{"id":"https://openalex.org/W2081979944","doi":"https://doi.org/10.1080/03610910802440327","title":"Weibull and Gamma Renewal Approximation Using Generalized Exponential Functions","display_name":"Weibull and Gamma Renewal Approximation Using Generalized Exponential Functions","publication_year":2008,"publication_date":"2008-11-15","ids":{"openalex":"https://openalex.org/W2081979944","doi":"https://doi.org/10.1080/03610910802440327","mag":"2081979944"},"language":"en","primary_location":{"id":"doi:10.1080/03610910802440327","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910802440327","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/A5012285299","display_name":"Tongdan Jin","orcid":"https://orcid.org/0000-0001-7845-9936"},"institutions":[{"id":"https://openalex.org/I131740757","display_name":"Texas A&M International University","ror":"https://ror.org/028861t28","country_code":"US","type":"education","lineage":["https://openalex.org/I131740757"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tongdan Jin","raw_affiliation_strings":["Department of Mathematical and Physical Sciences , Texas A&M International University , Laredo, Texas, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical and Physical Sciences , Texas A&M International University , Laredo, Texas, USA","institution_ids":["https://openalex.org/I131740757"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082238660","display_name":"Lakshmana S. Gonigunta","orcid":null},"institutions":[{"id":"https://openalex.org/I131740757","display_name":"Texas A&M International University","ror":"https://ror.org/028861t28","country_code":"US","type":"education","lineage":["https://openalex.org/I131740757"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lakshmana Gonigunta","raw_affiliation_strings":["Department of Management Information Sciences , Texas A&M International University , Laredo, Texas, USA"],"affiliations":[{"raw_affiliation_string":"Department of Management Information Sciences , Texas A&M International University , Laredo, Texas, USA","institution_ids":["https://openalex.org/I131740757"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012285299"],"corresponding_institution_ids":["https://openalex.org/I131740757"],"apc_list":null,"apc_paid":null,"fwci":0.54082237,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.71206483,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"1","first_page":"154","last_page":"171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9993000030517578,"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":0.9362329840660095},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.7547150254249573},{"id":"https://openalex.org/keywords/shape-parameter","display_name":"Shape parameter","score":0.7044127583503723},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.6943702697753906},{"id":"https://openalex.org/keywords/gamma-distribution","display_name":"Gamma distribution","score":0.6818941235542297},{"id":"https://openalex.org/keywords/generalized-gamma-distribution","display_name":"Generalized gamma distribution","score":0.6590222716331482},{"id":"https://openalex.org/keywords/inverse-gamma-distribution","display_name":"Inverse-gamma distribution","score":0.6003643274307251},{"id":"https://openalex.org/keywords/gamma-function","display_name":"Gamma function","score":0.5709061622619629},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5508142709732056},{"id":"https://openalex.org/keywords/natural-exponential-family","display_name":"Natural exponential family","score":0.531726598739624},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.5276564359664917},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4999704360961914},{"id":"https://openalex.org/keywords/laplace-distribution","display_name":"Laplace distribution","score":0.49440574645996094},{"id":"https://openalex.org/keywords/generalized-integer-gamma-distribution","display_name":"Generalized integer gamma distribution","score":0.4844112992286682},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4670760929584503},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.4263843595981598},{"id":"https://openalex.org/keywords/exponentiated-weibull-distribution","display_name":"Exponentiated Weibull distribution","score":0.4118337333202362},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2232038974761963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21582567691802979},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14936041831970215},{"id":"https://openalex.org/keywords/distribution-fitting","display_name":"Distribution fitting","score":0.1483079493045807},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.1264643371105194}],"concepts":[{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.9362329840660095},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.7547150254249573},{"id":"https://openalex.org/C199435849","wikidata":"https://www.wikidata.org/wiki/Q3179293","display_name":"Shape parameter","level":2,"score":0.7044127583503723},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.6943702697753906},{"id":"https://openalex.org/C149717495","wikidata":"https://www.wikidata.org/wiki/Q117806","display_name":"Gamma distribution","level":2,"score":0.6818941235542297},{"id":"https://openalex.org/C42337464","wikidata":"https://www.wikidata.org/wiki/Q5532478","display_name":"Generalized