{"id":"https://openalex.org/W7220697106","doi":"https://doi.org/10.1038/s41598-026-68245-8","title":"A novel Arctan-based model: Bayesian analysis, progressive censoring, and practical applications","display_name":"A novel Arctan-based model: Bayesian analysis, progressive censoring, and practical applications","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220697106","doi":"https://doi.org/10.1038/s41598-026-68245-8"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-026-68245-8","doi":"https://doi.org/10.1038/s41598-026-68245-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-68245-8","pdf_url":"https://www.nature.com/articles/s41598-026-68245-8_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-026-68245-8_reference.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048338546","display_name":"Amal Soliman Hassan","orcid":"https://orcid.org/0000-0003-4442-8458","observed_orcids":["https://orcid.org/0000-0003-4442-8458"]},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Amal S. Hassan","raw_affiliation_strings":["Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-4442-8458","affiliations":[{"raw_affiliation_string":"Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002013958","display_name":"Amer Ibrahim Al\u2010Omari","orcid":"https://orcid.org/0000-0002-6901-8263","observed_orcids":["https://orcid.org/0000-0002-6901-8263"]},"institutions":[{"id":"https://openalex.org/I31079310","display_name":"Al al-Bayt University","ror":"https://ror.org/028jh2126","country_code":"JO","type":"education","lineage":["https://openalex.org/I31079310"]}],"countries":["JO"],"is_corresponding":true,"raw_author_name":"Amer I. Al-Omari","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq, 25113, Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq, 25113, Jordan","institution_ids":["https://openalex.org/I31079310"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018454567","display_name":"Ghadah A. Alomani","orcid":"https://orcid.org/0000-0002-7856-6579","observed_orcids":["https://orcid.org/0000-0002-7856-6579"]},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ghadah Alomani","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057758203","display_name":"Maisaa M. Hassan","orcid":"https://orcid.org/0009-0006-1973-3978","observed_orcids":["https://orcid.org/0009-0006-1973-3978"]},"institutions":[{"id":"https://openalex.org/I890898191","display_name":"Modern Academy","ror":"https://ror.org/02exeb428","country_code":"EG","type":"education","lineage":["https://openalex.org/I890898191"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Maisaa M. Hassan","raw_affiliation_strings":["Modern Academy for Computer Science and Management Technology, Maadi, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Modern Academy for Computer Science and Management Technology, Maadi, Egypt","institution_ids":["https://openalex.org/I890898191"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002013958"],"corresponding_institution_ids":["https://openalex.org/I31079310"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":1.0,"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":1.0,"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/T13500","display_name":"Probability and Statistical Research","score":0.0,"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.0,"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/lifetime-distributions","display_name":"lifetime distributions","score":0.546999990940094},{"id":"https://openalex.org/keywords/progressive-censoring","display_name":"progressive censoring","score":0.6919999718666077},{"id":"https://openalex.org/keywords/bayesian-estimation","display_name":"Bayesian estimation","score":0.9169999957084656},{"id":"https://openalex.org/keywords/maximum-likelihood-estimation","display_name":"maximum likelihood estimation","score":0.9369999766349792},{"id":"https://openalex.org/keywords/mean-residual-life","display_name":"mean residual life","score":0.753000020980835},{"id":"https://openalex.org/keywords/entropy-measures","display_name":"entropy measures","score":0.972000002861023},{"id":"https://openalex.org/keywords/error-exponent","display_name":"reliability function","score":0.8100000023841858},{"id":"https://openalex.org/keywords/metropolis-hastings-algorithm","display_name":"Metropolis-Hastings algorithm","score":0.7710000276565552}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.727400004863739},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5999000072479248},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5174000263214111},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.37369999289512634},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3617999851703644},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3172999918460846},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.3075000047683716},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C2778049539","wikidata":"https://www.wikidata.org/wiki/Q17002908","display_name":"Bayesian optimization","level":2,"score":0.2353000044822693}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1038/s41598-026-68245-8","doi":"https://doi.org/10.1038/s41598-026-68245-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-68245-8","pdf_url":"https://www.nature.com/articles/s41598-026-68245-8_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1038/s41598-026-68245-8","doi":"https://doi.org/10.1038/s41598-026-68245-8","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-68245-8","pdf_url":"https://www.nature.com/articles/s41598-026-68245-8_reference.