{"id":"https://openalex.org/W3041929711","doi":"https://doi.org/10.3390/sym12071140","title":"The Exponential-Centred Skew-Normal Distribution","display_name":"The Exponential-Centred Skew-Normal Distribution","publication_year":2020,"publication_date":"2020-07-08","ids":{"openalex":"https://openalex.org/W3041929711","doi":"https://doi.org/10.3390/sym12071140","mag":"3041929711"},"language":"en","primary_location":{"id":"doi:10.3390/sym12071140","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071140","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1140/pdf?version=1594867888","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/2073-8994/12/7/1140/pdf?version=1594867888","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058528126","display_name":"Guillermo Mart\u00ednez\u2010Fl\u00f3rez","orcid":"https://orcid.org/0000-0001-6441-5377"},"institutions":[{"id":"https://openalex.org/I243754102","display_name":"Universidade Federal do Cear\u00e1","ror":"https://ror.org/03srtnf24","country_code":"BR","type":"education","lineage":["https://openalex.org/I243754102"]},{"id":"https://openalex.org/I324290372","display_name":"University of C\u00f3rdoba","ror":"https://ror.org/04nmbd607","country_code":"CO","type":"education","lineage":["https://openalex.org/I324290372"]}],"countries":["BR","CO"],"is_corresponding":false,"raw_author_name":"Guillermo Mart\u00ednez-Fl\u00f3rez","raw_affiliation_strings":["Departamento de Matem\u00e1ticas y Estad\u00edstica, Facultad de Ciencias B\u00e1sicas, Universidad de C\u00f3rdoba, C\u00f3rdoba 2300, Colombia","Programa de P\u00f3s-Gradua\u00e7\u00e3o em Modelagem e M\u00e9todos Quantitativos, Universidade Federal do Cear\u00e1, Fortaleza 60020-181, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Facultad de Ciencias B\u00e1sicas, Universidad de C\u00f3rdoba, C\u00f3rdoba 2300, Colombia","institution_ids":["https://openalex.org/I324290372"]},{"raw_affiliation_string":"Programa de P\u00f3s-Gradua\u00e7\u00e3o em Modelagem e M\u00e9todos Quantitativos, Universidade Federal do Cear\u00e1, Fortaleza 60020-181, Brazil","institution_ids":["https://openalex.org/I243754102"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008863188","display_name":"Carlos Barrera-Causil","orcid":"https://orcid.org/0000-0001-7288-7710"},"institutions":[{"id":"https://openalex.org/I4210141572","display_name":"Instituto Tecnol\u00f3gico Metropolitano","ror":"https://ror.org/03zb5p722","country_code":"CO","type":"education","lineage":["https://openalex.org/I4210141572"]}],"countries":["CO"],"is_corresponding":false,"raw_author_name":"Carlos Barrera-Causil","raw_affiliation_strings":["Davinci Research Group, Faculty of Applied and Exact Sciences, Metropolitan Technological Institute, Medell\u00edn 050034, Colombia"],"raw_orcid":"https://orcid.org/0000-0001-7288-7710","affiliations":[{"raw_affiliation_string":"Davinci Research Group, Faculty of Applied and Exact Sciences, Metropolitan Technological Institute, Medell\u00edn 050034, Colombia","institution_ids":["https://openalex.org/I4210141572"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074316484","display_name":"Fernando Marmolejo\u2010Ramos","orcid":"https://orcid.org/0000-0003-4680-1287"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Fernando Marmolejo-Ramos","raw_affiliation_strings":["Centre for Change and Complexity in Learning, The University of South Australia, Adelaide 5000, Australia"],"raw_orcid":"https://orcid.org/0000-0003-4680-1287","affiliations":[{"raw_affiliation_string":"Centre for Change and Complexity in Learning, The University of South Australia, Adelaide 5000, Australia","institution_ids":["https://openalex.org/I170239107"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074316484"],"corresponding_institution_ids":["https://openalex.org/I170239107"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.3292,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82350513,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"7","first_page":"1140","last_page":"1140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9776999950408936,"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":0.9625999927520752,"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/skew","display_name":"Skew","score":0.8861598968505859},{"id":"https://openalex.org/keywords/skew-normal-distribution","display_name":"Skew normal distribution","score":0.7691255807876587},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.5851150155067444},{"id":"https://openalex.org/keywords/normal-distribution","display_name":"Normal distribution","score":0.5809697508811951},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5793418288230896},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.49997901916503906},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.48606398701667786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4494832456111908},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40023073554039},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3859662115573883},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3781464397907257},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35851866006851196},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.335615336894989},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1794162392616272},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17683354020118713}],"concepts":[{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.8861598968505859},{"id":"https://openalex.org/C43694697","wikidata":"https://www.wikidata.org/wiki/Q3258551","display_name":"Skew