{"id":"https://openalex.org/W2319089635","doi":null,"title":"Computable Error Bounds for Approximations of Transformed Chi-Squared Variables and Its Statistical Applications","display_name":"Computable Error Bounds for Approximations of Transformed Chi-Squared Variables and Its Statistical Applications","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2319089635","mag":"2319089635"},"language":"en","primary_location":{"id":"mag:2319089635","doi":null,"is_oa":false,"landing_page_url":"https://istina.msu.ru/publications/article/19485266/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","indexed_in":[],"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/A5040370191","display_name":"Vladimir Vasilievich Ulyanov","orcid":"https://orcid.org/0000-0001-8467-3007","observed_orcids":["https://orcid.org/0000-0001-8467-3007"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vladimir V. Ulyanov","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-8467-3007","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013193006","display_name":"Gerd Christoph","orcid":"https://orcid.org/0000-0002-0850-5404","observed_orcids":["https://orcid.org/0000-0002-0850-5404"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gerd Christoph","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0850-5404","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110022973","display_name":"Y. Fujikoshi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Y. Fujikoshi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2532392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"17"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.57669997215271,"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/T13500","display_name":"Probability and Statistical Research","score":0.57669997215271,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.3686999976634979,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0142000000923872,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/chi-square-distribution","display_name":"chi-square distribution","score":0.8360000252723694},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.7990000247955322},{"id":"https://openalex.org/keywords/approximation-error","display_name":"approximation error","score":0.3720000088214874},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"numerical approximation","score":0.4099999964237213},{"id":"https://openalex.org/keywords/statistical-applications","display_name":"statistical applications","score":0.5059999823570251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5007336139678955},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.49176791310310364},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.48977231979370117},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44691404700279236},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.36799174547195435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3281250298023224},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32483184337615967}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2319089635","doi":null,"is_oa":false,"landing_page_url":"https://istina.msu.ru/publications/article/19485266/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1981492379","https://openalex.org/W2068728923"],"related_works":["https://openalex.org/W1986269615","https://openalex.org/W7100117839","https://openalex.org/W6885049074","https://openalex.org/W6922428226","https://openalex.org/W2299432914","https://openalex.org/W6941323278","https://openalex.org/W1982878323","https://openalex.org/W2123043202","https://openalex.org/W6903941873","https://openalex.org/W2580198753"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-10-02T10:15:12.560889","created_date":"2016-06-24T00:00:00"}