{"id":"https://openalex.org/W4409247701","doi":"https://doi.org/10.3390/axioms14040281","title":"A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine","display_name":"A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine","publication_year":2025,"publication_date":"2025-04-07","ids":{"openalex":"https://openalex.org/W4409247701","doi":"https://doi.org/10.3390/axioms14040281"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14040281","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040281","pdf_url":null,"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://doi.org/10.3390/axioms14040281","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5117071038","display_name":"Aadil Ahmad Mir","orcid":null},"institutions":[{"id":"https://openalex.org/I135388327","display_name":"University of Kashmir","ror":"https://ror.org/032xfst36","country_code":"IN","type":"education","lineage":["https://openalex.org/I135388327"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Aadil Ahmad Mir","raw_affiliation_strings":["Department of Statistics, University of Kashmir, Srinagar 190006, India"],"raw_orcid":"https://orcid.org/0009-0009-3169-1311","affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Kashmir, Srinagar 190006, India","institution_ids":["https://openalex.org/I135388327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101304428","display_name":"Shamshad Ur Rasool","orcid":null},"institutions":[{"id":"https://openalex.org/I135388327","display_name":"University of Kashmir","ror":"https://ror.org/032xfst36","country_code":"IN","type":"education","lineage":["https://openalex.org/I135388327"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shamshad Ur Rasool","raw_affiliation_strings":["Department of Statistics, University of Kashmir, Srinagar 190006, India"],"raw_orcid":"https://orcid.org/0009-0001-6396-5278","affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Kashmir, Srinagar 190006, India","institution_ids":["https://openalex.org/I135388327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000534592","display_name":"S. P. Ahmad","orcid":"https://orcid.org/0000-0003-1809-1396"},"institutions":[{"id":"https://openalex.org/I135388327","display_name":"University of Kashmir","ror":"https://ror.org/032xfst36","country_code":"IN","type":"education","lineage":["https://openalex.org/I135388327"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. P. Ahmad","raw_affiliation_strings":["Department of Statistics, University of Kashmir, Srinagar 190006, India"],"raw_orcid":"https://orcid.org/0000-0003-1809-1396","affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Kashmir, Srinagar 190006, India","institution_ids":["https://openalex.org/I135388327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008001574","display_name":"Ajaz A. Bhat","orcid":"https://orcid.org/0000-0003-3079-5097"},"institutions":[{"id":"https://openalex.org/I4264650","display_name":"Islamic University of Science and Technology","ror":"https://ror.org/02kdtt649","country_code":"IN","type":"education","lineage":["https://openalex.org/I4264650"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"A. A. Bhat","raw_affiliation_strings":["Department of Mathematical Sciences, Islamic University of Science and Technology, Pulwama 192122, India"],"raw_orcid":"https://orcid.org/0000-0003-3079-5097","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Islamic University of Science and Technology, Pulwama 192122, India","institution_ids":["https://openalex.org/I4264650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054637936","display_name":"Taghreed M. Jawa","orcid":"https://orcid.org/0000-0001-5023-0806"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Taghreed M. Jawa","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Sciences, Taif University, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5023-0806","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Sciences, Taif University, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Neveen Sayed-Ahmed","orcid":"https://orcid.org/0009-0008-3412-4489"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Neveen Sayed-Ahmed","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Sciences, Taif University, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0009-0008-3412-4489","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Sciences, Taif University, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060040866","display_name":"Ahlam H. Tolba","orcid":"https://orcid.org/0000-0001-8938-9187"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahlam H. Tolba","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-8938-9187","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5117071038"],"corresponding_institution_ids":["https://openalex.org/I135388327"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":15.74,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.99141141,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"281","last_page":"281"},"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":0.9997000098228455,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9882000088691711,"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/probability-distribution","display_name":"Probability