{"id":"https://openalex.org/W2124218657","doi":"https://doi.org/10.3390/e14030480","title":"Interval Entropy and Informative Distance","display_name":"Interval Entropy and Informative Distance","publication_year":2012,"publication_date":"2012-03-02","ids":{"openalex":"https://openalex.org/W2124218657","doi":"https://doi.org/10.3390/e14030480","mag":"2124218657"},"language":"en","primary_location":{"id":"doi:10.3390/e14030480","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030480","pdf_url":"https://www.mdpi.com/1099-4300/14/3/480/pdf?version=1424784844","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/14/3/480/pdf?version=1424784844","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034602252","display_name":"F. Misagh","orcid":"https://orcid.org/0000-0002-7567-462X"},"institutions":[{"id":"https://openalex.org/I155419210","display_name":"Islamic Azad University, Science and Research Branch","ror":"https://ror.org/03187yj51","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I155419210"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Fakhroddin Misagh","raw_affiliation_strings":["Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, 14778-93855, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, 14778-93855, Iran","institution_ids":["https://openalex.org/I155419210"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027263209","display_name":"Gholamhossein Yari","orcid":"https://orcid.org/0000-0001-6714-2896"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Gholamhossein Yari","raw_affiliation_strings":["School of Mathematics, Iran University of Science and Technology, Tehran, 16846-13114, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Iran University of Science and Technology, Tehran, 16846-13114, Iran","institution_ids":["https://openalex.org/I67009956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034602252"],"corresponding_institution_ids":["https://openalex.org/I155419210"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.268,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.89760117,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"14","issue":"3","first_page":"480","last_page":"490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9954000115394592,"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9631999731063843,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7148851156234741},{"id":"https://openalex.org/keywords/differential-entropy","display_name":"Differential entropy","score":0.6377317309379578},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6059668660163879},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.5948590636253357},{"id":"https://openalex.org/keywords/residual-entropy","display_name":"Residual entropy","score":0.5768823027610779},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5251557230949402},{"id":"https://openalex.org/keywords/min-entropy","display_name":"Min entropy","score":0.514746904373169},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.5089273452758789},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.4951390326023102},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.48840659856796265},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.48710060119628906},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.47516578435897827},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.47323358058929443},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.44985803961753845},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.42286789417266846},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4189798831939697},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.41700273752212524},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.41397911310195923},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3427771329879761},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.26340487599372864},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22300255298614502},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22036191821098328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17743560671806335},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1495703160762787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1091231107711792},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.10907799005508423},{"id":"https://openalex.org/keywords/configuration-entropy","display_name":"Configuration entropy","score":0.08512496948242188}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7148851156234741},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.6377317309379578},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6059668660163879},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.5948590636253357},{"id":"https://openalex.org/C97785096","wikidata":"https://www.wikidata.org/wiki/Q771478","display_name":"Residual entropy","level":3,"score":0.5768823027610779},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5251557230949402},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.514746904373169},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.5089273452758789},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.4951390326023102},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.48840659856796265},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.48710060119628906},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.47516578435897827},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47323358058929443},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.44985803961753845},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.42286789417266846},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4189798831939697},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.41700273752212524},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.41397911310195923},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3427771329879761},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.26340487599372864},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22300255298614502},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22036191821098328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17743560671806335},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1495703160762787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1091231107711792},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.10907799005508423},{"id":"https://openalex.org/C124589349","wikidata":"https://www.wikidata.org/wiki/Q3726376","display_name":"Configuration entropy","level":2,"score":0.08512496948242188},{"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/e14030480","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030480","pdf_url":"https://www.mdpi.com/1099-4300/14/3/480/pdf?version=1424784844","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.296.8357","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.8357","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mdpi.com/1099-4300/14/3/480/pdf/","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:0a5cc878a778410abd69333777b465b5","is_oa":true,"landing_page_url":"https://doaj.org/article/0a5cc878a778410abd69333777b465b5","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":"Entropy, Vol 14, Iss 3, Pp 480-490 (2012)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/14/3/480/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e14030480","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":"Entropy; Volume 14; Issue 3; Pages: 480-490","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e14030480","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030480","pdf_url":"https://www.mdpi.com/1099-4300/14/3/480/pdf?version=1424784844","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6399999856948853,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2124218657.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1570212550","https://openalex.org/W1965555277","https://openalex.org/W1972196504","https://openalex.org/W1995875735","https://openalex.org/W2042868078","https://openalex.org/W2056783660","https://openalex.org/W2062516286","https://openalex.org/W2065366199","https://openalex.org/W2075642196","https://openalex.org/W2085153458","https://openalex.org/W2112757233","https://openalex.org/W2122657392","https://openalex.org/W2150877608","https://openalex.org/W2319945247","https://openalex.org/W2799055878","https://openalex.org/W6636481239","https://openalex.org/W6661146169"],"related_works":["https://openalex.org/W3092679530","https://openalex.org/W2139507220","https://openalex.org/W2127945237","https://openalex.org/W2952724564","https://openalex.org/W2469410023","https://openalex.org/W2757279842","https://openalex.org/W2187143106","https://openalex.org/W4226247096","https://openalex.org/W2124218657","https://openalex.org/W2008835467"],"abstract_inverted_index":{"The":[0],"Shannon":[1],"interval":[2,32,53,80],"entropy":[3,33],"function":[4],"as":[5],"a":[6,43],"useful":[7],"dynamic":[8],"measure":[9,44],"of":[10,24,45,54,58,66,77],"uncertainty":[11],"for":[12],"two":[13,48],"sided":[14],"truncated":[15],"random":[16],"variables":[17],"has":[18],"been":[19],"proposed":[20],"in":[21,56],"the":[22,37,52],"literature":[23],"reliability.":[25],"In":[26],"this":[27,67],"paper,":[28],"we":[29,41,83],"show":[30],"that":[31],"can":[34],"uniquely":[35],"determine":[36],"distribution":[38],"function.":[39],"Furthermore,":[40],"propose":[42],"discrepancy":[46,78],"between":[47],"lifetime":[49],"distributions":[50],"at":[51],"time":[55],"base":[57],"Kullback-Leibler":[59],"discrimination":[60],"information.":[61],"We":[62],"study":[63],"various":[64],"properties":[65],"measure,":[68],"including":[69],"its":[70,85],"connection":[71],"with":[72],"residual":[73],"and":[74,79,82,87],"past":[75],"measures":[76],"entropy,":[81],"obtain":[84],"upper":[86],"lower":[88],"bounds.":[89]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-22T09:01:20.584952","created_date":"2025-10-10T00:00:00"}