gamma distribution","level":3,"score":0.6590222716331482},{"id":"https://openalex.org/C4646027","wikidata":"https://www.wikidata.org/wiki/Q3258521","display_name":"Inverse-gamma distribution","level":5,"score":0.6003643274307251},{"id":"https://openalex.org/C82240120","wikidata":"https://www.wikidata.org/wiki/Q190573","display_name":"Gamma function","level":2,"score":0.5709061622619629},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5508142709732056},{"id":"https://openalex.org/C60775368","wikidata":"https://www.wikidata.org/wiki/Q17099337","display_name":"Natural exponential family","level":3,"score":0.531726598739624},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.5276564359664917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4999704360961914},{"id":"https://openalex.org/C183057437","wikidata":"https://www.wikidata.org/wiki/Q671617","display_name":"Laplace distribution","level":3,"score":0.49440574645996094},{"id":"https://openalex.org/C10477448","wikidata":"https://www.wikidata.org/wiki/Q5532482","display_name":"Generalized integer gamma distribution","level":3,"score":0.4844112992286682},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4670760929584503},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.4263843595981598},{"id":"https://openalex.org/C95770405","wikidata":"https://www.wikidata.org/wiki/Q5421539","display_name":"Exponentiated Weibull distribution","level":3,"score":0.4118337333202362},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2232038974761963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21582567691802979},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14936041831970215},{"id":"https://openalex.org/C160947583","wikidata":"https://www.wikidata.org/wiki/Q2083147","display_name":"Distribution fitting","level":3,"score":0.1483079493045807},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.1264643371105194},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C57205106","wikidata":"https://www.wikidata.org/wiki/Q3258519","display_name":"Inverse-chi-squared distribution","level":4,"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:10.1080/03610910802440327","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910802440327","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1496753898","https://openalex.org/W1970458650","https://openalex.org/W1971870250","https://openalex.org/W1979912268","https://openalex.org/W1982239813","https://openalex.org/W1986458941","https://openalex.org/W1987547632","https://openalex.org/W1993967305","https://openalex.org/W2008486416","https://openalex.org/W2012962702","https://openalex.org/W2028006048","https://openalex.org/W2039263441","https://openalex.org/W2045027442","https://openalex.org/W2060944736","https://openalex.org/W2077346801","https://openalex.org/W2108063682","https://openalex.org/W2112345887","https://openalex.org/W2116319303","https://openalex.org/W2130388500","https://openalex.org/W2132393331","https://openalex.org/W2134270577","https://openalex.org/W2162055137","https://openalex.org/W2169235621","https://openalex.org/W2332871474","https://openalex.org/W6679688394"],"related_works":["https://openalex.org/W2009246008","https://openalex.org/W2547792281","https://openalex.org/W202202135","https://openalex.org/W2182909841","https://openalex.org/W1986915310","https://openalex.org/W2183425169","https://openalex.org/W2155247005","https://openalex.org/W2018418083","https://openalex.org/W1761810493","https://openalex.org/W2185145539"],"abstract_inverted_index":{"When":[0],"the":[1,5,8,11,34,40,50,77,94,105,117,120,128,138,146],"inter-renewal":[2],"time":[3],"follows":[4],"Weibull":[6,42,80,106],"or":[7,43,81],"Gamma":[9,44,82,118,129],"distribution,":[10,119],"analytical":[12,85],"renewal":[13],"function":[14,37,59],"(RF)":[15],"usually":[16],"is":[17,87,97],"not":[18],"tractable,":[19],"and":[20,46,100],"approximation":[21],"method":[22,70],"has":[23],"been":[24],"used.":[25],"Instead":[26],"of":[27,141],"approximating":[28],"RF":[29,51,74,86,107],"directly,":[30],"this":[31],"article":[32],"proposes":[33],"generalized":[35,57],"exponential":[36,58],"to":[38,103],"approximate":[39,104],"underlying":[41],"distributions,":[45,83],"then":[47],"solves":[48],"for":[49,56],"using":[52],"Laplace":[53],"transform.":[54],"Parameters":[55],"can":[60,71,123],"be":[61],"obtained":[62],"by":[63],"solving":[64],"a":[65],"simple":[66],"optimization":[67],"problem.":[68],"The":[69],"obtain":[72],"accurate":[73,99],"approximations":[75,126],"where":[76],"inter-renewals":[78],"follow":[79],"yet":[84],"still":[88],"desirable.":[89],"Comprehensive":[90],"analysis":[91],"shows":[92],"that":[93],"new":[95],"model":[96,122],"mathematically":[98],"computationally":[101],"convenient":[102],"given":[108],"its":[109],"shape":[110,130,142],"parameter":[111,131],"\u03b2":[112],"\u2208":[113,133],"[1,":[114,134],"5].":[115],"For":[116],"proposed":[121],"achieve":[124],"good":[125],"when":[127,144],"k":[132],"10].":[135],"These":[136],"are":[137],"typical":[139],"ranges":[140],"parameters":[143],"modeling":[145],"product":[147],"reliability":[148],"with":[149],"increasing":[150],"failure":[151],"rate":[152],"in":[153],"many":[154],"practical":[155],"applications.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}