{"id":"https://openalex.org/W3211128224","doi":"https://doi.org/10.1080/03610918.2021.1995752","title":"Nonparametric sequential estimation of the cumulative function by orthogonal series and application in reliability","display_name":"Nonparametric sequential estimation of the cumulative function by orthogonal series and application in reliability","publication_year":2021,"publication_date":"2021-10-26","ids":{"openalex":"https://openalex.org/W3211128224","doi":"https://doi.org/10.1080/03610918.2021.1995752","mag":"3211128224"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2021.1995752","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2021.1995752","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/A5012373440","display_name":"Karima Lagha","orcid":null},"institutions":[{"id":"https://openalex.org/I187560010","display_name":"University of B\u00e9ja\u00efa","ror":"https://ror.org/03yb2hp88","country_code":"DZ","type":"education","lineage":["https://openalex.org/I187560010"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Karima Lagha","raw_affiliation_strings":["Laboratory LaMOS, University of Bejaia","Laboratory LaMOS, University of Bejaia, Bejaia, Algeria"],"affiliations":[{"raw_affiliation_string":"Laboratory LaMOS, University of Bejaia","institution_ids":["https://openalex.org/I187560010"]},{"raw_affiliation_string":"Laboratory LaMOS, University of Bejaia, Bejaia, Algeria","institution_ids":["https://openalex.org/I187560010"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027089979","display_name":"Lamia Djerroud","orcid":null},"institutions":[{"id":"https://openalex.org/I187560010","display_name":"University of B\u00e9ja\u00efa","ror":"https://ror.org/03yb2hp88","country_code":"DZ","type":"education","lineage":["https://openalex.org/I187560010"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Lamia Djerroud","raw_affiliation_strings":["Laboratory LaMOS, University of Bejaia","Laboratory LaMOS, University of Bejaia, Bejaia, Algeria"],"affiliations":[{"raw_affiliation_string":"Laboratory LaMOS, University of Bejaia","institution_ids":["https://openalex.org/I187560010"]},{"raw_affiliation_string":"Laboratory LaMOS, University of Bejaia, Bejaia, Algeria","institution_ids":["https://openalex.org/I187560010"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053585589","display_name":"Sma\u00efl Adjabi","orcid":"https://orcid.org/0000-0001-5024-6322"},"institutions":[{"id":"https://openalex.org/I187560010","display_name":"University of B\u00e9ja\u00efa","ror":"https://ror.org/03yb2hp88","country_code":"DZ","type":"education","lineage":["https://openalex.org/I187560010"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Smail Adjabi","raw_affiliation_strings":["Laboratory LaMOS, University of Bejaia","Laboratory LaMOS, University of Bejaia, Bejaia, Algeria"],"affiliations":[{"raw_affiliation_string":"Laboratory LaMOS, University of Bejaia","institution_ids":["https://openalex.org/I187560010"]},{"raw_affiliation_string":"Laboratory LaMOS, University of Bejaia, Bejaia, Algeria","institution_ids":["https://openalex.org/I187560010"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012373440"],"corresponding_institution_ids":["https://openalex.org/I187560010"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16503157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"52","issue":"11","first_page":"5633","last_page":"5654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9994999766349792,"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":0.9994999766349792,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9825000166893005,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9663000106811523,"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":0.8156479597091675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.670508623123169},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5722251534461975},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5674996376037598},{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":0.5670375227928162},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5635569095611572},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5534690022468567},{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.5020413398742676},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.43487539887428284},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.42812296748161316},{"id":"https://openalex.org/keywords/log-normal-distribution","display_name":"Log-normal