{"id":"https://openalex.org/W2496143004","doi":"https://doi.org/10.3390/sym8080077","title":"The Role of Orthogonal Polynomials in Tailoring Spherical Distributions to Kurtosis Requirements","display_name":"The Role of Orthogonal Polynomials in Tailoring Spherical Distributions to Kurtosis Requirements","publication_year":2016,"publication_date":"2016-08-05","ids":{"openalex":"https://openalex.org/W2496143004","doi":"https://doi.org/10.3390/sym8080077","mag":"2496143004"},"language":"en","primary_location":{"id":"doi:10.3390/sym8080077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym8080077","pdf_url":"https://www.mdpi.com/2073-8994/8/8/77/pdf?version=1470392298","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/2073-8994/8/8/77/pdf?version=1470392298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029709606","display_name":"Luca Bagnato","orcid":"https://orcid.org/0000-0003-3129-5385"},"institutions":[{"id":"https://openalex.org/I103320735","display_name":"Universit\u00e0 Cattolica del Sacro Cuore","ror":"https://ror.org/03h7r5v07","country_code":"IT","type":"education","lineage":["https://openalex.org/I103320735"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luca Bagnato","raw_affiliation_strings":["Dipartimento di Discipline matematiche, Finanza matematica ed Econometria, Universit\u00e0 Cattolica del Sacro Cuore, Largo Gemelli 1, Milano 20123, Italy"],"raw_orcid":"https://orcid.org/0000-0003-3129-5385","affiliations":[{"raw_affiliation_string":"Dipartimento di Discipline matematiche, Finanza matematica ed Econometria, Universit\u00e0 Cattolica del Sacro Cuore, Largo Gemelli 1, Milano 20123, Italy","institution_ids":["https://openalex.org/I103320735"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079677435","display_name":"Mario Faliva","orcid":"https://orcid.org/0000-0002-7882-1111"},"institutions":[{"id":"https://openalex.org/I103320735","display_name":"Universit\u00e0 Cattolica del Sacro Cuore","ror":"https://ror.org/03h7r5v07","country_code":"IT","type":"education","lineage":["https://openalex.org/I103320735"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Mario Faliva","raw_affiliation_strings":["Dipartimento di Discipline matematiche, Finanza matematica ed Econometria, Universit\u00e0 Cattolica del Sacro Cuore, Largo Gemelli 1, Milano 20123, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7882-1111","affiliations":[{"raw_affiliation_string":"Dipartimento di Discipline matematiche, Finanza matematica ed Econometria, Universit\u00e0 Cattolica del Sacro Cuore, Largo Gemelli 1, Milano 20123, Italy","institution_ids":["https://openalex.org/I103320735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081526151","display_name":"Maria Grazia Zoia","orcid":"https://orcid.org/0000-0002-8169-781X"},"institutions":[{"id":"https://openalex.org/I103320735","display_name":"Universit\u00e0 Cattolica del Sacro Cuore","ror":"https://ror.org/03h7r5v07","country_code":"IT","type":"education","lineage":["https://openalex.org/I103320735"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Maria Zoia","raw_affiliation_strings":["Dipartimento di Discipline matematiche, Finanza matematica ed Econometria, Universit\u00e0 Cattolica del Sacro Cuore, Largo Gemelli 1, Milano 20123, Italy"],"raw_orcid":"https://orcid.org/0000-0002-8169-781X","affiliations":[{"raw_affiliation_string":"Dipartimento di Discipline matematiche, Finanza matematica ed Econometria, Universit\u00e0 Cattolica del Sacro Cuore, Largo Gemelli 1, Milano 20123, Italy","institution_ids":["https://openalex.org/I103320735"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081526151"],"corresponding_institution_ids":["https://openalex.org/I103320735"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07957572,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":"8","first_page":"77","last_page":"77"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9868999719619751,"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":0.9868999719619751,"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":0.9801999926567078,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9731000065803528,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9355772137641907},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.7593479156494141},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.7114381194114685},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6830376386642456},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6683706045150757},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5568345189094543},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4850575029850006},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.466429740190506},