{"id":"https://openalex.org/W2949955647","doi":"https://doi.org/10.3390/sym11060781","title":"Beta Exponentiated Modified Weibull Distribution: Properties and Application","display_name":"Beta Exponentiated Modified Weibull Distribution: Properties and Application","publication_year":2019,"publication_date":"2019-06-12","ids":{"openalex":"https://openalex.org/W2949955647","doi":"https://doi.org/10.3390/sym11060781","mag":"2949955647"},"language":"en","primary_location":{"id":"doi:10.3390/sym11060781","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060781","pdf_url":"https://www.mdpi.com/2073-8994/11/6/781/pdf?version=1560340969","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/2073-8994/11/6/781/pdf?version=1560340969","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055680774","display_name":"Mirza Naveed Shahzad","orcid":"https://orcid.org/0000-0001-7310-9144"},"institutions":[{"id":"https://openalex.org/I99165933","display_name":"University of Gujrat","ror":"https://ror.org/01xe5fb92","country_code":"PK","type":"education","lineage":["https://openalex.org/I99165933"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Mirza Naveed Shahzad","raw_affiliation_strings":["Department of Statistics, University of Gujrat, Gujrat 50700, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-7310-9144","affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Gujrat, Gujrat 50700, Pakistan","institution_ids":["https://openalex.org/I99165933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016849246","display_name":"Ehsan Ullah","orcid":"https://orcid.org/0000-0003-0107-6608"},"institutions":[{"id":"https://openalex.org/I99165933","display_name":"University of Gujrat","ror":"https://ror.org/01xe5fb92","country_code":"PK","type":"education","lineage":["https://openalex.org/I99165933"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ehsan Ullah","raw_affiliation_strings":["Department of Statistics, University of Gujrat, Gujrat 50700, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Gujrat, Gujrat 50700, Pakistan","institution_ids":["https://openalex.org/I99165933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068739257","display_name":"Abid Hussanan","orcid":"https://orcid.org/0000-0003-4545-3110"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Abid Hussanan","raw_affiliation_strings":["Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam","Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068739257"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.8615,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.91963326,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":"6","first_page":"781","last_page":"781"},"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":0.9905999898910522,"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9070000052452087,"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/weibull-distribution","display_name":"Weibull distribution","score":0.8862817287445068},{"id":"https://openalex.org/keywords/exponentiated-weibull-distribution","display_name":"Exponentiated Weibull distribution","score":0.7495157122612},{"id":"https://openalex.org/keywords/weibull-modulus","display_name":"Weibull modulus","score":0.652075469493866},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6294223070144653},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.567190408706665},{"id":"https://openalex.org/keywords/distribution-fitting","display_name":"Distribution fitting","score":0.5661368370056152},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4765937030315399},{"id":"https://openalex.org/keywords/bathtub","display_name":"Bathtub","score":0.46231135725975037},{"id":"https://openalex.org/keywords/log-logistic-distribution","display_name":"Log-logistic distribution","score":0.462216317653656},{"id":"https://openalex.org/keywords/weibull-fading","display_name":"Weibull fading","score":0.4538874924182892},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4439311623573303},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.43391352891921997},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.420444130897522},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4190182089805603},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4154170751571655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17070326209068298},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12223559617996216},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.09094458818435669},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.0898216962814331},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0626036524772644}],"concepts":[{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.8862817287445068},{"id":"https://openalex.org/C95770405","wikidata":"https://www.wikidata.org/wiki/Q5421539","display_name":"Exponentiated Weibull distribution","level":3,"score":0.7495157122612},{"id":"https://openalex.org/C130630143","wikidata":"https://www.wikidata.org/wiki/Q7979803","display_name":"Weibull modulus","level":3,"score":0.652075469493866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6294223070144653},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.567190408706665},{"id":"https://openalex.org/C160947583","wikidata":"https://www.wikidata.org/wiki/Q2083147","display_name":"Distribution fitting","level":3,"score":0.5661368370056152},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4765937030315399},{"id":"https://openalex.org/C2777728836","wikidata":"https://www.wikidata.org/wiki/Q152095","display_name":"Bathtub","level":2,"score":0.46231135725975037},{"id":"https://openalex.org/C66971888","wikidata":"https://www.wikidata.org/wiki/Q3258534","display_name":"Log-logistic