{"id":"https://openalex.org/W4392096308","doi":"https://doi.org/10.3390/axioms13030146","title":"Some Properties of Zipf\u2019s Law and Applications","display_name":"Some Properties of Zipf\u2019s Law and Applications","publication_year":2024,"publication_date":"2024-02-23","ids":{"openalex":"https://openalex.org/W4392096308","doi":"https://doi.org/10.3390/axioms13030146"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13030146","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13030146","pdf_url":"https://www.mdpi.com/2075-1680/13/3/146/pdf?version=1708699942","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/2075-1680/13/3/146/pdf?version=1708699942","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045358823","display_name":"Speran\u0163a Cecilia Bolea","orcid":null},"institutions":[{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Speranta Cecilia Bolea","raw_affiliation_strings":["Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania","institution_ids":["https://openalex.org/I58077936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077269912","display_name":"Mironela P\u00eern\u0103u","orcid":null},"institutions":[{"id":"https://openalex.org/I100749904","display_name":"Titu Maiorescu University","ror":"https://ror.org/0367qb939","country_code":"RO","type":"education","lineage":["https://openalex.org/I100749904"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Mironela Pirnau","raw_affiliation_strings":["Faculty of Informatics, Titu Maiorescu University, 040441 Bucharest, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Informatics, Titu Maiorescu University, 040441 Bucharest, Romania","institution_ids":["https://openalex.org/I100749904"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043014758","display_name":"Silviu-Ioan Bejinariu","orcid":"https://orcid.org/0000-0003-2681-4478"},"institutions":[{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Silviu-Ioan Bejinariu","raw_affiliation_strings":["Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania","institution_ids":["https://openalex.org/I58077936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029450098","display_name":"Vasile Apopei","orcid":null},"institutions":[{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Vasile Apopei","raw_affiliation_strings":["Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania","institution_ids":["https://openalex.org/I58077936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059332073","display_name":"Daniela G\u00eefu","orcid":"https://orcid.org/0000-0001-8116-053X"},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Daniela Gifu","raw_affiliation_strings":["Faculty of Computer Science, \u201cAlexandru Ioan Cuza\u201d University of Ia\u015fi, 700483 Ia\u0219i, Romania","Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, \u201cAlexandru Ioan Cuza\u201d University of Ia\u015fi, 700483 Ia\u0219i, Romania","institution_ids":["https://openalex.org/I138164181"]},{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania","institution_ids":["https://openalex.org/I58077936"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009030184","display_name":"Horia-Nicolai Teodorescu","orcid":"https://orcid.org/0000-0001-8685-7838"},"institutions":[{"id":"https://openalex.org/I4210108695","display_name":"Gheorghe Asachi Technical University of Ia\u0219i","ror":"https://ror.org/014zxnz40","country_code":"RO","type":"education","lineage":["https://openalex.org/I4210108695"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Horia-Nicolai Teodorescu","raw_affiliation_strings":["Department Applied Electronics, Technical University of Ia\u0219i, 700050 Ia\u0219i, Romania","Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department Applied Electronics, Technical University of Ia\u0219i, 700050 Ia\u0219i, Romania","institution_ids":["https://openalex.org/I4210108695"]},{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Ia\u015fi Branch, 700481 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Institute of Computer Science, Romanian Academy Iasi Branch, 700481 Iasi, Romania","institution_ids":["https://openalex.org/I58077936"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5009030184","https://openalex.org/A5045358823"],"corresponding_institution_ids":["https://openalex.org/I4210108695","https://openalex.org/I58077936"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.3146,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.87713496,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"13","issue":"3","first_page":"146","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9639999866485596,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9639999866485596,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9526000022888184,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9337999820709229,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/zipfs-law","display_name":"Zipf's law","score":0.9938216209411621},{"id":"https://openalex.org/keywords/power-law","display_name":"Power law","score":0.5461682677268982},{"id":"https://openalex.org/keywords/relevance","display_name":"Relevance (law)","score":0.49345627427101135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.432706356048584},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4137059152126312},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3879629373550415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36415064334869385},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3268882632255554},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15608000755310059},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07192602753639221}],"concepts":[{"id":"https://openalex.org/C125932096","wikidata":"https://www.wikidata.org/wiki/Q205472","display_name":"Zipf's law","level":2,"score":0.9938216209411621},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.5461682677268982},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.49345627427101135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.432706356048584},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4137059152126312},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3879629373550415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36415064334869385},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3268882632255554},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15608000755310059},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07192602753639221},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13030146","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13030146","pdf_url":"https://www.mdpi.com/2075-1680/13/3/146/pdf?version=1708699942","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:f071d251e3c14c628ed917f8769492ab","is_oa":true,"landing_page_url":"https://doaj.org/article/f071d251e3c14c628ed917f8769492ab","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":"Axioms, Vol 13, Iss 3, p 146 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13030146","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13030146","pdf_url":"https://www.mdpi.com/2075-1680/13/3/146/pdf?version=1708699942","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":[{"id":"https://metadata.un.org/sdg/16","score":0.7200000286102295,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392096308.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1507719567","https://openalex.org/W1527603700","https://openalex.org/W1977206595","https://openalex.org/W1980509985","https://openalex.org/W1993803315","https://openalex.org/W2021257428","https://openalex.org/W2036418910","https://openalex.org/W2039965043","https://openalex.org/W2096748633","https://openalex.org/W2106317195","https://openalex.org/W2113625868","https://openalex.org/W2124469295","https://openalex.org/W2154612479","https://openalex.org/W2159491186","https://openalex.org/W2163170240","https://openalex.org/W2261150581","https://openalex.org/W2318575377","https://openalex.org/W2562665409","https://openalex.org/W2590321369","https://openalex.org/W2734150319","https://openalex.org/W2893685411","https://openalex.org/W2949465136","https://openalex.org/W2954657388","https://openalex.org/W2969233311","https://openalex.org/W4200435207","https://openalex.org/W4220708734","https://openalex.org/W4231037951","https://openalex.org/W4296742976","https://openalex.org/W4366827547","https://openalex.org/W4383747052","https://openalex.org/W4387460722","https://openalex.org/W6677001665","https://openalex.org/W6681654339","https://openalex.org/W6856948496"],"related_works":["https://openalex.org/W3103059940","https://openalex.org/W2359494425","https://openalex.org/W2990040850","https://openalex.org/W2098897829","https://openalex.org/W1591934807","https://openalex.org/W2381875313","https://openalex.org/W2385862456","https://openalex.org/W1668269284","https://openalex.org/W1614181660","https://openalex.org/W2741366111"],"abstract_inverted_index":{"The":[0,114],"article":[1],"extends":[2],"the":[3,26,32,36,40,45,51,65,71,74,77,83,88,120],"theoretical":[4,84],"and":[5,30,50,73,94],"applicative":[6],"analysis":[7,121],"of":[8,17,19,35,58,76,99,107,109,122],"Zipf\u2019s":[9,20,59,112],"law.":[10,113],"We":[11,53],"are":[12,47,131],"concerned":[13],"with":[14,87,104,124,126],"a":[15],"set":[16],"properties":[18],"law":[21,28,41,60],"that":[22,61,101,106],"derive":[23],"directly":[24],"from":[25,31,82,92],"power":[27],"expression":[29],"discrete":[33],"nature":[34],"objects":[37,46],"to":[38],"which":[39],"is":[42,105],"applied,":[43],"when":[44],"words,":[48],"lemmas,":[49],"like.":[52],"also":[54,132],"search":[55],"for":[56],"variations":[57],"can":[62],"help":[63],"explain":[64],"noisy":[66],"results":[67],"empirically":[68,78],"reported":[69],"in":[70,119],"literature":[72],"departures":[75],"obtained":[79],"nonlinear":[80],"graph":[81],"linear":[85],"one,":[86],"variants":[89],"analyzed":[90],"differing":[91],"Mandelbrot":[93],"lognormal":[95],"distributions.":[96],"A":[97],"problem":[98,116],"interest":[100],"we":[102],"deal":[103],"mixtures":[108],"populations":[110],"obeying":[111],"last":[115],"has":[117],"relevance":[118],"texts":[123],"words":[125],"various":[127],"etymologies.":[128],"Computational":[129],"aspects":[130],"addressed.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}