{"id":"https://openalex.org/W4408410824","doi":"https://doi.org/10.3390/axioms14030209","title":"A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution","display_name":"A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution","publication_year":2025,"publication_date":"2025-03-13","ids":{"openalex":"https://openalex.org/W4408410824","doi":"https://doi.org/10.3390/axioms14030209"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14030209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030209","pdf_url":"https://www.mdpi.com/2075-1680/14/3/209/pdf?version=1741856684","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/2075-1680/14/3/209/pdf?version=1741856684","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070207714","display_name":"Salma Omar Bleed","orcid":"https://orcid.org/0000-0002-4410-750X"},"institutions":[{"id":"https://openalex.org/I3132692309","display_name":"Alasmarya Islamic University","ror":"https://ror.org/01gr30f96","country_code":"LY","type":"education","lineage":["https://openalex.org/I3132692309"]}],"countries":["LY"],"is_corresponding":true,"raw_author_name":"Salma Omar Bleed","raw_affiliation_strings":["Department of Statistics, College of Science, Al-Asmariya Islamic University, Zliten 218521, Libya"],"raw_orcid":"https://orcid.org/0000-0002-4410-750X","affiliations":[{"raw_affiliation_string":"Department of Statistics, College of Science, Al-Asmariya Islamic University, Zliten 218521, Libya","institution_ids":["https://openalex.org/I3132692309"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Aisha A. Ben Taher","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161365","display_name":"Libyan Academy","ror":"https://ror.org/05s3qq987","country_code":"LY","type":"education","lineage":["https://openalex.org/I4210161365"]}],"countries":["LY"],"is_corresponding":false,"raw_author_name":"Aisha A. Ben Taher","raw_affiliation_strings":["Department of Mathematical Sciences, Libyan Academy, Misrata 2449, Libya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Libyan Academy, Misrata 2449, Libya","institution_ids":["https://openalex.org/I4210161365"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101652735","display_name":"Taha Radwan","orcid":"https://orcid.org/0000-0003-1466-8821"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Taha Radwan","raw_affiliation_strings":["Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-1466-8821","affiliations":[{"raw_affiliation_string":"Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070207714"],"corresponding_institution_ids":["https://openalex.org/I3132692309"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04929428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"3","first_page":"209","last_page":"209"},"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":0.9872999787330627,"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":0.9613999724388123,"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/stage","display_name":"Stage (stratigraphy)","score":0.4996986389160156},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4705866873264313},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33705586194992065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2712861895561218},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.2466060221195221},{"id":"https://openalex.org/keywords/paleontology","display_name":"Paleontology","score":0.08285462856292725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07272017002105713}],"concepts":[{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.4996986389160156},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4705866873264313},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33705586194992065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2712861895561218},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.2466060221195221},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.08285462856292725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07272017002105713}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14030209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030209","pdf_url":"https://www.mdpi.com/2075-1680/14/3/209/pdf?version=1741856684","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:doaj.org/article:9a5965d849ee4f8c847b948c8d493c6c","is_oa":true,"landing_page_url":"https://doaj.org/article/9a5965d849ee4f8c847b948c8d493c6c","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 14, Iss 3, p 209 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14030209","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14030209","pdf_url":"https://www.mdpi.com/2075-1680/14/3/209/pdf?version=1741856684","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":[],"awards":[{"id":"https://openalex.org/G2186466424","display_name":null,"funder_award_id":"QU-APC-2025","funder_id":"https://openalex.org/F4320324403","funder_display_name":"Qassim University"}],"funders":[{"id":"https://openalex.org/F4320324403","display_name":"Qassim University","ror":"https://ror.org/01wsfe280"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408410824.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1579303078","https://openalex.org/W1632540354","https://openalex.org/W1973137995","https://openalex.org/W1992193456","https://openalex.org/W2040713331","https://openalex.org/W2075172568","https://openalex.org/W2265399340","https://openalex.org/W2316045306","https://openalex.org/W4231739827","https://openalex.org/W4232383088","https://openalex.org/W6638642818","https://openalex.org/W6669280079"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"This":[0,67],"article":[1,131],"proposes":[2],"a":[3,28,62,143],"solution":[4],"to":[5,15,54,60,70,90,95,112,155,169],"the":[6,10,20,23,31,42,55,71,97,101,107,114,118,130,135,139,157,161,171],"problem":[7],"of":[8,12,22,65,73,100,117,134,138,160,173],"limiting":[9],"representation":[11],"three-stage":[13],"phenomena":[14],"linear":[16],"forms":[17],"and":[18,103,125,149],"addresses":[19],"stability":[21],"second":[24],"stage":[25],"by":[26],"introducing":[27],"novel":[29],"distribution,":[30,35],"Fragmented":[32],"Kumar-Trapez":[33],"(FKT)":[34],"which":[36],"includes":[37],"two":[38],"additional":[39],"parameters":[40,43,51,99,116],"beyond":[41],"used":[44,168],"for":[45],"an":[46,150],"existing":[47],"standard":[48],"model.":[49],"These":[50],"provide":[52],"flexibility":[53],"density":[56,77],"function,":[57],"enabling":[58],"it":[59],"model":[61],"wide":[63],"range":[64,98],"shapes.":[66],"work":[68],"contributes":[69],"understanding":[72],"distributions":[74,105],"whose":[75],"probability":[76],"functions":[78],"are":[79,153],"divided":[80],"into":[81],"three":[82],"parts,":[83],"addressing":[84],"key":[85],"questions":[86],"such":[87,92],"as:":[88],"How":[89,94,111],"handle":[91],"distributions?":[93],"estimate":[96,113],"trapezoidal":[102],"proposed":[104,119,140],"using":[106,121],"maximum":[108,123],"likelihood":[109,124],"method?":[110],"unknown":[115],"distribution":[120],"both":[122],"Bayesian":[126],"methods?":[127],"In":[128],"addition,":[129],"explores":[132],"some":[133],"mathematical":[136],"properties":[137],"distribution.":[141,163],"Finally,":[142],"simulation":[144],"study":[145],"on":[146],"generated":[147],"data":[148],"illustrated":[151],"example":[152],"conducted":[154],"demonstrate":[156],"practical":[158],"importance":[159],"FKT":[162],"WinBUGS":[164],"1.4":[165],"program":[166],"is":[167],"illustrate":[170],"application":[172],"MCMC":[174],"simulation.":[175]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}