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","doaj","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1249588976","display_name":null,"funder_award_id":"PNURSP2026R226","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"}],"funders":[{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220697106.pdf","grobid_xml":"https://content.openalex.org/works/W7220697106.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1964366808","https://openalex.org/W2030911724","https://openalex.org/W2118085505","https://openalex.org/W2322557778","https://openalex.org/W2497324178","https://openalex.org/W2505756961","https://openalex.org/W2570898034","https://openalex.org/W2792417255","https://openalex.org/W2969926172","https://openalex.org/W3119152419","https://openalex.org/W3210684668","https://openalex.org/W4200333310","https://openalex.org/W4226074775","https://openalex.org/W4313192582","https://openalex.org/W4379536376","https://openalex.org/W4384525594","https://openalex.org/W4386283005","https://openalex.org/W4386754480","https://openalex.org/W4400064120","https://openalex.org/W4410936629","https://openalex.org/W4411680185","https://openalex.org/W4414229199","https://openalex.org/W7125591018","https://openalex.org/W7162529307"],"related_works":["https://openalex.org/W7170144585","https://openalex.org/W7155018100","https://openalex.org/W4387587648","https://openalex.org/W7166544438","https://openalex.org/W7221445929","https://openalex.org/W4320919052","https://openalex.org/W4291366294","https://openalex.org/W4416993133","https://openalex.org/W7169720523","https://openalex.org/W4414069640"],"abstract_inverted_index":{"For":[0],"modeling":[1],"and":[2,90,123,127,137,156,177,184,206,230,254,268],"analyzing":[3],"complex":[4,15],"datasets":[5,222],"in":[6,18,228,287],"various":[7],"scientific":[8],"fields,":[9],"probability":[10],"distributions":[11],"are":[12,28,188,202],"crucial.":[13],"Nevertheless,":[14],"characteristics":[16,112],"found":[17],"real-world":[19,221],"data,":[20,133],"like":[21,152],"skewness,":[22],"heavy":[23],"tails,":[24],"or":[25],"high":[26,203],"variability,":[27],"frequently":[29],"missed":[30],"by":[31,65],"classical":[32,82],"distributions.":[33],"This":[34],"study":[35],"suggests":[36],"a":[37,97],"novel":[38],"extension":[39],"of":[40,95,99,162,213,251,257,280,283],"the":[41,47,50,67,73,81,104,108,120,142,153,160,163,199,214,236,239,243,258,264,271,278,281,284],"power":[42,52,69,83],"hazard":[43,53,70,84,154],"model":[44,79,216,241,286],"based":[45],"on":[46],"arctan-X":[48,74],"family,":[49],"arctan":[51],"(AT-PH)":[54],"distribution,":[55],"to":[56,224,248],"overcome":[57],"these":[58],"drawbacks.":[59],"The":[60,77,210],"AT-PH":[61,143,240],"distribution":[62,71,144],"is":[63,168,217],"constructed":[64],"integrating":[66],"baseline":[68],"with":[72,171],"family":[75],"framework.":[76],"suggested":[78,200],"improves":[80],"distribution's":[85],"adaptability":[86],"without":[87],"adding":[88],"parameters":[89,145],"makes":[91],"it":[92],"more":[93],"capable":[94],"handling":[96,288],"range":[98],"data":[100,266,273],"behaviors.":[101],"To":[102],"lay":[103],"theoretical":[105],"groundwork":[106],"for":[107,141,263,270],"model,":[109],"several":[110],"important":[111,149],"were":[113],"determined,":[114],"such":[115],"as":[116,146,148],"moments,":[117,119],"incomplete":[118],"mean":[121],"residual":[122,125],"reversed":[124],"life,":[126],"entropy":[128],"measures.":[129],"Using":[130],"progressively":[131],"censored":[132],"we":[134],"obtain":[135],"Bayesian":[136,166,185],"maximum":[138],"likelihood":[139],"estimates":[140],"well":[147],"reliability":[150,157],"metrics":[151],"rate":[155],"functions.":[158,180],"Through":[159],"use":[161],"Metropolis\u2013Hastings":[164],"algorithm,":[165],"analysis":[167],"carried":[169],"out":[170],"independent":[172],"gamma":[173],"priors":[174],"under":[175,193],"asymmetric":[176],"symmetric":[178],"loss":[179],"Asymptotic":[181],"confidence":[182],"intervals":[183,187],"credible":[186],"investigated.":[189],"Monte":[190],"Carlo":[191],"simulations,":[192],"progressive":[194],"censoring":[195],"schemes,":[196],"show":[197,277],"that":[198],"techniques":[201],"numerical":[204],"stability":[205],"exceptional":[207],"computational":[208],"accuracy.":[209],"practical":[211],"usefulness":[212],"proposed":[215,285],"shown":[218],"through":[219],"two":[220],"relating":[223],"engineering":[225],"(fiber":[226],"strength":[227],"glass)":[229],"hydrogeology":[231],"(maximum":[232],"flood":[233],"level).":[234],"From":[235],"statistical":[237],"analysis,":[238],"surpasses":[242],"other":[244],"competing":[245],"models":[246],"due":[247],"lower":[249],"values":[250,256],"information":[252],"criteria":[253],"greater":[255],"Kolmogorov\u2013Smirnov":[259],"test":[260],"p-value":[261],"(0.972":[262],"first":[265],"set":[267],"0.4572":[269],"second":[272],"set).":[274],"Performance":[275],"comparisons":[276],"promise":[279],"flexibility":[282],"complicated":[289],"failure":[290],"cases.":[291]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-07T00:00:00"}