{"id":"https://openalex.org/W3109645803","doi":"https://doi.org/10.3390/axioms11030084","title":"Generalized Beta Prime Distribution Applied to Finite Element Error Approximation","display_name":"Generalized Beta Prime Distribution Applied to Finite Element Error Approximation","publication_year":2022,"publication_date":"2022-02-22","ids":{"openalex":"https://openalex.org/W3109645803","doi":"https://doi.org/10.3390/axioms11030084","mag":"3109645803"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11030084","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030084","pdf_url":"https://www.mdpi.com/2075-1680/11/3/84/pdf?version=1645685615","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/3/84/pdf?version=1645685615","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003172935","display_name":"Jo\u00ebl Chaskalovic","orcid":"https://orcid.org/0000-0003-1263-5313"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210133716","display_name":"Institut Jean Le Rond d'Alembert","ror":"https://ror.org/043we9s22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210095849","https://openalex.org/I4210133716"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jo\u00ebl Chaskalovic","raw_affiliation_strings":["Jean Le Rond d\u2019Alembert Institute, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France"],"affiliations":[{"raw_affiliation_string":"Jean Le Rond d\u2019Alembert Institute, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France","institution_ids":["https://openalex.org/I4210133716","https://openalex.org/I39804081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014379082","display_name":"Franck Assous","orcid":"https://orcid.org/0000-0001-6280-6497"},"institutions":[{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Franck Assous","raw_affiliation_strings":["Department of Mathematics, Ariel University, Ariel 40700, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ariel University, Ariel 40700, Israel","institution_ids":["https://openalex.org/I52170813"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003172935"],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210133716"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.1864,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58048715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"3","first_page":"84","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"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":0.9980000257492065,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9908999800682068,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.753894567489624},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6146384477615356},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5898647308349609},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.5411734580993652},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5005011558532715},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49274924397468567},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4861418902873993},{"id":"https://openalex.org/keywords/finite-element-limit-analysis","display_name":"Finite element limit analysis","score":0.46220067143440247},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.43520307540893555},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4162721633911133},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.41527673602104187},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3695494532585144},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18243974447250366},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17135241627693176},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15986856818199158},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.13269585371017456}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.753894567489624},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6146384477615356},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5898647308349609},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.5411734580993652},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5005011558532715},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49274924397468567},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4861418902873993},{"id":"https://openalex.org/C93949632","wikidata":"https://www.wikidata.org/wiki/Q5450392","display_name":"Finite element limit analysis","level":4,"score":0.46220067143440247},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.43520307540893555},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4162721633911133},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.41527673602104187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3695494532585144},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18243974447250366},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17135241627693176},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15986856818199158},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.13269585371017456},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms11030084","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030084","pdf_url":"https://www.mdpi.com/2075-1680/11/3/84/pdf?version=1645685615","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03832086v1","is_oa":true,"landing_page_url":"https://cnrs.hal.science/hal-03832086","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, 2022, 11 (3), pp.84. &#x27E8;10.3390/axioms11030084&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:ddad0b7bc224433d857e148c1b56bc1a","is_oa":true,"landing_page_url":"https://doaj.org/article/ddad0b7bc224433d857e148c1b56bc1a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 3, p 84 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/3/84/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11030084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 3; Pages: 84","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11030084","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11030084","pdf_url":"https://www.mdpi.com/2075-1680/11/3/84/pdf?version=1645685615","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3109645803.pdf","grobid_xml":"https://content.openalex.org/works/W3109645803.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W105675650","https://openalex.org/W1515623627","https://openalex.org/W1998560353","https://openalex.org/W2005436751","https://openalex.org/W2075665712","https://openalex.org/W2076625949","https://openalex.org/W2082187902","https://openalex.org/W2332839435","https://openalex.org/W2399908251","https://openalex.org/W2479014450","https://openalex.org/W2795162166","https://openalex.org/W2895188618","https://openalex.org/W2963564659","https://openalex.org/W2963685981","https://openalex.org/W2994993073","https://openalex.org/W3004771696","https://openalex.org/W3031733054","https://openalex.org/W3099671035","https://openalex.org/W3103055458","https://openalex.org/W3134305408","https://openalex.org/W3215216471","https://openalex.org/W4200161749","https://openalex.org/W4205634890","https://openalex.org/W4251436587","https://openalex.org/W4252488881","https://openalex.org/W6785848069"],"related_works":["https://openalex.org/W1567939749","https://openalex.org/W1977906733","https://openalex.org/W2367880982","https://openalex.org/W2350013512","https://openalex.org/W2021654023","https://openalex.org/W1573186872","https://openalex.org/W4254088695","https://openalex.org/W2134127411","https://openalex.org/W2185206193","https://openalex.org/W2165887158"],"abstract_inverted_index":{"In":[0,149],"this":[1,86],"paper,":[2],"we":[3,60,88],"propose":[4,61],"a":[5,121,131],"new":[6,57],"family":[7],"of":[8,42,46,95,138],"probability":[9,58,110,137],"laws":[10,59],"based":[11,38],"on":[12,39,68],"the":[13,20,32,40,43,49,72,81,93,96,99,103,109,136,139],"Generalized":[14],"Beta":[15],"Prime":[16],"distribution":[17],"to":[18,54],"evaluate":[19],"relative":[21,33],"accuracy":[22,36],"between":[23,98],"two":[24],"Lagrange":[25],"finite":[26,34,74,122,132,152],"elements":[27],"Pk1":[28,73,124],"and":[29,102],"Pk2,(k1&lt;k2).":[30],"Usually,":[31],"element":[35,75,123,133,153],"is":[37,76,155],"comparison":[41],"asymptotic":[44],"speed":[45],"convergence,":[47],"when":[48,115],"mesh":[50],"size":[51],"h":[52,116],"goes":[53,117],"zero.":[55],"The":[56],"here":[62],"highlight":[63],"that":[64],"there":[65],"exists,":[66],"depending":[67],"h,":[69],"cases":[70],"where":[71],"more":[77,127,142,156],"likely":[78,157],"accurate":[79,143],"than":[80,130,147],"Pk2":[82,154],"element.":[83],"To":[84],"confirm":[85],"assertion,":[87],"highlight,":[89],"using":[90],"numerical":[91],"examples,":[92],"quality":[94],"fit":[97],"statistical":[100],"frequencies":[101],"corresponding":[104],"probabilities,":[105],"as":[106],"determined":[107],"by":[108],"law.":[111],"This":[112],"illustrates":[113],"that,":[114],"away":[118],"from":[119],"zero,":[120],"may":[125],"produce":[126],"precise":[128],"results":[129],"Pk2,":[134],"since":[135],"event":[140],"\u201cPk1is":[141],"thanPk2\u201d":[144],"becomes":[145],"greater":[146],"0.5.":[148],"these":[150],"cases,":[151],"overqualified.":[158]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-12-07T00:00:00"}