distribution","score":0.42808279395103455},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.4190128445625305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22155159711837769},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.21655163168907166}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8156479597091675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.670508623123169},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5722251534461975},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5674996376037598},{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.5670375227928162},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5635569095611572},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5534690022468567},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.5020413398742676},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43487539887428284},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.42812296748161316},{"id":"https://openalex.org/C151620405","wikidata":"https://www.wikidata.org/wiki/Q826116","display_name":"Log-normal distribution","level":2,"score":0.42808279395103455},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.4190128445625305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22155159711837769},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.21655163168907166},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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":1,"locations":[{"id":"doi:10.1080/03610918.2021.1995752","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2021.1995752","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":22,"referenced_works":["https://openalex.org/W231360518","https://openalex.org/W414247571","https://openalex.org/W1984122233","https://openalex.org/W1986078173","https://openalex.org/W1988568575","https://openalex.org/W2006762757","https://openalex.org/W2018538722","https://openalex.org/W2026126531","https://openalex.org/W2067359653","https://openalex.org/W2068659855","https://openalex.org/W2079587951","https://openalex.org/W2104822561","https://openalex.org/W2162300068","https://openalex.org/W2203405306","https://openalex.org/W2288747288","https://openalex.org/W2316533424","https://openalex.org/W2422683983","https://openalex.org/W2520661443","https://openalex.org/W2576572248","https://openalex.org/W2992131518","https://openalex.org/W4254932737","https://openalex.org/W4390868916"],"related_works":["https://openalex.org/W3083898685","https://openalex.org/W1973754976","https://openalex.org/W2113227311","https://openalex.org/W2804662986","https://openalex.org/W2889670096","https://openalex.org/W2901719776","https://openalex.org/W3164394228","https://openalex.org/W74879638","https://openalex.org/W2321361761","https://openalex.org/W2160662276"],"abstract_inverted_index":{"This":[0],"article":[1],"proposes":[2],"the":[3,8,30,34,46,61,70,75,96,121,132,135,166],"orthogonal":[4],"series":[5],"method":[6,84],"for":[7],"cumulative":[9],"distribution":[10],"function":[11],"estimation":[12],"based":[13],"on":[14],"a":[15,86,105],"random":[16,97],"number":[17],"of":[18,33,48,60,69,74,134],"observations":[19,62],"Nt,":[20],"which":[21],"may":[22],"be":[23],"recorded":[24],"in":[25,128],"time":[26],"(0,t].":[27],"We":[28,54],"give":[29],"statistical":[31],"properties":[32],"estimator":[35,76,112],"(bias,":[36],"variance,":[37],"mean":[38,41],"square":[39,42],"error,":[40,44],"integrated":[43],"and":[45,50,63,85,116,137,148],"rate":[47,139],"convergence)":[49],"some":[51],"asymptotic":[52],"properties.":[53],"consider":[55],"that":[56,165],"Nt":[57],"is":[58,77,108,113,124],"independent":[59],"Nt\u2192P\u221e":[64],"as":[65],"t\u2192\u221e.":[66],"The":[67,82,110,162],"choice":[68],"smoothing":[71],"parameter":[72],"(bandwidth)":[73],"investigated":[78,125],"by":[79,90,158],"two":[80],"methods:":[81],"Kronmal\u2013Tarter":[83],"new":[87],"technique":[88],"proposed":[89,160,167],"Saadi":[91],"et":[92],"al.":[93],"adapted":[94],"to":[95,120,130],"sample":[98],"size":[99],"case.":[100],"A":[101,151],"detailed":[102],"study":[103,131],"with":[104,126],"Dirichlet":[106],"basis":[107],"presented.":[109],"obtained":[111],"asymptotically":[114],"unbiased":[115],"consistent.":[117],"An":[118],"application":[119],"reliability":[122,136],"field":[123],"simulations":[127],"order":[129],"behavior":[133],"failure":[138],"estimators,":[140],"from":[141],"different":[142],"life":[143],"distributions,":[144],"namely:":[145],"Lognormal,":[146],"Gamma,":[147],"Weibull":[149],"distributions.":[150],"real":[152],"lifetime":[153],"data":[154],"sets":[155],"are":[156,169],"analyzed":[157],"our":[159],"approach.":[161],"results":[163],"show":[164],"estimators":[168],"performant.":[170]},"counts_by_year":[],"updated_date":"2026-03-06T06:45:51.903784","created_date":"2025-10-10T00:00:00"}