normal distribution","level":3,"score":0.7691255807876587},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.5851150155067444},{"id":"https://openalex.org/C102094743","wikidata":"https://www.wikidata.org/wiki/Q133871","display_name":"Normal distribution","level":2,"score":0.5809697508811951},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5793418288230896},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49997901916503906},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.48606398701667786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4494832456111908},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40023073554039},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3859662115573883},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3781464397907257},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35851866006851196},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.335615336894989},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1794162392616272},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17683354020118713},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym12071140","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071140","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1140/pdf?version=1594867888","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:urm_publish:9916434010501831","is_oa":true,"landing_page_url":"https://find.library.unisa.edu.au/discovery/fulldisplay/alma9916434010501831/61USOUTHAUS_INST:ROR","pdf_url":null,"source":{"id":"https://openalex.org/S4306402528","display_name":"UniSA Research Outputs Repository (University of South Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I170239107","host_organization_name":"University of South Australia","host_organization_lineage":["https://openalex.org/I170239107"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:21065ce9136f4f85a05be34ded48382f","is_oa":true,"landing_page_url":"https://doaj.org/article/21065ce9136f4f85a05be34ded48382f","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 12, Iss 7, p 1140 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/7/1140/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym12071140","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/sym12071140","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071140","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1140/pdf?version=1594867888","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W94194614","https://openalex.org/W244508629","https://openalex.org/W621293842","https://openalex.org/W1986795801","https://openalex.org/W1991328527","https://openalex.org/W2030106096","https://openalex.org/W2068148900","https://openalex.org/W2071225185","https://openalex.org/W2074970793","https://openalex.org/W2114012275","https://openalex.org/W2120860882","https://openalex.org/W2142635246","https://openalex.org/W2144716516","https://openalex.org/W2164593448","https://openalex.org/W2168175751","https://openalex.org/W2311068064","https://openalex.org/W2784207889","https://openalex.org/W2926395306","https://openalex.org/W2980491806","https://openalex.org/W3026506694","https://openalex.org/W6603863532"],"related_works":["https://openalex.org/W2913537149","https://openalex.org/W2165459567","https://openalex.org/W1741818375","https://openalex.org/W2107563144","https://openalex.org/W2340552106","https://openalex.org/W4226049696","https://openalex.org/W2521126215","https://openalex.org/W2997430734","https://openalex.org/W4289406402","https://openalex.org/W1530335070"],"abstract_inverted_index":{"Data":[0],"from":[1],"some":[2],"research":[3],"fields":[4],"tend":[5],"to":[6,47],"exhibit":[7],"a":[8,34,38,62],"positive":[9,71],"skew.":[10],"For":[11],"example,":[12],"in":[13,91],"experimental":[14],"psychology,":[15],"reaction":[16],"times":[17],"(RTs)":[18],"are":[19,85],"characterised":[20],"as":[21],"being":[22],"positively":[23,49],"skewed.":[24],"However,":[25],"it":[26,52,88],"is":[27,45,89],"not":[28],"unlikely":[29],"that":[30,64],"RTs":[31],"can":[32,65],"take":[33],"normal":[35],"or,":[36],"even,":[37],"negative":[39,69],"shape.":[40],"While":[41],"the":[42,73,82],"Ex-Gaussian":[43],"distribution":[44,63,84],"suitable":[46],"model":[48],"skewed":[50,57],"data,":[51],"cannot":[53],"cope":[54],"with":[55,67],"negatively":[56],"data.":[58],"This":[59],"manuscript":[60],"proposes":[61],"deal":[66],"both":[68],"and":[70,87],"skews:":[72],"exponential-centred":[74],"skew-normal":[75],"(ECSN)":[76],"distribution.":[77],"The":[78],"mathematical":[79],"properties":[80],"of":[81],"proposed":[83],"reported,":[86],"featured":[90],"two":[92],"non-synthetic":[93],"datasets.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-07-16T00:00:00"}