{"id":"https://openalex.org/W7128729501","doi":"https://doi.org/10.1017/jpr.2025.10061","title":"Bivariate shock models driven by the geometric counting process","display_name":"Bivariate shock models driven by the geometric counting process","publication_year":2026,"publication_date":"2026-02-12","ids":{"openalex":"https://openalex.org/W7128729501","doi":"https://doi.org/10.1017/jpr.2025.10061"},"language":"en","primary_location":{"id":"doi:10.1017/jpr.2025.10061","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10061","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/994303D4A7FB272EC4B9AF7CF648EFD4/S0021900225100612a.pdf/div-class-title-bivariate-shock-models-driven-by-the-geometric-counting-process-div.pdf","source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/994303D4A7FB272EC4B9AF7CF648EFD4/S0021900225100612a.pdf/div-class-title-bivariate-shock-models-driven-by-the-geometric-counting-process-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074225603","display_name":"Marco Capaldo","orcid":"https://orcid.org/0000-0002-0255-8935"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Marco Capaldo","raw_affiliation_strings":["Universit\u00e0 degli Studi di Salerno"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Salerno","institution_ids":["https://openalex.org/I131729948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043883647","display_name":"Serena Spina","orcid":"https://orcid.org/0000-0001-6408-7596"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Serena Spina","raw_affiliation_strings":["Universit\u00e0 degli Studi di Salerno"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Salerno","institution_ids":["https://openalex.org/I131729948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043883647","https://openalex.org/A5074225603"],"corresponding_institution_ids":["https://openalex.org/I131729948"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17728816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"2","first_page":"849","last_page":"863"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.1639000028371811,"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":0.1639000028371811,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.13120000064373016,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11720","display_name":"Probability and Risk Models","score":0.10300000011920929,"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/bivariate-analysis","display_name":"Bivariate analysis","score":0.8648999929428101},{"id":"https://openalex.org/keywords/shock","display_name":"Shock (circulatory)","score":0.4819999933242798},{"id":"https://openalex.org/keywords/counting-process","display_name":"Counting process","score":0.4489000141620636},{"id":"https://openalex.org/keywords/geometric-distribution","display_name":"Geometric distribution","score":0.4341000020503998},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.42570000886917114},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4162999987602234},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.38690000772476196},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.3824000060558319}],"concepts":[{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.8648999929428101},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8646000027656555},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5479999780654907},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C2781104640","wikidata":"https://www.wikidata.org/wiki/Q11827313","display_name":"Counting process","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C39947850","wikidata":"https://www.wikidata.org/wiki/Q729523","display_name":"Geometric distribution","level":3,"score":0.4341000020503998},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4162999987602234},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C42600057","wikidata":"https://www.wikidata.org/wiki/Q2915096","display_name":"Survival function","level":3,"score":0.36149999499320984},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.33649998903274536},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.33079999685287476},{"id":"https://openalex.org/C110507122","wikidata":"https://www.wikidata.org/wiki/Q1356856","display_name":"Renewal theory","level":2,"score":0.32120001316070557},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.31439998745918274},{"id":"https://openalex.org/C79495835","wikidata":"https://www.wikidata.org/wiki/Q5520315","display_name":"Gamma process","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C153363305","wikidata":"https://www.wikidata.org/wiki/Q1306887","display_name":"Geometric series","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C123954133","wikidata":"https://www.wikidata.org/wiki/Q7595775","display_name":"Stable