{"id":"https://openalex.org/W3128071215","doi":"https://doi.org/10.3390/e23020194","title":"A New Family of Continuous Probability Distributions","display_name":"A New Family of Continuous Probability Distributions","publication_year":2021,"publication_date":"2021-02-05","ids":{"openalex":"https://openalex.org/W3128071215","doi":"https://doi.org/10.3390/e23020194","mag":"3128071215","pmid":"https://pubmed.ncbi.nlm.nih.gov/33562575"},"language":"en","primary_location":{"id":"doi:10.3390/e23020194","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23020194","pdf_url":"https://www.mdpi.com/1099-4300/23/2/194/pdf?version=1612855191","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/2/194/pdf?version=1612855191","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015592835","display_name":"Mahmoud El-Morshedy","orcid":"https://orcid.org/0000-0002-7585-5519"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]},{"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","SA"],"is_corresponding":true,"raw_author_name":"M. El-Morshedy","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia","Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-7585-5519","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086562119","display_name":"Fahad Sameer Alshammari","orcid":"https://orcid.org/0000-0002-5402-8960"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fahad Sameer Alshammari","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-5402-8960","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033097731","display_name":"Y. S. Hamed","orcid":"https://orcid.org/0000-0002-0365-0282"},"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":"Yasser S. Hamed","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-0365-0282","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017464849","display_name":"Mohamed S. Eliwa","orcid":"https://orcid.org/0000-0001-5619-210X"},"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":"Mohammed S. Eliwa","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-5619-210X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036983324","display_name":"Haitham M. Yousof","orcid":"https://orcid.org/0000-0003-4589-4944"},"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":"Haitham M. Yousof","raw_affiliation_strings":["Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-4589-4944","affiliations":[{"raw_affiliation_string":"Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt","institution_ids":["https://openalex.org/I207547235"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5015592835"],"corresponding_institution_ids":["https://openalex.org/I142608572","https://openalex.org/I159247623"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.8437,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.97175278,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"23","issue":"2","first_page":"194","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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":0.991100013256073,"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/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/copula","display_name":"Copula (linguistics)","score":0.7592871189117432},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.6925240159034729},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.6350610852241516},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5882907509803772},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.5694238543510437},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5396438241004944},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.5202756524085999},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4621264636516571},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.45525890588760376},{"id":"https://openalex.org/keywords/gumbel-distribution","display_name":"Gumbel distribution","score":0.4394226670265198},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.43468862771987915},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.4193716049194336},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40624764561653137},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3168351948261261},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2623131573200226},{"id":"https://openalex.org/keywords/extreme-value-theory","display_name":"Extreme value theory","score":0.1593340039253235},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08904552459716797}],"concepts":[{"id":"https://openalex.org/C17618745","wikidata":"https://www.wikidata.org/wiki/Q207509","display_name":"Copula (linguistics)","level":2,"score":0.7592871189117432},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.6925240159034729},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6350610852241516},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5882907509803772},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.5694238543510437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5396438241004944},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.5202756524085999},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4621264636516571},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.45525890588760376},{"id":"https://openalex.org/C137610916","wikidata":"https://www.wikidata.org/wiki/Q1096862","display_name":"Gumbel