{"id":"https://openalex.org/W1979144155","doi":"https://doi.org/10.1016/s0012-365x(99)00246-0","title":"A lower bound on the probability of a finite union of events","display_name":"A lower bound on the probability of a finite union of events","publication_year":2000,"publication_date":"2000-03-01","ids":{"openalex":"https://openalex.org/W1979144155","doi":"https://doi.org/10.1016/s0012-365x(99)00246-0","mag":"1979144155"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(99)00246-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00246-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-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/A5068237243","display_name":"H. Kuai","orcid":null},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"H. Kuai","raw_affiliation_strings":["Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada K7L 3N6","Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada, K7L 3N6"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada K7L 3N6","institution_ids":["https://openalex.org/I204722609"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada, K7L 3N6","institution_ids":["https://openalex.org/I204722609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065742137","display_name":"Fady Alajaji","orcid":"https://orcid.org/0000-0002-7980-724X"},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"F. Alajaji","raw_affiliation_strings":["Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada K7L 3N6","Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada, K7L 3N6"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada K7L 3N6","institution_ids":["https://openalex.org/I204722609"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada, K7L 3N6","institution_ids":["https://openalex.org/I204722609"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008641491","display_name":"Glen Takahara","orcid":null},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"G. Takahara","raw_affiliation_strings":["Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada K7L 3N6","Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada, K7L 3N6"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada K7L 3N6","institution_ids":["https://openalex.org/I204722609"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen's University, Kingston, Ont., Canada, K7L 3N6","institution_ids":["https://openalex.org/I204722609"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065742137"],"corresponding_institution_ids":["https://openalex.org/I204722609"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.5305,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.75649106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"215","issue":"1-3","first_page":"147","last_page":"158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.984000027179718,"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"}},"topics":[{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.984000027179718,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9645000100135803,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9581999778747559,"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/mathematics","display_name":"Mathematics","score":0.8139282464981079},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.7988364696502686},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7834155559539795},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.7340632677078247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6882355809211731},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5460607409477234},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5089621543884277},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24025234580039978},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14036348462104797},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.054564088582992554}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8139282464981079},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7988364696502686},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7834155559539795},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.7340632677078247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6882355809211731},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5460607409477234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5089621543884277},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24025234580039978},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14036348462104797},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.054564088582992554},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0012-365x(99)00246-0","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)00246-0","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.50.3138","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.3138","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://markov.mast.queensu.ca/Papers/kuai_dm99.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6600000262260437}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1985131175","https://openalex.org/W2092271237","https://openalex.org/W2098111206","https://openalex.org/W2168925234"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2942366970","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2562400057","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W4360593462","https://openalex.org/W2194570607"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
