{"id":"https://openalex.org/W2904097440","doi":"https://doi.org/10.3390/sym10120724","title":"Generalized Modified Slash Birnbaum\u2013Saunders Distribution","display_name":"Generalized Modified Slash Birnbaum\u2013Saunders Distribution","publication_year":2018,"publication_date":"2018-12-06","ids":{"openalex":"https://openalex.org/W2904097440","doi":"https://doi.org/10.3390/sym10120724","mag":"2904097440"},"language":"en","primary_location":{"id":"doi:10.3390/sym10120724","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10120724","pdf_url":"https://www.mdpi.com/2073-8994/10/12/724/pdf?version=1544078091","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/2073-8994/10/12/724/pdf?version=1544078091","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021055806","display_name":"Jimmy Reyes","orcid":"https://orcid.org/0000-0002-2921-3056"},"institutions":[{"id":"https://openalex.org/I129739261","display_name":"Universidad de Antofagasta","ror":"https://ror.org/04eyc6d95","country_code":"CL","type":"education","lineage":["https://openalex.org/I129739261"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Jimmy Reyes","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile","institution_ids":["https://openalex.org/I129739261"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069331662","display_name":"Inmaculada Barranco\u2010Chamorro","orcid":"https://orcid.org/0000-0002-9064-2597"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Inmaculada Barranco-Chamorro","raw_affiliation_strings":["Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universidad de Sevilla, 41000 Sevilla, Spain"],"raw_orcid":"https://orcid.org/0000-0002-9064-2597","affiliations":[{"raw_affiliation_string":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universidad de Sevilla, 41000 Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056938538","display_name":"Diego I. Gallardo","orcid":"https://orcid.org/0000-0001-8184-7403"},"institutions":[{"id":"https://openalex.org/I201487725","display_name":"University of Atacama","ror":"https://ror.org/022yres73","country_code":"CL","type":"education","lineage":["https://openalex.org/I201487725"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Diego I. Gallardo","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"],"raw_orcid":"https://orcid.org/0000-0001-8184-7403","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile","institution_ids":["https://openalex.org/I201487725"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003444918","display_name":"H\u00e9ctor W. G\u00f3mez","orcid":"https://orcid.org/0000-0003-3726-5507"},"institutions":[{"id":"https://openalex.org/I129739261","display_name":"Universidad de Antofagasta","ror":"https://ror.org/04eyc6d95","country_code":"CL","type":"education","lineage":["https://openalex.org/I129739261"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"H\u00e9ctor W. G\u00f3mez","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile","institution_ids":["https://openalex.org/I129739261"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5003444918"],"corresponding_institution_ids":["https://openalex.org/I129739261"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.3823,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.93834363,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"10","issue":"12","first_page":"724","last_page":"724"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9997000098228455,"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":0.9997000098228455,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9746999740600586,"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":0.968999981880188,"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/kurtosis","display_name":"Kurtosis","score":0.9539182186126709},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6274515390396118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.627432107925415},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6089431643486023},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.538161039352417},{"id":"https://openalex.org/keywords/skewness","display_name":"Skewness","score":0.5021963119506836},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.4895807206630707},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4442424178123474},{"id":"https://openalex.org/keywords/slash","display_name":"Slash (logging)","score":0.42173463106155396},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.40246713161468506},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33988091349601746},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18020781874656677}],"concepts":[{"id":"https://openalex.org/C166963901","wikidata":"https://www.wikidata.org/wiki/Q287251","display_name":"Kurtosis","level":2,"score":0.9539182186126709},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6274515390396118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.627432107925415},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6089431643486023},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.538161039352417},{"id":"https://openalex.org/C122342681","wikidata":"https://www.wikidata.org/wiki/Q330828","display_name":"Skewness","level":2,"score":0.5021963119506836},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.4895807206630707},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4442424178123474},{"id":"https://openalex.org/C2779243077","wikidata":"https://www.wikidata.org/wiki/Q7538777","display_name":"Slash (logging)","level":2,"score":0.42173463106155396},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.40246713161468506},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33988091349601746},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18020781874656677},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C97137747","wikidata":"https://www.wikidata.org/wiki/Q38112","display_name":"Forestry","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym10120724","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10120724","pdf_url":"https://www.mdpi.com/2073-8994/10/12/724/pdf?version=1544078091","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:dnet:idus________::e4fdb855cb1ef6a19ef56f4ba22b8d6e","is_oa":false,"landing_page_url":"https://idus.us.es/handle//11441/83234","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:700bb2e91b184528b6f3cf56809f9ab6","is_oa":true,"landing_page_url":"https://doaj.org/article/700bb2e91b184528b6f3cf56809f9ab6","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 10, Iss 12, p 724 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/12/724/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10120724","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/sym10120724","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10120724","pdf_url":"https://www.mdpi.com/2073-8994/10/12/724/pdf?version=1544078091","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":17,"referenced_works":["https://openalex.org/W1589112945","https://openalex.org/W1975644945","https://openalex.org/W1977141703","https://openalex.org/W1981413502","https://openalex.org/W2005875379","https://openalex.org/W2005944024","https://openalex.org/W2040135426","https://openalex.org/W2049633694","https://openalex.org/W2058873683","https://openalex.org/W2089803176","https://openalex.org/W2142635246","https://openalex.org/W2477794859","https://openalex.org/W2497083046","https://openalex.org/W2886522607","https://openalex.org/W6635194960","https://openalex.org/W6660306011","https://openalex.org/W6753911825"],"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":[1,47],"paper,":[2],"a":[3,35],"generalization":[4],"of":[5,23,59],"the":[6,20,24,28,64,71],"modified":[7,90],"slash":[8],"Birnbaum\u2013Saunders":[9],"(BS)":[10],"distribution":[11,31,37,49],"is":[12,16,32,44,50,87],"introduced.":[13],"The":[14],"model":[15,53],"defined":[17],"by":[18,34,39],"using":[19],"stochastic":[21],"representation":[22],"BS":[25,60],"distribution,":[26],"where":[27],"standard":[29],"normal":[30],"replaced":[33],"symmetric":[36],"proposed":[38,62],"Reyes":[40],"et":[41],"al.":[42],"It":[43],"proved":[45],"that":[46,110],"new":[48],"able":[51],"to":[52],"more":[54],"kurtosis":[55,82],"than":[56],"other":[57],"extensions":[58],"previously":[61],"in":[63,117],"literature.":[65],"Closed":[66],"expressions":[67],"are":[68,103],"given":[69],"for":[70,114],"pdf":[72],"(probability":[73],"density":[74],"functio),":[75],"along":[76],"with":[77],"their":[78],"moments,":[79],"skewness":[80],"and":[81,93,106],"coefficients.":[83],"Inference":[84],"carried":[85],"out":[86],"based":[88],"on":[89],"moments":[91],"method":[92],"maximum":[94],"likelihood":[95],"(ML).":[96],"To":[97],"obtain":[98],"ML":[99],"estimates,":[100],"two":[101],"approaches":[102],"considered:":[104],"Newton\u2013Raphson":[105],"EM-algorithm.":[107],"Applications":[108],"reveal":[109],"it":[111],"has":[112],"potential":[113],"doing":[115],"well":[116],"real":[118],"problems.":[119]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
