{"id":"https://openalex.org/W4400944072","doi":"https://doi.org/10.3390/axioms13080496","title":"Some Results on the Free Poisson Distribution","display_name":"Some Results on the Free Poisson Distribution","publication_year":2024,"publication_date":"2024-07-24","ids":{"openalex":"https://openalex.org/W4400944072","doi":"https://doi.org/10.3390/axioms13080496"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13080496","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms13080496","pdf_url":"https://www.mdpi.com/2075-1680/13/8/496/pdf?version=1721824811","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/8/496/pdf?version=1721824811","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000311601","display_name":"Ayed R. A. Alanzi","orcid":"https://orcid.org/0000-0002-5337-2276"},"institutions":[{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ayed. R. A. Alanzi","raw_affiliation_strings":["Department of Mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia","Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-5337-2276","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]},{"raw_affiliation_string":"Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5095377573","display_name":"Ohud A. Alqasem","orcid":"https://orcid.org/0009-0002-4020-6647"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ohud A. Alqasem","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"],"raw_orcid":"https://orcid.org/0009-0002-4020-6647","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071851708","display_name":"Maysaa Elmahi Abd Elwahab","orcid":"https://orcid.org/0009-0000-7059-405X"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Maysaa Elmahi Abd Elwahab","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089048863","display_name":"Raouf Fakhfakh","orcid":"https://orcid.org/0000-0003-2233-4899"},"institutions":[{"id":"https://openalex.org/I142899784","display_name":"University of Sfax","ror":"https://ror.org/04d4sd432","country_code":"TN","type":"education","lineage":["https://openalex.org/I142899784"]},{"id":"https://openalex.org/I199702508","display_name":"Jouf University","ror":"https://ror.org/02zsyt821","country_code":"SA","type":"education","lineage":["https://openalex.org/I199702508"]}],"countries":["SA","TN"],"is_corresponding":true,"raw_author_name":"Raouf Fakhfakh","raw_affiliation_strings":["Department of Mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia","Laboratory of Probability and Statistics, Faculty of Sciences of Sfax, University of Sfax, Sfax 3000, Tunisia"],"raw_orcid":"https://orcid.org/0000-0003-2233-4899","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia","institution_ids":["https://openalex.org/I199702508"]},{"raw_affiliation_string":"Laboratory of Probability and Statistics, Faculty of Sciences of Sfax, University of Sfax, Sfax 3000, Tunisia","institution_ids":["https://openalex.org/I142899784"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089048863"],"corresponding_institution_ids":["https://openalex.org/I142899784","https://openalex.org/I199702508"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.6458,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.71054965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"8","first_page":"496","last_page":"496"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices 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/T11716","display_name":"Random Matrices 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/T11830","display_name":"Point processes and geometric inequalities","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/poisson-distribution","display_name":"Poisson distribution","score":0.7873005867004395},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.7529391050338745},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.641085147857666},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.5671206712722778},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5654222369194031},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4658900797367096},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44173580408096313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3659491240978241},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1888832449913025},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07176744937896729}],"concepts":[{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.7873005867004395},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.7529391050338745},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.641085147857666},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.5671206712722778},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5654222369194031},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4658900797367096},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44173580408096313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3659491240978241},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1888832449913025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07176744937896729},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms13080496","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms13080496","pdf_url":"https://www.mdpi.com/2075-1680/13/8/496/pdf?version=1721824811","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0abd9f1e4314438a9aa4da87dc498052","is_oa":false,"landing_page_url":"https://doaj.org/article/0abd9f1e4314438a9aa4da87dc498052","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 8, p 496 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/13/8/496/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13080496","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":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms13080496","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms13080496","pdf_url":"https://www.mdpi.com/2075-1680/13/8/496/pdf?version=1721824811","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5899999737739563}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400944072.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1570229043","https://openalex.org/W1594682445","https://openalex.org/W1600303801","https://openalex.org/W1925318460","https://openalex.org/W1988344476","https://openalex.org/W2314742568","https://openalex.org/W2318335932","https://openalex.org/W2963009812","https://openalex.org/W2964011754","https://openalex.org/W2964180569","https://openalex.org/W3098442735","https://openalex.org/W3102394916","https://openalex.org/W4233185824","https://openalex.org/W4292235929","https://openalex.org/W4294656594","https://openalex.org/W4388130149","https://openalex.org/W6637516499","https://openalex.org/W6858178048"],"related_works":["https://openalex.org/W4255837520","https://openalex.org/W2387011115","https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W4243903653","https://openalex.org/W2016165693","https://openalex.org/W2952106254","https://openalex.org/W119541165","https://openalex.org/W2315835829"],"abstract_inverted_index":{"Let":[0],"K+(\u03bci)={Qsi\u03bci,si\u2208(m0\u03bci,m+\u03bci)},":[1],"i=1,2,":[2],"be":[3],"two":[4],"CSK":[5,45],"families":[6],"generated":[7],"by":[8],"the":[9,22,30,57,66,72,83,92,98,103],"nondegenerate":[10,52],"probability":[11,53,58],"measures":[12,25,59,106],"\u03bc1":[13,61],"and":[14,35,62,70],"\u03bc2":[15,63],"with":[16],"support":[17],"bounded":[18],"from":[19],"above.":[20],"Define":[21],"set":[23],"of":[24,33,65,105],"L=K+(\u03bc1)\u2022K+(\u03bc2)={Qs1\u03bc1\u2022Qs2\u03bc2,s1\u2208(m0\u03bc1,m+\u03bc1)ands2\u2208(m0\u03bc2,m+\u03bc2)},":[26],"where":[27],"Qs1\u03bc1\u2022Qs2\u03bc2":[28],"denotes":[29],"Fermi":[31,99],"convolution":[32,95,100],"Qs1\u03bc1":[34],"Qs2\u03bc2.":[36],"We":[37],"prove":[38],"that":[39],"if":[40,89],"L":[41],"is":[42,87],"still":[43],"a":[44],"family":[46,104],"(that":[47],"is,":[48],"L=K+(\u03c3)":[49],"for":[50],"some":[51],"measure":[54],"()\u03c3),":[55],"then":[56],"\u03c3,":[60],"are":[64],"free":[67,73,84,94],"Poisson":[68,74,85],"type":[69],"follow":[71],"law":[75],"up":[76],"to":[77],"affinity.":[78],"The":[79],"same":[80],"result,":[81],"regarding":[82],"measure,":[86],"obtained":[88],"we":[90],"consider":[91],"t-deformed":[93],"t":[96],"replacing":[97],"\u2022":[101],"in":[102],"L.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
