponding":[165],"intervals":[166],"lead,":[167],"in":[168,205],"general,":[169,206],"different":[171],"mean,":[175],"etc.":[178],"It":[179,197],"therefore":[181],"desirable":[182],"find":[184],"range":[186],"possible":[188],"when":[193],"xi.":[196],"known":[199],"evaluating":[201],"ranges":[203],"is,":[204],"NP-hard.":[207],"main":[209],"objective":[210],"thesis":[213],"design":[216],"feasible":[217],"(i.e.,":[218],"polynomial-time)":[219],"algorithms":[220,227],"practically":[222],"important":[223],"situations.":[224],"Several":[225],"are":[228],"described":[229],"proved":[231],"be":[233],"correct.":[234]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}