distribution","level":3,"score":0.4394226670265198},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.43468862771987915},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.4193716049194336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40624764561653137},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3168351948261261},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2623131573200226},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.1593340039253235},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08904552459716797}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23020194","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23020194","pdf_url":"https://www.mdpi.com/1099-4300/23/2/194/pdf?version=1612855191","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33562575","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33562575","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:d8a3ef67f2534af78e7cbb1be167313e","is_oa":true,"landing_page_url":"https://doaj.org/article/d8a3ef67f2534af78e7cbb1be167313e","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":"Entropy, Vol 23, Iss 2, p 194 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/2/194/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23020194","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":"Entropy; Volume 23; Issue 2; Pages: 194","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7915776","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7915776","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23020194","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23020194","pdf_url":"https://www.mdpi.com/1099-4300/23/2/194/pdf?version=1612855191","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3128071215.pdf"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W144270610","https://openalex.org/W1606015693","https://openalex.org/W1909248777","https://openalex.org/W1992821923","https://openalex.org/W2012130689","https://openalex.org/W2032490797","https://openalex.org/W2036209393","https://openalex.org/W2037320554","https://openalex.org/W2038941270","https://openalex.org/W2042806760","https://openalex.org/W2061984794","https://openalex.org/W2067050279","https://openalex.org/W2119436275","https://openalex.org/W2158114082","https://openalex.org/W2167403607","https://openalex.org/W2264611592","https://openalex.org/W2410322314","https://openalex.org/W2563285174","https://openalex.org/W2620679979","https://openalex.org/W2789991694","https://openalex.org/W2883785478","https://openalex.org/W2889064625","https://openalex.org/W2896061849","https://openalex.org/W2902938147","https://openalex.org/W2906640625","https://openalex.org/W2907134704","https://openalex.org/W2964277900","https://openalex.org/W2998122110","https://openalex.org/W3008640623","https://openalex.org/W3010579914","https://openalex.org/W3011447047","https://openalex.org/W3015773004","https://openalex.org/W3023009180","https://openalex.org/W3033089225","https://openalex.org/W3035310783","https://openalex.org/W3038051845","https://openalex.org/W3086399772","https://openalex.org/W3090161142","https://openalex.org/W3110989813","https://openalex.org/W3117837103","https://openalex.org/W3125180093","https://openalex.org/W3137282901","https://openalex.org/W4242533288","https://openalex.org/W6667058769","https://openalex.org/W6738586193","https://openalex.org/W6749036464","https://openalex.org/W6752886461","https://openalex.org/W6754111636","https://openalex.org/W6755465731","https://openalex.org/W6757401543","https://openalex.org/W6766085723","https://openalex.org/W6777404899","https://openalex.org/W6779640607"],"related_works":["https://openalex.org/W2293264460","https://openalex.org/W3009271360","https://openalex.org/W4387723075","https://openalex.org/W2065711427","https://openalex.org/W2279180773","https://openalex.org/W2460210093","https://openalex.org/W1491652911","https://openalex.org/W66368164","https://openalex.org/W3107594666","https://openalex.org/W2989892462"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,61],"new":[4,31,119],"parametric":[5],"compound":[6],"G":[7,18,33],"family":[8,20],"of":[9,38,99,102,117],"continuous":[10],"probability":[11],"distributions":[12],"called":[13],"the":[14,36,67,70,85,95,100,103,115,118],"Poisson":[15],"generalized":[16],"exponential":[17,68],"(PGEG)":[19],"is":[21,64,81,91],"derived":[22],"and":[23,48,60,69],"studied.":[24],"Relevant":[25],"mathematical":[26],"properties":[27],"are":[28,53,58,111],"derived.":[29],"Some":[30],"bivariate":[32],"families":[34],"using":[35],"theorems":[37],"\"Farlie-Gumbel-Morgenstern":[39],"copula\",":[40,44,47],"\"the":[41,45,49],"modified":[42],"Farlie-Gumbel-Morgenstern":[43],"Clayton":[46],"Renyi's":[50],"entropy":[51],"copula\"":[52],"presented.":[54],"Many":[55],"special":[56,62],"members":[57],"derived,":[59],"attention":[63],"devoted":[65],"to":[66,83,93,113],"one":[71],"parameter":[72],"Pareto":[73],"type":[74],"II":[75],"model.":[76],"The":[77],"maximum":[78,104],"likelihood":[79,105],"method":[80],"used":[82],"estimate":[84],"model":[86],"parameters.":[87],"A":[88],"graphical":[89],"simulation":[90],"performed":[92],"assess":[94],"finite":[96],"sample":[97],"behavior":[98],"estimators":[101],"method.":[106],"Two":[107],"real-life":[108],"data":[109],"applications":[110],"proposed":[112],"illustrate":[114],"importance":[116],"family.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":13}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