distribution","level":4,"score":0.462216317653656},{"id":"https://openalex.org/C64834810","wikidata":"https://www.wikidata.org/wiki/Q7979802","display_name":"Weibull fading","level":5,"score":0.4538874924182892},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4439311623573303},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.43391352891921997},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.420444130897522},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4190182089805603},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4154170751571655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17070326209068298},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12223559617996216},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.09094458818435669},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0898216962814331},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0626036524772644},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C56985126","wikidata":"https://www.wikidata.org/wiki/Q854039","display_name":"Rayleigh fading","level":4,"score":0.0},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11060781","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060781","pdf_url":"https://www.mdpi.com/2073-8994/11/6/781/pdf?version=1560340969","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:3ebfad1c643d4c7280fd811ee4a4d7c6","is_oa":true,"landing_page_url":"https://doaj.org/article/3ebfad1c643d4c7280fd811ee4a4d7c6","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 11, Iss 6, p 781 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/6/781/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11060781","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/sym11060781","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11060781","pdf_url":"https://www.mdpi.com/2073-8994/11/6/781/pdf?version=1560340969","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":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W83129845","https://openalex.org/W1658049058","https://openalex.org/W1965514245","https://openalex.org/W1966706927","https://openalex.org/W1969763686","https://openalex.org/W1971568850","https://openalex.org/W1990158936","https://openalex.org/W1991525989","https://openalex.org/W1995059026","https://openalex.org/W2005863198","https://openalex.org/W2006458583","https://openalex.org/W2019558974","https://openalex.org/W2021794795","https://openalex.org/W2037655373","https://openalex.org/W2057741915","https://openalex.org/W2063558080","https://openalex.org/W2063980565","https://openalex.org/W2073911314","https://openalex.org/W2087365710","https://openalex.org/W2088023283","https://openalex.org/W2092685198","https://openalex.org/W2108168804","https://openalex.org/W2112105596","https://openalex.org/W2114852361","https://openalex.org/W2129391948","https://openalex.org/W2130388500","https://openalex.org/W2143902124","https://openalex.org/W2145606257","https://openalex.org/W2164376681","https://openalex.org/W2231798766","https://openalex.org/W2331135048","https://openalex.org/W2727420541","https://openalex.org/W2735939896","https://openalex.org/W2952433865","https://openalex.org/W3201950121","https://openalex.org/W3203765264","https://openalex.org/W3205388066","https://openalex.org/W4230155399","https://openalex.org/W4230670048","https://openalex.org/W4285719527","https://openalex.org/W6636957837","https://openalex.org/W6741179540"],"related_works":["https://openalex.org/W2057305954","https://openalex.org/W1478186840","https://openalex.org/W2442908085","https://openalex.org/W2900986898","https://openalex.org/W2108168804","https://openalex.org/W784558617","https://openalex.org/W808604686","https://openalex.org/W2949955647","https://openalex.org/W2060986939","https://openalex.org/W2346566181"],"abstract_inverted_index":{"One":[0],"of":[1,71,77,94,118,134,148],"the":[2,8,46,69,72,78,95,119,135,146,156],"most":[3],"prominent":[4],"statistical":[5,75],"distributions":[6,62],"is":[7,41,143],"Weibull":[9,31,39,139],"distribution.":[10,73],"The":[11,55,74,91,116,132,151],"recent":[12],"modifications":[13],"in":[14,23,33,113],"this":[15,34],"distribution":[16,40,44,57,97,140,159],"have":[17,99],"enhanced":[18],"its":[19],"application":[20],"but":[21],"only":[22],"specific":[24],"fields.":[25],"To":[26],"introduce":[27],"a":[28,64,100],"more":[29],"generalized":[30],"distribution,":[32],"work":[35],"beta":[36,136],"exponentiated":[37,137],"modified":[38,138],"established.":[42],"This":[43],"consolidate":[45],"exponential,":[47],"skewed":[48],"and":[49,83,88,106,127],"symmetric":[50],"shapes":[51],"into":[52],"one":[53],"density.":[54],"proposed":[56,79,96,120,158],"also":[58],"contains":[59],"nineteen":[60],"lifetime":[61],"as":[63],"special":[65],"case,":[66],"which":[67],"shows":[68],"flexibility":[70],"properties":[76],"model":[80,121],"are":[81,122],"derived":[82],"discussed,":[84],"including":[85],"reliability":[86,114],"analysis":[87],"order":[89],"statistics.":[90],"hazard":[92],"function":[93],"can":[98],"unimodal,":[101],"decreasing,":[102],"bathtub,":[103,105],"upside-down":[104],"increasing":[107],"shape":[108],"that":[109,155],"make":[110],"it":[111],"effective":[112],"analysis.":[115],"parameters":[117],"evaluated":[123],"by":[124,145],"maximum":[125],"likelihood":[126],"least":[128],"squares":[129],"estimation":[130],"methods.":[131],"significance":[133],"for":[141],"modeling":[142],"illustrated":[144],"study":[147,153],"real":[149],"data.":[150],"numerical":[152],"indicates":[154],"new":[157],"gives":[160],"better":[161],"results":[162],"than":[163],"other":[164],"comparable":[165],"distributions.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}