process","level":3,"score":0.2720000147819519},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.2712000012397766},{"id":"https://openalex.org/C187825244","wikidata":"https://www.wikidata.org/wiki/Q372071","display_name":"Probability-generating function","level":4,"score":0.2709999978542328},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/jpr.2025.10061","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10061","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/994303D4A7FB272EC4B9AF7CF648EFD4/S0021900225100612a.pdf/div-class-title-bivariate-shock-models-driven-by-the-geometric-counting-process-div.pdf","source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/jpr.2025.10061","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10061","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/994303D4A7FB272EC4B9AF7CF648EFD4/S0021900225100612a.pdf/div-class-title-bivariate-shock-models-driven-by-the-geometric-counting-process-div.pdf","source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1145458839","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G1511544777","display_name":null,"funder_award_id":"E53C23001670001","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3752830834","display_name":null,"funder_award_id":"CUP E53C23001670001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G4772130973","display_name":null,"funder_award_id":"E53C23001670001","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"},{"id":"https://openalex.org/G4945003250","display_name":null,"funder_award_id":"CUP E53C23001670001","funder_id":"https://openalex.org/F4320334079","funder_display_name":"Gruppo Nazionale per il Calcolo Scientifico"},{"id":"https://openalex.org/G5245466801","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G5488169599","display_name":null,"funder_award_id":"E53C23001670001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G5796505130","display_name":null,"funder_award_id":"PRIN 2022 PNRR","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G7118361430","display_name":null,"funder_award_id":"MUR-PRIN 2022","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8452110207","display_name":null,"funder_award_id":"MUR-PRIN 2022 PNRR","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128729501.pdf","grobid_xml":"https://content.openalex.org/works/W7128729501.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W562988351","https://openalex.org/W1971985773","https://openalex.org/W1976137872","https://openalex.org/W1998174167","https://openalex.org/W2018991507","https://openalex.org/W2025165702","https://openalex.org/W2053245665","https://openalex.org/W2068120420","https://openalex.org/W2069797166","https://openalex.org/W2070107915","https://openalex.org/W2084644495","https://openalex.org/W2092976247","https://openalex.org/W2093045275","https://openalex.org/W2141344114","https://openalex.org/W2183294866","https://openalex.org/W2325518367","https://openalex.org/W2328055924","https://openalex.org/W2490005139","https://openalex.org/W2509000746","https://openalex.org/W2620003726","https://openalex.org/W2687658479","https://openalex.org/W2794441437","https://openalex.org/W2796389273","https://openalex.org/W2810787979","https://openalex.org/W3016357200","https://openalex.org/W3159971645","https://openalex.org/W4200263040","https://openalex.org/W4245777296","https://openalex.org/W4311764290","https://openalex.org/W4378649449","https://openalex.org/W4383681675","https://openalex.org/W4387117935","https://openalex.org/W4389792354","https://openalex.org/W4398327429"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,29],"consider":[2],"shock":[3],"models":[4],"governed":[5],"by":[6,63,82],"the":[7,14,44,51,72,83,99],"bivariate":[8],"geometric":[9],"counting":[10],"process.":[11],"By":[12],"assuming":[13,64],"competing":[15],"risks":[16],"framework,":[17],"failures":[18],"are":[19,61,102],"due":[20],"to":[21],"one":[22],"of":[23,43,46,50,85,98],"two":[24],"mutually":[25],"exclusive":[26],"causes":[27],"(shocks).":[28],"obtain":[30],"and":[31,48],"study":[32],"some":[33],"relevant":[34],"functions,":[35,41],"such":[36],"as":[37],"failure":[38,52,90],"densities,":[39],"survival":[40],"probability":[42],"cause":[45],"failure,":[47],"moments":[49],"time":[53],"conditioned":[54],"on":[55],"a":[56,77],"specific":[57],"cause.":[58],"Such":[59],"functions":[60],"specified":[62],"that":[65],"systems":[66],"or":[67],"living":[68],"organisms":[69],"fail":[70],"at":[71],"first":[73],"instant":[74],"in":[75],"which":[76],"random":[78,100],"threshold":[79,101],"is":[80],"reached":[81],"sum":[84],"received":[86],"shocks.":[87],"Under":[88],"this":[89],"scheme,":[91],"various":[92],"cases":[93],"arising":[94],"for":[95],"suitable":[96],"choices":[97],"provided":[103],"too.":[104]},"counts_by_year":[],"updated_date":"2026-06-25T06:16:34.145877","created_date":"2026-02-13T00:00:00"}