{"id":"https://openalex.org/W4321786824","doi":"https://doi.org/10.3390/sym15030586","title":"Statistical Inference of the Half Logistic Modified Kies Exponential Model with Modeling to Engineering Data","display_name":"Statistical Inference of the Half Logistic Modified Kies Exponential Model with Modeling to Engineering Data","publication_year":2023,"publication_date":"2023-02-23","ids":{"openalex":"https://openalex.org/W4321786824","doi":"https://doi.org/10.3390/sym15030586"},"language":"en","primary_location":{"id":"doi:10.3390/sym15030586","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030586","pdf_url":"https://www.mdpi.com/2073-8994/15/3/586/pdf?version=1677161173","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/3/586/pdf?version=1677161173","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066244781","display_name":"Safar M. Alghamdi","orcid":"https://orcid.org/0000-0001-6656-5344"},"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":"Safar M. Alghamdi","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-6656-5344","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074635060","display_name":"Mansour Shrahili","orcid":"https://orcid.org/0000-0003-3456-8393"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mansour Shrahili","raw_affiliation_strings":["Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-3456-8393","affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048338546","display_name":"Amal S. Hassan","orcid":"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":true,"raw_author_name":"Amal S. Hassan","raw_affiliation_strings":["Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza 12613, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-4442-8458","affiliations":[{"raw_affiliation_string":"Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza 12613, Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087146100","display_name":"Ahmed M. Gemeay","orcid":"https://orcid.org/0000-0001-6767-4016"},"institutions":[{"id":"https://openalex.org/I21376657","display_name":"Tanta University","ror":"https://ror.org/016jp5b92","country_code":"EG","type":"education","lineage":["https://openalex.org/I21376657"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahmed M. Gemeay","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-6767-4016","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt","institution_ids":["https://openalex.org/I21376657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029121877","display_name":"Ibrahim Elbatal","orcid":"https://orcid.org/0000-0003-3479-5967"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ibrahim Elbatal","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026468035","display_name":"Mohammed Elgarhy","orcid":"https://orcid.org/0000-0002-1333-3862"},"institutions":[{"id":"https://openalex.org/I113643904","display_name":"Beni-Suef University","ror":"https://ror.org/05pn4yv70","country_code":"EG","type":"education","lineage":["https://openalex.org/I113643904"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Mohammed Elgarhy","raw_affiliation_strings":["Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-1333-3862","affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt","institution_ids":["https://openalex.org/I113643904"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5048338546"],"corresponding_institution_ids":["https://openalex.org/I145487455"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":9.6641,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.98756928,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"15","issue":"3","first_page":"586","last_page":"586"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9915000200271606,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantile","display_name":"Quantile","score":0.5995705127716064},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5219002366065979},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5182480812072754},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.515798807144165},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.492575466632843},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.48219218850135803},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.47194069623947144},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.44673866033554077},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.43062618374824524},{"id":"https://openalex.org/keywords/distribution-fitting","display_name":"Distribution fitting","score":0.4304199516773224},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3824637234210968},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09764137864112854}],"concepts":[{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.5995705127716064},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5219002366065979},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5182480812072754},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.515798807144165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.492575466632843},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.48219218850135803},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.47194069623947144},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.44673866033554077},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.43062618374824524},{"id":"https://openalex.org/C160947583","wikidata":"https://www.wikidata.org/wiki/Q2083147","display_name":"Distribution