{"id":"https://openalex.org/W3203602845","doi":"https://doi.org/10.3390/sym13101868","title":"Exponentiated Generalized Inverted Gompertz Distribution: Properties and Estimation Methods with Applications to Symmetric and Asymmetric Data","display_name":"Exponentiated Generalized Inverted Gompertz Distribution: Properties and Estimation Methods with Applications to Symmetric and Asymmetric Data","publication_year":2021,"publication_date":"2021-10-04","ids":{"openalex":"https://openalex.org/W3203602845","doi":"https://doi.org/10.3390/sym13101868","mag":"3203602845"},"language":"en","primary_location":{"id":"doi:10.3390/sym13101868","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101868","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1868/pdf?version=1634883753","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/2073-8994/13/10/1868/pdf?version=1634883753","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":"Mahmoud 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/A5001243210","display_name":"Adel A. El-Faheem","orcid":null},"institutions":[{"id":"https://openalex.org/I86310350","display_name":"Aswan University","ror":"https://ror.org/048qnr849","country_code":"EG","type":"education","lineage":["https://openalex.org/I86310350"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Adel A. El-Faheem","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt","institution_ids":["https://openalex.org/I86310350"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021240607","display_name":"Afrah Al\u2010Bossly","orcid":"https://orcid.org/0000-0001-9623-5872"},"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":"Afrah Al-Bossly","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":null,"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":"last","author":{"id":"https://openalex.org/A5023832260","display_name":"Mohamed El-Dawoody","orcid":"https://orcid.org/0000-0001-9710-1550"},"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/I86310350","display_name":"Aswan University","ror":"https://ror.org/048qnr849","country_code":"EG","type":"education","lineage":["https://openalex.org/I86310350"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Mohamed El-Dawoody","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, Aswan University, Aswan 81528, Egypt"],"raw_orcid":null,"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, Aswan University, Aswan 81528, Egypt","institution_ids":["https://openalex.org/I86310350"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"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":0.7012,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.73906325,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"13","issue":"10","first_page":"1868","last_page":"1868"},"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.921999990940094,"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":0.9081000089645386,"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/kurtosis","display_name":"Kurtosis","score":0.7396801114082336},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6455448865890503},{"id":"https://openalex.org/keywords/skewness","display_name":"Skewness","score":0.5740774273872375},{"id":"https://openalex.org/keywords/quantile-function","display_name":"Quantile function","score":0.5534230470657349},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5402107238769531},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5118007063865662},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.461694598197937},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4335598349571228},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"Moment-generating function","score":0.305044949054718},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.2638155221939087}],"concepts":[{"id":"https://openalex.org/C166963901","wikidata":"https://www.wikidata.org/wiki/Q287251","display_name":"Kurtosis","level":2,"score":0.7396801114082336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6455448865890503},{"id":"https://openalex.org/C122342681","wikidata":"https://www.wikidata.org/wiki/Q330828","display_name":"Skewness","level":2,"score":0.5740774273872375},{"id":"https://openalex.org/C47121976","wikidata":"https://www.wikidata.org/wiki/Q3489473","display_name":"Quantile function","level":4,"score":0.5534230470657349},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5402107238769531},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5118007063865662},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.461694598197937},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4335598349571228},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.305044949054718},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.2638155221939087},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13101868","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101868","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1868/pdf?version=1634883753","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:bc29fd300edc46199ee4a0a7b62876a3","is_oa":true,"landing_page_url":"https://doaj.org/article/bc29fd300edc46199ee4a0a7b62876a3","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":"Symmetry, Vol 13, Iss 10, p 1868 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/10/1868/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13101868","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/sym13101868","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101868","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1868/pdf?version=1634883753","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3203602845.pdf","grobid_xml":"https://content.openalex.org/works/W3203602845.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1589112945","https://openalex.org/W1964366808","https://openalex.org/W2005944024","https://openalex.org/W2029645921","https://openalex.org/W2058115831","https://openalex.org/W2063805616","https://openalex.org/W2077569953","https://openalex.org/W2081932090","https://openalex.org/W2090035663","https://openalex.org/W2094923943","https://openalex.org/W2098804561","https://openalex.org/W2123291367","https://openalex.org/W2132504853","https://openalex.org/W2157230072","https://openalex.org/W2186238461","https://openalex.org/W2322557778","https://openalex.org/W2503485756","https://openalex.org/W2605606134","https://openalex.org/W2887686475","https://openalex.org/W2995579671","https://openalex.org/W3051248049","https://openalex.org/W3092823782","https://openalex.org/W3107600132","https://openalex.org/W3114547982","https://openalex.org/W3125094194","https://openalex.org/W4285719527","https://openalex.org/W6635194960","https://openalex.org/W6678629879","https://openalex.org/W6735534810","https://openalex.org/W6736781505","https://openalex.org/W6782001491"],"related_works":["https://openalex.org/W4225568567","https://openalex.org/W4286378979","https://openalex.org/W1496883226","https://openalex.org/W4297337052","https://openalex.org/W2028605949","https://openalex.org/W2282665605","https://openalex.org/W3216026256","https://openalex.org/W3129919015","https://openalex.org/W4390742338","https://openalex.org/W2037499216"],"abstract_inverted_index":{"In":[0],"this":[1,52,161],"article,":[2],"a":[3],"new":[4,118],"four-parameter":[5],"lifetime":[6],"model":[7,26,86,119,142,162],"called":[8],"the":[9,27,39,55,84,94,114,117,123,128,134,140],"exponentiated":[10],"generalized":[11],"inverted":[12],"Gompertz":[13],"distribution":[14,22],"is":[15,23,35,109,143,158,163],"studied":[16,85],"and":[17,34,41,63,72,77,102,133,153,156,166],"proposed.":[18],"The":[19,81,137],"newly":[20],"proposed":[21,141],"able":[24],"to":[25,112,151],"lifetimes":[28],"with":[29],"upside-down":[30],"bathtub-shaped":[31],"hazard":[32,58],"rates":[33],"suitable":[36],"for":[37,170],"describing":[38],"negative":[40],"positive":[42],"skewness.":[43],"A":[44,106],"detailed":[45],"description":[46],"of":[47,51,83,116,139],"some":[48],"various":[49,91],"properties":[50],"model,":[53],"including":[54],"reliability":[56],"function,":[57,60,62,69],"rate":[59],"quantile":[61],"median,":[64],"mode,":[65],"moments,":[66],"moment":[67],"generating":[68],"entropies,":[70],"kurtosis,":[71],"skewness,":[73],"mean":[74,129],"waiting":[75],"lifetime,":[76],"others":[78],"are":[79,87],"presented.":[80],"parameters":[82],"appreciated":[88],"using":[89,127],"four":[90,124,147],"estimation":[92,125],"methods,":[93],"maximum":[95],"likelihood,":[96],"least":[97,100],"squares,":[98,101],"weighted":[99],"Cram\u00e9r-von":[103],"Mises":[104],"methods.":[105],"simulation":[107],"study":[108],"carried":[110],"out":[111],"examine":[113],"performance":[115],"estimators":[120],"based":[121],"on":[122],"methods":[126],"squared":[130],"errors":[131],"(MSEs)":[132],"bias":[135],"estimates.":[136],"flexibility":[138],"clarified":[144],"by":[145],"studying":[146],"different":[148],"engineering":[149],"applications":[150],"symmetric":[152],"asymmetric":[154],"data,":[155],"it":[157],"found":[159],"that":[160],"more":[164],"flexible":[165],"works":[167],"quite":[168],"well":[169],"modeling":[171],"these":[172],"data.":[173]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
