{"id":"https://openalex.org/W7132851549","doi":"https://doi.org/10.1016/j.ress.2026.112425","title":"New approximations for the renewal function of the Weibull distribution","display_name":"New approximations for the renewal function of the Weibull distribution","publication_year":2026,"publication_date":"2026-02-28","ids":{"openalex":"https://openalex.org/W7132851549","doi":"https://doi.org/10.1016/j.ress.2026.112425"},"language":"en","primary_location":{"id":"doi:10.1016/j.ress.2026.112425","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.ress.2026.112425","pdf_url":null,"source":{"id":"https://openalex.org/S202403813","display_name":"Reliability Engineering & System Safety","issn_l":"0951-8320","issn":["0951-8320","1879-0836"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Reliability Engineering &amp; System Safety","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/A5127525190","display_name":"Christos G. Papadopoulos","orcid":null},"institutions":[{"id":"https://openalex.org/I154757721","display_name":"University of Piraeus","ror":"https://ror.org/02qs84g94","country_code":"GR","type":"education","lineage":["https://openalex.org/I154757721"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Christos G. Papadopoulos","raw_affiliation_strings":["Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece"],"raw_orcid":"https://orcid.org/0009-0007-9342-9226","affiliations":[{"raw_affiliation_string":"Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece","institution_ids":["https://openalex.org/I154757721"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028829778","display_name":"Konstadinos G. Politis","orcid":null},"institutions":[{"id":"https://openalex.org/I154757721","display_name":"University of Piraeus","ror":"https://ror.org/02qs84g94","country_code":"GR","type":"education","lineage":["https://openalex.org/I154757721"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Konstadinos Politis","raw_affiliation_strings":["Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece"],"raw_orcid":"https://orcid.org/0000-0002-0892-4262","affiliations":[{"raw_affiliation_string":"Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece","institution_ids":["https://openalex.org/I154757721"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028829778"],"corresponding_institution_ids":["https://openalex.org/I154757721"],"apc_list":{"value":4190,"currency":"USD","value_usd":4190},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.44850264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"272","issue":null,"first_page":"112425","last_page":"112425"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9417999982833862,"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":0.9417999982833862,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.019600000232458115,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.004600000102072954,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":0.8615000247955322},{"id":"https://openalex.org/keywords/renewal-theory","display_name":"Renewal theory","score":0.7529000043869019},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5300999879837036},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5041000247001648},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.47360000014305115},{"id":"https://openalex.org/keywords/distribution-function","display_name":"Distribution function","score":0.43549999594688416},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4072999954223633},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.3889999985694885}],"concepts":[{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.8615000247955322},{"id":"https://openalex.org/C110507122","wikidata":"https://www.wikidata.org/wiki/Q1356856","display_name":"Renewal theory","level":2,"score":0.7529000043869019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6726999878883362},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5698999762535095},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5300999879837036},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5041000247001648},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.47360000014305115},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4072999954223633},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.3889999985694885},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.34850001335144043},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31700000166893005},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2874000072479248},{"id":"https://openalex.org/C95770405","wikidata":"https://www.wikidata.org/wiki/Q5421539","display_name":"Exponentiated Weibull distribution","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C130630143","wikidata":"https://www.wikidata.org/wiki/Q7979803","display_name":"Weibull modulus","level":3,"score":0.27549999952316284},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2596000134944916}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.ress.2026.112425","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.ress.2026.112425","pdf_url":null,"source":{"id":"https://openalex.org/S202403813","display_name":"Reliability Engineering & System Safety","issn_l":"0951-8320","issn":["0951-8320","1879-0836"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Reliability Engineering &amp; System Safety","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331361","display_name":"University of Piraeus Research Centre","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1965225725","https://openalex.org/W1970458650","https://openalex.org/W1979912268","https://openalex.org/W1989345661","https://openalex.org/W2004639865","https://openalex.org/W2020891525","https://openalex.org/W2028006048","https://openalex.org/W2050434690","https://openalex.org/W2077346801","https://openalex.org/W2087834984","https://openalex.org/W2088123622","https://openalex.org/W2094562318","https://openalex.org/W2105430299","https://openalex.org/W2134057305","https://openalex.org/W2134759928","https://openalex.org/W2151506366","https://openalex.org/W2162055137","https://openalex.org/W2319924045","https://openalex.org/W2324063877","https://openalex.org/W2332871474","https://openalex.org/W2794341822","https://openalex.org/W2968814857","https://openalex.org/W2970137692","https://openalex.org/W2986615937","https://openalex.org/W3026139167","https://openalex.org/W3113721704","https://openalex.org/W3129929460","https://openalex.org/W3138609685","https://openalex.org/W4220995663","https://openalex.org/W4221109590","https://openalex.org/W4224300633","https://openalex.org/W4225973352","https://openalex.org/W4251579377","https://openalex.org/W4295034928","https://openalex.org/W4313367318","https://openalex.org/W4317851134","https://openalex.org/W4319304788","https://openalex.org/W4319989293","https://openalex.org/W4392878836","https://openalex.org/W4394990099","https://openalex.org/W4396712503","https://openalex.org/W4400313794","https://openalex.org/W4401503226","https://openalex.org/W4408953851","https://openalex.org/W4412683569"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-06T06:45:51.903784","created_date":"2026-03-01T00:00:00"}