distribution","score":0.43259772658348083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4158675968647003},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25224947929382324},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15469223260879517}],"concepts":[{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.43259772658348083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4158675968647003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25224947929382324},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15469223260879517}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14040281","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040281","pdf_url":null,"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:4dd5814c11164ea38e82bda54efa7d40","is_oa":true,"landing_page_url":"https://doaj.org/article/4dd5814c11164ea38e82bda54efa7d40","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 4, p 281 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14040281","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040281","pdf_url":null,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W22905875","https://openalex.org/W187841622","https://openalex.org/W1964366808","https://openalex.org/W2046262695","https://openalex.org/W2077079869","https://openalex.org/W2092685198","https://openalex.org/W2130388500","https://openalex.org/W2344736800","https://openalex.org/W2428472680","https://openalex.org/W2467305554","https://openalex.org/W2473549009","https://openalex.org/W2514487384","https://openalex.org/W2772367125","https://openalex.org/W3037169197","https://openalex.org/W3091593397","https://openalex.org/W3207845493","https://openalex.org/W3210514589","https://openalex.org/W3213142327","https://openalex.org/W4200151383","https://openalex.org/W4214574412","https://openalex.org/W4214653066","https://openalex.org/W4252742442","https://openalex.org/W4283712008","https://openalex.org/W4288100482","https://openalex.org/W4293214476","https://openalex.org/W4376126474","https://openalex.org/W4394912493","https://openalex.org/W4394928545","https://openalex.org/W4395014684","https://openalex.org/W4399304885","https://openalex.org/W4402558738","https://openalex.org/W4406462050","https://openalex.org/W4406820734","https://openalex.org/W4407921439","https://openalex.org/W6717494615","https://openalex.org/W6726159266","https://openalex.org/W6779631089","https://openalex.org/W6841114464","https://openalex.org/W6842073103","https://openalex.org/W6888791798","https://openalex.org/W6945259779","https://openalex.org/W6945300717","https://openalex.org/W6963886237"],"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":[0,147],"study":[1],"introduces":[2],"a":[3,14,55],"novel":[4],"trigonometric-based":[5],"family":[6],"of":[7,28,38,59,97,155],"distributions":[8,157],"for":[9,163,169],"modeling":[10,143],"continuous":[11],"data":[12,145],"through":[13],"newly":[15],"proposed":[16],"framework":[17,154],"known":[18],"as":[19,122],"the":[20,26,29,42,60,152,167],"ASP":[21],"family,":[22,40],"where":[23],"\u2018ASP\u2019":[24],"represents":[25],"initials":[27],"authors":[30],"Aadil,":[31],"Shamshad,":[32],"and":[33,66,94,115],"Parvaiz.":[34],"A":[35],"specific":[36],"subclass":[37],"this":[39],"termed":[41],"\u201cASP":[43],"Rayleigh":[44],"distribution\u201d":[45],"(ASPRD),":[46],"is":[47],"introduced":[48],"that":[49,110],"features":[50],"two":[51],"parameters.":[52],"We":[53],"conducted":[54],"comprehensive":[56],"statistical":[57,173],"analysis":[58],"ASPRD,":[61],"exploring":[62],"its":[63,68,129,140],"key":[64],"properties":[65],"demonstrating":[67],"superior":[69],"adaptability.":[70],"The":[71],"model":[72],"parameters":[73],"are":[74],"estimated":[75],"using":[76],"four":[77],"classical":[78],"estimation":[79,83,87,92,99,106],"methods:":[80],"maximum":[81,95],"likelihood":[82],"(MLE),":[84],"least":[85,90],"squares":[86,91],"(LSE),":[88],"weighted":[89],"(WLSE),":[93],"product":[96],"spaces":[98],"(MPSE).":[100],"Extensive":[101],"simulation":[102],"studies":[103],"confirm":[104],"these":[105],"techniques\u2019":[107],"robustness,":[108],"showing":[109],"biases,":[111],"mean":[112,117],"squared":[113,118],"errors,":[114],"root":[116],"errors":[119],"consistently":[120],"decrease":[121],"sample":[123],"sizes":[124],"increase.":[125],"To":[126],"further":[127],"validate":[128],"applicability,":[130],"we":[131],"employ":[132],"ASPRD":[133],"on":[134],"three":[135],"real-world":[136],"engineering":[137],"datasets,":[138],"showcasing":[139],"effectiveness":[141],"in":[142,172],"complex":[144],"structures.":[146],"work":[148],"not":[149],"only":[150],"strengthens":[151],"theoretical":[153],"probability":[156],"but":[158],"also":[159],"provides":[160],"valuable":[161],"tools":[162],"practical":[164],"applications,":[165],"paving":[166],"way":[168],"future":[170],"advancements":[171],"modeling.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}