fitting","level":3,"score":0.4304199516773224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3824637234210968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09764137864112854}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15030586","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030586","pdf_url":"https://www.mdpi.com/2073-8994/15/3/586/pdf?version=1677161173","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b9a2c365f8774548ab62c10e47f73538","is_oa":false,"landing_page_url":"https://doaj.org/article/b9a2c365f8774548ab62c10e47f73538","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 3, p 586 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/3/586/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15030586","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15030586","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030586","pdf_url":"https://www.mdpi.com/2073-8994/15/3/586/pdf?version=1677161173","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4321786824.pdf"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1496753898","https://openalex.org/W1523095595","https://openalex.org/W1971568850","https://openalex.org/W2017796068","https://openalex.org/W2063558080","https://openalex.org/W2089852843","https://openalex.org/W2094923943","https://openalex.org/W2112105596","https://openalex.org/W2151411627","https://openalex.org/W2168504156","https://openalex.org/W2179148718","https://openalex.org/W2263958071","https://openalex.org/W2395116946","https://openalex.org/W2473549009","https://openalex.org/W2620601502","https://openalex.org/W2774617223","https://openalex.org/W2792417255","https://openalex.org/W2909155859","https://openalex.org/W2996977568","https://openalex.org/W2999703726","https://openalex.org/W3017923824","https://openalex.org/W3046602795","https://openalex.org/W3048710400","https://openalex.org/W3119477762","https://openalex.org/W3124432045","https://openalex.org/W3125735550","https://openalex.org/W3155825961","https://openalex.org/W3168120343","https://openalex.org/W3171354104","https://openalex.org/W4200400803","https://openalex.org/W4200516709","https://openalex.org/W4210394693","https://openalex.org/W4224617588","https://openalex.org/W4229973820","https://openalex.org/W4280648619","https://openalex.org/W4283643975","https://openalex.org/W4296475364","https://openalex.org/W6672781747","https://openalex.org/W6676610297","https://openalex.org/W6678323213","https://openalex.org/W6693264812","https://openalex.org/W6712124432","https://openalex.org/W6780938505","https://openalex.org/W6842790716"],"related_works":["https://openalex.org/W1981223513","https://openalex.org/W3124525987","https://openalex.org/W2141426340","https://openalex.org/W1556020586","https://openalex.org/W2351863666","https://openalex.org/W2357734103","https://openalex.org/W4285453214","https://openalex.org/W4312779177","https://openalex.org/W2527731966","https://openalex.org/W4291316326"],"abstract_inverted_index":{"The":[0,74,151,193],"half-logistic":[1],"modified":[2,22],"Kies":[3,23],"exponential":[4,24],"(HLMKEx)":[5],"distribution":[6,25,44,164,205],"is":[7,13],"a":[8],"novel":[9],"three-parameter":[10],"model":[11],"that":[12],"introduced":[14],"in":[15,30,156,178,197],"the":[16,21,38,42,71,84,116,124,137,162,168,179,185,190,203,209],"current":[17],"work":[18],"to":[19,35,69,158,183,199],"expand":[20],"and":[26,49,57,90,130,133,146,187],"improve":[27],"its":[28,36,108],"flexibility":[29],"modeling":[31],"real-world":[32],"data.":[33],"Due":[34],"versatility,":[37],"density":[39],"function":[40],"of":[41,92,97,118,126,140,181,189],"HLMKEx":[43,72,75],"offers":[45],"symmetrical,":[46],"asymmetrical,":[47],"unimodal,":[48],"reversed-J-shaped,":[50],"as":[51,53,83,99,101],"well":[52,100],"increasing,":[54],"reversed-J":[55],"shaped,":[56],"upside-down":[58],"hazard":[59],"rate":[60],"forms.":[61],"An":[62],"infinite":[63],"linear":[64],"representation":[65],"can":[66,165,206],"be":[67],"used":[68],"represent":[70],"density.":[73],"model\u2019s":[76],"fundamental":[77],"mathematical":[78],"features":[79],"are":[80,104,113,176],"obtained,":[81],"such":[82],"quantile":[85],"function,":[86],"moments,":[87,89],"incomplete":[88],"moments":[91],"residuals.":[93],"Additionally,":[94],"some":[95],"measures":[96,139],"uncertainty":[98],"stochastic":[102],"ordering":[103],"derived.":[105],"To":[106],"estimate":[107],"parameters,":[109],"eight":[110],"estimation":[111],"methods":[112],"used.":[114],"With":[115],"use":[117],"detailed":[119],"simulation":[120,152],"data,":[121],"we":[122],"compare":[123],"performance":[125],"each":[127],"estimating":[128],"technique":[129],"obtain":[131],"partial":[132],"total":[134],"ranks":[135],"for":[136],"accuracy":[138],"absolute":[141,148],"bias,":[142],"mean":[143,147],"squared":[144],"error,":[145],"relative":[149],"error.":[150],"results":[153],"demonstrate":[154,184,195],"that,":[155,196],"contrast":[157,198],"other":[159,200],"competing":[160,201],"distributions,":[161,202],"proposed":[163],"actually":[166,207],"fit":[167,208],"data":[169,174,210],"more":[170,211],"accurately.":[171,212],"Two":[172],"actual":[173],"sets":[175],"investigated":[177],"field":[180],"engineering":[182],"adaptability":[186],"application":[188],"suggested":[191],"distribution.":[192],"findings":[194],"provided":[204]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8}],"updated_date":"2026-06-04T09:04:59.091469","created_date":"2025-10-10T00:00:00"}
