{"id":"https://openalex.org/W2613195533","doi":"https://doi.org/10.1109/tit.2017.2749310","title":"Bounds on Variance for Unimodal Distributions","display_name":"Bounds on Variance for Unimodal Distributions","publication_year":2017,"publication_date":"2017-09-06","ids":{"openalex":"https://openalex.org/W2613195533","doi":"https://doi.org/10.1109/tit.2017.2749310","mag":"2613195533"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2749310","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2749310","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1510.08341","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Hye Won Chung","orcid":"https://orcid.org/0000-0002-8947-9956"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Hye Won Chung","raw_affiliation_strings":["School of Electrical Engineering, KAIST, Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-8947-9956","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, KAIST, Daejeon, South Korea","institution_ids":["https://openalex.org/I157485424"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Brian M. Sadler","orcid":null},"institutions":[{"id":"https://openalex.org/I166416128","display_name":"DEVCOM Army Research Laboratory","ror":"https://ror.org/011hc8f90","country_code":"US","type":"government","lineage":["https://openalex.org/I1304082316","https://openalex.org/I1330347796","https://openalex.org/I166416128","https://openalex.org/I2802705668","https://openalex.org/I4210154437"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brian M. Sadler","raw_affiliation_strings":["U.S. Army Research Laboratory, Adelphi, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"U.S. Army Research Laboratory, Adelphi, MD, USA","institution_ids":["https://openalex.org/I166416128"]}]},{"author_position":"last","author":{"id":null,"display_name":"Alfred O. Hero","orcid":"https://orcid.org/0000-0002-2531-9670"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alfred O. Hero","raw_affiliation_strings":["EECS Department, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0000-0002-2531-9670","affiliations":[{"raw_affiliation_string":"EECS Department, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157485424"],"apc_list":null,"apc_paid":null,"fwci":1.2141,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.78176538,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"63","issue":"11","first_page":"6936","last_page":"6949"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.774399995803833,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.774399995803833,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.03909999877214432,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.03400000184774399,"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/differential-entropy","display_name":"Differential entropy","score":0.8057000041007996},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.6826000213623047},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6790000200271606},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6437000036239624},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6359000205993652},{"id":"https://openalex.org/keywords/min-entropy","display_name":"Min entropy","score":0.5198000073432922},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.5011000037193298},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4189999997615814},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.41819998621940613}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8748000264167786},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.8057000041007996},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.6826000213623047},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6790000200271606},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6437000036239624},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6359000205993652},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.5198000073432922},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.5011000037193298},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4189999997615814},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.41819998621940613},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41449999809265137},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3935000002384186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37700000405311584},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3709000051021576},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.35749998688697815},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.34619998931884766},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.3353999853134155},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.32179999351501465},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C320580","wikidata":"https://www.wikidata.org/wiki/Q5380810","display_name":"Entropy power inequality","level":5,"score":0.31380000710487366},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3073999881744385},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.3034000098705292},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2994999885559082},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.2703000009059906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26600000262260437},{"id":"https://openalex.org/C89735579","wikidata":"https://www.wikidata.org/wiki/Q6795894","display_name":"Maximum entropy spectral estimation","level":3,"score":0.26109999418258667},{"id":"https://openalex.org/C62100291","wikidata":"https://www.wikidata.org/wiki/Q1936288","display_name":"Total variation","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2017.2749310","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2749310","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1510.08341","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.08341","pdf_url":"https://arxiv.org/pdf/1510.08341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1510.08341","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.08341","pdf_url":"https://arxiv.org/pdf/1510.08341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8346236733","display_name":null,"funder_award_id":"W911NF-15-1-0479","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G932903589","display_name":null,"funder_award_id":"W911NF-11-1-0391","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1501178284","https://openalex.org/W1988269584","https://openalex.org/W1997817740","https://openalex.org/W2000015806","https://openalex.org/W2003268963","https://openalex.org/W2047450510","https://openalex.org/W2053952124","https://openalex.org/W2062626064","https://openalex.org/W2093265547","https://openalex.org/W2121952483","https://openalex.org/W2126204693","https://openalex.org/W2128439793","https://openalex.org/W2136817255","https://openalex.org/W2140529724","https://openalex.org/W2336140998","https://openalex.org/W2744679084","https://openalex.org/W2963504190","https://openalex.org/W2963763760","https://openalex.org/W3121701465","https://openalex.org/W4241397713","https://openalex.org/W4246293990","https://openalex.org/W6631640075","https://openalex.org/W6640343737"],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1],"a":[2,101],"direct":[3],"relationship":[4],"between":[5,76],"the":[6,9,36,47,50,63,68,72,82,89,94,106],"variance":[7,26,48,73],"and":[8,16,60],"differential":[10,69,83,95],"entropy":[11,30,38,65,70,96],"for":[12,88,103],"subclasses":[13,52,90],"of":[14,29,49,53,91,105],"symmetric":[15],"asymmetric":[17],"unimodal":[18,54,92],"distributions":[19,55],"by":[20,62],"providing":[21],"an":[22],"upper":[23],"bound":[24,34,41],"on":[25,42],"in":[27,81],"terms":[28],"power.":[31,66],"Combining":[32],"this":[33],"with":[35],"well-known":[37],"power":[39],"lower":[40],"variance,":[43],"we":[44],"prove":[45],"that":[46,87],"appropriate":[51],"can":[56,97],"be":[57,98],"bounded":[58],"below":[59],"above":[61],"scaled":[64],"As":[67],"decreases,":[71],"is":[74],"sandwiched":[75],"two":[77],"exponentially":[78],"decreasing":[79],"functions":[80],"entropy.":[84],"This":[85],"establishes":[86],"distributions,":[93],"used":[99],"as":[100],"surrogate":[102],"concentration":[104],"distribution.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-05-19T00:00:00"}