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44185152649879456},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2627195715904236},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2201414704322815},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0836668610572815}],"concepts":[{"id":"https://openalex.org/C166963901","wikidata":"https://www.wikidata.org/wiki/Q287251","display_name":"Kurtosis","level":2,"score":0.9355772137641907},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.7593479156494141},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.7114381194114685},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6830376386642456},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6683706045150757},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5568345189094543},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4850575029850006},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.466429740190506},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44185152649879456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2627195715904236},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2201414704322815},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0836668610572815},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym8080077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym8080077","pdf_url":"https://www.mdpi.com/2073-8994/8/8/77/pdf?version=1470392298","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:101d8f9570144377a0e8ea14c0fbae4f","is_oa":true,"landing_page_url":"https://doaj.org/article/101d8f9570144377a0e8ea14c0fbae4f","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 8, Iss 8, p 77 (2016)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/8/8/77/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym8080077","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; Volume 8; Issue 8; Pages: 77","raw_type":"Text"},{"id":"pmh:oai:publicatt.unicatt.it:10807/85878","is_oa":true,"landing_page_url":"http://hdl.handle.net/10807/85878","pdf_url":null,"source":{"id":"https://openalex.org/S4306400564","display_name":"PubliCatt (Universit\u00e0 Cattolica del Sacro Cuore)","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/sym8080077","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym8080077","pdf_url":"https://www.mdpi.com/2073-8994/8/8/77/pdf?version=1470392298","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/W2496143004.pdf","grobid_xml":"https://content.openalex.org/works/W2496143004.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W10810736","https://openalex.org/W1502381559","https://openalex.org/W1568957629","https://openalex.org/W1570034505","https://openalex.org/W1971053858","https://openalex.org/W2011580583","https://openalex.org/W2016130389","https://openalex.org/W2044004061","https://openalex.org/W2087373255","https://openalex.org/W2094293852","https://openalex.org/W2238250302","https://openalex.org/W2963502607","https://openalex.org/W4300246981","https://openalex.org/W6600448088","https://openalex.org/W6634000698","https://openalex.org/W6690283901"],"related_works":["https://openalex.org/W2538623560","https://openalex.org/W3170604491","https://openalex.org/W1828158523","https://openalex.org/W2049578243","https://openalex.org/W2000145235","https://openalex.org/W2153643386","https://openalex.org/W2122079181","https://openalex.org/W1985848810","https://openalex.org/W2889939530","https://openalex.org/W3125396235"],"abstract_inverted_index":{"This":[0],"paper":[1],"carries":[2],"out":[3],"an":[4],"investigation":[5],"of":[6,38,49,77],"the":[7,24,36,75,78,89],"orthogonal-polynomial":[8],"approach":[9,90],"to":[10,14,22,35,56,64,95],"reshaping":[11],"symmetric":[12],"distributions":[13],"fit":[15],"in":[16,30],"with":[17,67,84],"data":[18],"requirements":[19],"so":[20],"as":[21],"cover":[23],"multivariate":[25,47,80],"case.":[26],"With":[27],"this":[28],"objective":[29],"mind,":[31],"reference":[32],"is":[33,93],"made":[34],"class":[37],"spherical":[39,59,98],"distributions,":[40],"given":[41],"that":[42],"they":[43],"provide":[44,71],"a":[45,58],"natural":[46],"generalization":[48],"univariate":[50],"even":[51],"densities.":[52],"After":[53],"showing":[54],"how":[55],"tailor":[57],"distribution":[60],"via":[61],"orthogonal":[62],"polynomials":[63],"better":[65],"comply":[66],"kurtosis":[68,86],"requirements,":[69],"we":[70],"operational":[72],"conditions":[73],"for":[74],"positiveness":[76],"resulting":[79],"Gram\u2013Charlier-like":[81],"expansion,":[82],"together":[83],"its":[85],"range.":[87],"Finally,":[88],"proposed":[91],"here":[92],"applied":[94],"some":[96],"selected":[97],"distributions.":[99]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}