{"id":"https://openalex.org/W3046190925","doi":"https://doi.org/10.1109/icc40277.2020.9149127","title":"On the Marcum Q-Function Behavior of the Left Tail Probability of the Lognormal Sum Distribution","display_name":"On the Marcum Q-Function Behavior of the Left Tail Probability of the Lognormal Sum Distribution","publication_year":2020,"publication_date":"2020-06-01","ids":{"openalex":"https://openalex.org/W3046190925","doi":"https://doi.org/10.1109/icc40277.2020.9149127","mag":"3046190925"},"language":"en","primary_location":{"id":"doi:10.1109/icc40277.2020.9149127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icc40277.2020.9149127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICC 2020 - 2020 IEEE International Conference on Communications (ICC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038087450","display_name":"Norman C. Beaulieu","orcid":"https://orcid.org/0000-0001-9233-219X"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Norman C. Beaulieu","raw_affiliation_strings":["School of Information and Communication Engineering and the Beijing Key Laboratory for Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Communication Engineering and the Beijing Key Laboratory for Network System Architecture and Convergence, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024479882","display_name":"Gan Luan","orcid":"https://orcid.org/0000-0002-8043-9288"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gan Luan","raw_affiliation_strings":["School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2217,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57207648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9993000030517578,"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":0.9993000030517578,"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/T12146","display_name":"Power Line Communications and Noise","score":0.9908999800682068,"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/T11720","display_name":"Probability and Risk Models","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/log-normal-distribution","display_name":"Log-normal distribution","score":0.8638412952423096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6629251837730408},{"id":"https://openalex.org/keywords/cumulative-distribution-function","display_name":"Cumulative distribution function","score":0.6071730852127075},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6035391688346863},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.5459460616111755},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.5223168730735779},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4368850290775299},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.43684399127960205},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36408132314682007},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3574908375740051},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3280930519104004},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29005247354507446},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1854022741317749},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07592949271202087}],"concepts":[{"id":"https://openalex.org/C151620405","wikidata":"https://www.wikidata.org/wiki/Q826116","display_name":"Log-normal distribution","level":2,"score":0.8638412952423096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6629251837730408},{"id":"https://openalex.org/C103784038","wikidata":"https://www.wikidata.org/wiki/Q386228","display_name":"Cumulative distribution function","level":3,"score":0.6071730852127075},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6035391688346863},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5459460616111755},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5223168730735779},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4368850290775299},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.43684399127960205},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36408132314682007},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3574908375740051},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3280930519104004},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29005247354507446},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1854022741317749},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07592949271202087}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icc40277.2020.9149127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icc40277.2020.9149127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICC 2020 - 2020 IEEE International Conference on Communications (ICC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W598996319","https://openalex.org/W658611389","https://openalex.org/W1582019318","https://openalex.org/W1606281467","https://openalex.org/W2122194418","https://openalex.org/W2124614136","https://openalex.org/W2138702332","https://openalex.org/W2158429877","https://openalex.org/W2188825645","https://openalex.org/W2261416239","https://openalex.org/W2337325719","https://openalex.org/W2345425201","https://openalex.org/W2587993332","https://openalex.org/W2613400311","https://openalex.org/W2739066612","https://openalex.org/W2742158254","https://openalex.org/W2792978536","https://openalex.org/W2887386752","https://openalex.org/W2908215763","https://openalex.org/W2952596376","https://openalex.org/W2953774778","https://openalex.org/W2963732797","https://openalex.org/W3009963299","https://openalex.org/W3102573515","https://openalex.org/W3104456045","https://openalex.org/W4205767108","https://openalex.org/W4238327122"],"related_works":["https://openalex.org/W4213267843","https://openalex.org/W318704523","https://openalex.org/W2080246011","https://openalex.org/W147736006","https://openalex.org/W2566241227","https://openalex.org/W3164394228","https://openalex.org/W3105397284","https://openalex.org/W2670807771","https://openalex.org/W1980528650","https://openalex.org/W1526257359"],"abstract_inverted_index":{"Sums":[0],"of":[1,13,23,32,35,56,64,74,96,127,155,181,186],"lognormal":[2,36,58,88,115,157,188,212],"random":[3,37],"variables":[4,38],"can":[5,175],"be":[6,176],"used":[7,177],"to":[8],"model":[9],"a":[10,125],"wide":[11],"range":[12],"real-life":[14],"phenomena,":[15],"and":[16,110,193],"their":[17],"probability":[18,28,52,77,99,151,185],"distribution":[19,29,53,118,152,190,214],"left":[20,30,54,153,183,215],"tails":[21],"are":[22],"crucial":[24],"interest.":[25],"Meanwhile,":[26],"the":[27,33,51,57,65,72,75,81,87,94,97,103,128,135,150,156,160,172,182,187,200,220],"tail":[31,55,154,184,216],"sum":[34,161,189,213,221],"has":[39],"no":[40],"closed-form":[41,44],"expressions.":[42],"A":[43,166],"first-order":[45,139,202],"Marcum":[46,140,173,203],"Q-function":[47,141,174,204],"lower":[48,66,142,205,217],"bound":[49,67,143,206,218],"for":[50,113,124,149],"two-sum":[59,116],"is":[60,68,91,111,132,191,207,224],"derived.":[61],"The":[62,138],"derivation":[63],"based":[69],"on":[70],"studying":[71],"geometry":[73],"nonzero":[76,98],"mass":[78,100],"region":[79,101],"in":[80,86,102],"Gaussian":[82,104],"plane,":[83],"rather":[84],"than":[85,123,209],"plane.":[89],"It":[90],"proved":[92],"that":[93,131,171,199],"boundary":[95,129],"plane":[105],"does":[106],"not":[107],"change":[108],"shape":[109],"identical":[112],"different":[114],"cumulative":[117],"function":[119],"(CDF)":[120],"arguments,":[121],"other":[122],"translation":[126],"curve":[130],"determined":[133],"by":[134],"CDF":[136,162,222],"argument.":[137],"becomes":[144],"an":[145,179,210],"increasingly":[146],"good":[147],"approximation":[148,180],"two-sum,":[158],"as":[159,178],"argument":[163,223],"approaches":[164],"zero.":[165],"recently":[167],"reported":[168],"empirical":[169],"observation":[170],"explained":[192],"partially":[194],"quantified.":[195],"Simulation":[196],"results":[197],"show":[198],"new":[201],"tighter":[208],"existing":[211],"when":[219],"sufficiently":[225],"small.":[226]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}