{"id":"https://openalex.org/W4317242835","doi":"https://doi.org/10.3390/axioms12010067","title":"Complete Study of an Original Power-Exponential Transformation Approach for Generalizing Probability Distributions","display_name":"Complete Study of an Original Power-Exponential Transformation Approach for Generalizing Probability Distributions","publication_year":2023,"publication_date":"2023-01-07","ids":{"openalex":"https://openalex.org/W4317242835","doi":"https://doi.org/10.3390/axioms12010067"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12010067","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010067","pdf_url":"https://www.mdpi.com/2075-1680/12/1/67/pdf?version=1673952864","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/2075-1680/12/1/67/pdf?version=1673952864","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026197385","display_name":"Mustafa S. Shama","orcid":"https://orcid.org/0000-0001-6700-2316"},"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"]},{"id":"https://openalex.org/I4210139959","display_name":"High Institute for Management Sciences","ror":"https://ror.org/04tcyer40","country_code":"EG","type":"education","lineage":["https://openalex.org/I4210139959"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Mustafa S. Shama","raw_affiliation_strings":["Department of Basic Sciences, CFY, King Saud University, Riyadh 12373, Saudi Arabia","Department of Mathematics, Osim Higher Institute of Administrative Science, Osim 12961, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-6700-2316","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, CFY, King Saud University, Riyadh 12373, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]},{"raw_affiliation_string":"Department of Mathematics, Osim Higher Institute of Administrative Science, Osim 12961, Egypt","institution_ids":["https://openalex.org/I4210139959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048293904","display_name":"Farid El Ktaibi","orcid":"https://orcid.org/0000-0002-2488-5224"},"institutions":[{"id":"https://openalex.org/I91044093","display_name":"Zayed University","ror":"https://ror.org/03snqfa66","country_code":"AE","type":"education","lineage":["https://openalex.org/I91044093"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Farid El Ktaibi","raw_affiliation_strings":["Department of Mathematics and Statistics, Zayed University, Abu Dhabi 144534, United Arab Emirates"],"raw_orcid":"https://orcid.org/0000-0002-2488-5224","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Zayed University, Abu Dhabi 144534, United Arab Emirates","institution_ids":["https://openalex.org/I91044093"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088092118","display_name":"Jamal N. Al Abbasi","orcid":"https://orcid.org/0000-0003-1581-785X"},"institutions":[{"id":"https://openalex.org/I56409017","display_name":"Nahrain University","ror":"https://ror.org/05v2p9075","country_code":"IQ","type":"education","lineage":["https://openalex.org/I56409017"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Jamal N. Al Abbasi","raw_affiliation_strings":["Department of Statistics, Al-Nahrain University, Baghdad 64074, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Al-Nahrain University, Baghdad 64074, Iraq","institution_ids":["https://openalex.org/I56409017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083045521","display_name":"Christophe Chesneau","orcid":"https://orcid.org/0000-0002-1522-9292"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Christophe Chesneau","raw_affiliation_strings":["Department of Mathematics, LMNO, CNRS-Universit\u00e9 de Caen, Campus II, Science 3, 14032 Caen, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, LMNO, CNRS-Universit\u00e9 de Caen, Campus II, Science 3, 14032 Caen, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I98702875"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090850000","display_name":"Ahmed Z. Afify","orcid":"https://orcid.org/0000-0002-6723-6785"},"institutions":[{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ahmed Z. Afify","raw_affiliation_strings":["Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-6723-6785","affiliations":[{"raw_affiliation_string":"Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt","institution_ids":["https://openalex.org/I207547235"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5083045521"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I98702875"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":3.0761,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.92659753,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"12","issue":"1","first_page":"67","last_page":"67"},"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":0.989799976348877,"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":0.9817000031471252,"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/exponential-family","display_name":"Exponential family","score":0.7858953475952148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6446936130523682},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5524555444717407},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5284749269485474},{"id":"https://openalex.org/keywords/natural-exponential-family","display_name":"Natural exponential family","score":0.4970896542072296},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4814278781414032},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4402448236942291},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4319499135017395},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.41865095496177673},{"id":"https://openalex.org/keywords/hazard","display_name":"Hazard","score":0.4155576527118683},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2888554036617279},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28480228781700134},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23398080468177795}],"concepts":[{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.7858953475952148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6446936130523682},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5524555444717407},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5284749269485474},{"id":"https://openalex.org/C60775368","wikidata":"https://www.wikidata.org/wiki/Q17099337","display_name":"Natural exponential family","level":3,"score":0.4970896542072296},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4814278781414032},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4402448236942291},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4319499135017395},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.41865095496177673},{"id":"https://openalex.org/C49261128","wikidata":"https://www.wikidata.org/wiki/Q1132455","display_name":"Hazard","level":2,"score":0.4155576527118683},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2888554036617279},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28480228781700134},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23398080468177795},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12010067","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010067","pdf_url":"https://www.mdpi.com/2075-1680/12/1/67/pdf?version=1673952864","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:2c387d9079484c5184432bd46e8b5362","is_oa":true,"landing_page_url":"https://doaj.org/article/2c387d9079484c5184432bd46e8b5362","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 12, Iss 1, p 67 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/1/67/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12010067","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":"Axioms; Volume 12; Issue 1; Pages: 67","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12010067","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12010067","pdf_url":"https://www.mdpi.com/2075-1680/12/1/67/pdf?version=1673952864","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4317242835.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1973137995","https://openalex.org/W1973429805","https://openalex.org/W2008149271","https://openalex.org/W2036209393","https://openalex.org/W2046262695","https://openalex.org/W2068833365","https://openalex.org/W2075449433","https://openalex.org/W2078253659","https://openalex.org/W2112345887","https://openalex.org/W2114845187","https://openalex.org/W2143902124","https://openalex.org/W2157230072","https://openalex.org/W2168504156","https://openalex.org/W2215991614","https://openalex.org/W2467305554","https://openalex.org/W2518465844","https://openalex.org/W2555343613","https://openalex.org/W2783912754","https://openalex.org/W2904399645","https://openalex.org/W2943519123","https://openalex.org/W2964028894","https://openalex.org/W2973954545","https://openalex.org/W3212857561","https://openalex.org/W4210610759","https://openalex.org/W4239826655","https://openalex.org/W4251428492","https://openalex.org/W4307267303","https://openalex.org/W4376999580","https://openalex.org/W6762306239","https://openalex.org/W6767827023","https://openalex.org/W6808271533"],"related_works":["https://openalex.org/W198350940","https://openalex.org/W4235791879","https://openalex.org/W2732416952","https://openalex.org/W2619715168","https://openalex.org/W2962823242","https://openalex.org/W4253492336","https://openalex.org/W2003245616","https://openalex.org/W1986558198","https://openalex.org/W32534769","https://openalex.org/W2083129711"],"abstract_inverted_index":{"In":[0,79],"this":[1,32,67,193],"paper,":[2],"we":[3],"propose":[4],"a":[5,130,177],"flexible":[6,72],"and":[7,29,175,209],"general":[8],"family":[9,33,86,116],"of":[10,31,66,83,113,143,154,162,166,187,192,200],"distributions":[11,42,82],"based":[12],"on":[13],"an":[14],"original":[15],"power-exponential":[16],"transformation":[17],"approach.":[18],"We":[19],"call":[20],"it":[21],"the":[22,36,40,75,81,84,114,124,135,141,155,163,167,185,188,198,221],"modified":[23,136],"generalized-G":[24],"(MGG)":[25],"family.":[26],"The":[27,64,160,190],"elegance":[28],"significance":[30],"lie":[34],"in":[35,108,213],"ability":[37],"to":[38,70,133,183,207],"modify":[39],"standard":[41],"by":[43,52,57,197],"changing":[44],"their":[45],"functional":[46],"forms":[47],"without":[48],"adding":[49,58],"new":[50,222],"parameters,":[51],"compounding":[53],"two":[54,61,201],"distributions,":[55],"or":[56,60,93],"one":[59],"shape":[62],"parameters.":[63],"aim":[65],"modification":[68],"is":[69,127,170,180,195],"provide":[71],"shapes":[73],"for":[74,101,119,220],"corresponding":[76],"probability":[77],"functions.":[78],"particular,":[80],"MGG":[85,115],"can":[87],"possess":[88],"increasing,":[89],"constant,":[90],"decreasing,":[91],"\u201cunimodal\u201d,":[92],"\u201cbathtub-shaped\u201c":[94],"hazard":[95],"rate":[96],"functions,":[97],"which":[98],"are":[99,117,158,218],"ideal":[100],"fitting":[102],"several":[103],"real":[104],"data":[105,203],"sets":[106],"encountered":[107],"applied":[109],"fields.":[110],"Some":[111,150],"members":[112],"proposed":[118],"special":[120],"distributions.":[121],"Following":[122],"that,":[123],"uniform":[125,137],"distribution":[126,132,139,157],"chosen":[128],"as":[129],"baseline":[131],"yield":[134],"(MU)":[138],"with":[140,147],"goal":[142],"efficiently":[144],"modeling":[145],"measures":[146],"bounded":[148],"values.":[149],"useful":[151],"key":[152],"properties":[153],"MU":[156,168],"determined.":[159],"estimation":[161],"unknown":[164],"parameters":[165],"model":[169,194],"discussed":[171],"using":[172],"seven":[173],"methods,":[174],"then,":[176],"simulation":[178],"study":[179],"carried":[181],"out":[182],"explore":[184],"performance":[186],"estimates.":[189],"flexibility":[191],"illustrated":[196],"analysis":[199],"real-life":[202],"sets.":[204],"When":[205],"compared":[206],"fair":[208],"well-known":[210],"competitor":[211],"models":[212],"contemporary":[214],"literature,":[215],"better-fitting":[216],"results":[217],"obtained":[219],"model.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
