{"id":"https://openalex.org/W1969306233","doi":"https://doi.org/10.1080/03610910903152631","title":"The Biased Transformation and Its Application in Goodness-of-Fit Tests for the Beta and Gamma Distribution","display_name":"The Biased Transformation and Its Application in Goodness-of-Fit Tests for the Beta and Gamma Distribution","publication_year":2009,"publication_date":"2009-09-03","ids":{"openalex":"https://openalex.org/W1969306233","doi":"https://doi.org/10.1080/03610910903152631","mag":"1969306233"},"language":"en","primary_location":{"id":"doi:10.1080/03610910903152631","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910903152631","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00544826","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005706108","display_name":"Mathias Raschke","orcid":"https://orcid.org/0000-0003-0182-5234"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mathias Raschke","raw_affiliation_strings":["Fa. M. Raschke, Teichgasse , Weimar , Germany"],"affiliations":[{"raw_affiliation_string":"Fa. M. Raschke, Teichgasse , Weimar , Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005706108"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3448,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.8854404,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"9","first_page":"1870","last_page":"1890"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9991000294685364,"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":0.9991000294685364,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9955999851226807,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9751999974250793,"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/anderson\u2013darling-test","display_name":"Anderson\u2013Darling test","score":0.738142192363739},{"id":"https://openalex.org/keywords/beta-distribution","display_name":"Beta distribution","score":0.7147018909454346},{"id":"https://openalex.org/keywords/generalized-beta-distribution","display_name":"Generalized beta distribution","score":0.7144208550453186},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.650353193283081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6448602676391602},{"id":"https://openalex.org/keywords/goodness-of-fit","display_name":"Goodness of fit","score":0.6293691396713257},{"id":"https://openalex.org/keywords/kolmogorov\u2013smirnov-test","display_name":"Kolmogorov\u2013Smirnov test","score":0.6193671822547913},{"id":"https://openalex.org/keywords/gamma-distribution","display_name":"Gamma distribution","score":0.5446102619171143},{"id":"https://openalex.org/keywords/beta","display_name":"BETA (programming language)","score":0.5120506882667542},{"id":"https://openalex.org/keywords/generalized-integer-gamma-distribution","display_name":"Generalized integer gamma distribution","score":0.49193570017814636},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4911000728607178},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4907546937465668},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47731146216392517},{"id":"https://openalex.org/keywords/generalized-pareto-distribution","display_name":"Generalized Pareto distribution","score":0.4612938165664673},{"id":"https://openalex.org/keywords/heavy-tailed-distribution","display_name":"Heavy-tailed distribution","score":0.45699378848075867},{"id":"https://openalex.org/keywords/generalized-gamma-distribution","display_name":"Generalized gamma distribution","score":0.45489591360092163},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.4407202899456024},{"id":"https://openalex.org/keywords/f-distribution","display_name":"F-distribution","score":0.42625629901885986},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.424967497587204},{"id":"https://openalex.org/keywords/extreme-value-theory","display_name":"Extreme value theory","score":0.41950953006744385},{"id":"https://openalex.org/keywords/distribution-fitting","display_name":"Distribution fitting","score":0.3557252883911133},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.3349568843841553},{"id":"https://openalex.org/keywords/statistical-hypothesis-testing","display_name":"Statistical hypothesis testing","score":0.26905357837677},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19352561235427856},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17276406288146973}],"concepts":[{"id":"https://openalex.org/C187758679","wikidata":"https://www.wikidata.org/wiki/Q491401","display_name":"Anderson\u2013Darling test","level":4,"score":0.738142192363739},{"id":"https://openalex.org/C21621910","wikidata":"https://www.wikidata.org/wiki/Q756254","display_name":"Beta distribution","level":2,"score":0.7147018909454346},{"id":"https://openalex.org/C121628295","wikidata":"https://www.wikidata.org/wiki/Q5532428","display_name":"Generalized beta distribution","level":4,"score":0.7144208550453186},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.650353193283081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6448602676391602},{"id":"https://openalex.org/C132480984","wikidata":"https://www.wikidata.org/wiki/Q2034239","display_name":"Goodness of fit","level":2,"score":0.6293691396713257},{"id":"https://openalex.org/C82581908","wikidata":"https://www.wikidata.org/wiki/Q575766","display_name":"Kolmogorov\u2013Smirnov test","level":3,"score":0.6193671822547913},{"id":"https://openalex.org/C149717495","wikidata":"https://www.wikidata.org/wiki/Q117806","display_name":"Gamma distribution","level":2,"score":0.5446102619171143},{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.5120506882667542},{"id":"https://openalex.org/C10477448","wikidata":"https://www.wikidata.org/wiki/Q5532482","display_name":"Generalized integer gamma distribution","level":3,"score":0.49193570017814636},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4911000728607178},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4907546937465668},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47731146216392517},{"id":"https://openalex.org/C133514767","wikidata":"https://www.wikidata.org/wiki/Q5532448","display_name":"Generalized Pareto distribution","level":3,"score":0.4612938165664673},{"id":"https://openalex.org/C1602530","wikidata":"https://www.wikidata.org/wiki/Q1472677","display_name":"Heavy-tailed distribution","level":3,"score":0.45699378848075867},{"id":"https://openalex.org/C42337464","wikidata":"https://www.wikidata.org/wiki/Q5532478","display_name":"Generalized gamma distribution","level":3,"score":0.45489591360092163},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.4407202899456024},{"id":"https://openalex.org/C4162061","wikidata":"https://www.wikidata.org/wiki/Q177144","display_name":"F-distribution","level":3,"score":0.42625629901885986},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.424967497587204},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.41950953006744385},{"id":"https://openalex.org/C160947583","wikidata":"https://www.wikidata.org/wiki/Q2083147","display_name":"Distribution fitting","level":3,"score":0.3557252883911133},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3349568843841553},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.26905357837677},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19352561235427856},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17276406288146973},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/03610910903152631","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910903152631","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00544826v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00544826","pdf_url":null,"source":{"id":"https://openalex.org/S4406922276","display_name":"INRIA a CCSD electronic archive server","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Communications in Statistics - Simulation and Computation, 2009, 38 (09), pp.1870-1890. &#x27E8;10.1080/03610910903152631&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:tara.tcd.ie:2262/46784","is_oa":false,"landing_page_url":"http://hdl.handle.net/2262/46784","pdf_url":null,"source":{"id":"https://openalex.org/S4306400387","display_name":"Trinity's Access to Research Output (TARA) (Trinity College Dublin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205274468","host_organization_name":"Trinity College Dublin","host_organization_lineage":["https://openalex.org/I205274468"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00544826v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00544826","pdf_url":null,"source":{"id":"https://openalex.org/S4406922276","display_name":"INRIA a CCSD electronic archive server","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Communications in Statistics - Simulation and Computation, 2009, 38 (09), pp.1870-1890. &#x27E8;10.1080/03610910903152631&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"score":0.5899999737739563,"id":"https://metadata.un.org/sdg/1","display_name":"No poverty"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W129305155","https://openalex.org/W1544729927","https://openalex.org/W1561885747","https://openalex.org/W1849980010","https://openalex.org/W1973429805","https://openalex.org/W2000305036","https://openalex.org/W2009416598","https://openalex.org/W2011484769","https://openalex.org/W2025036387","https://openalex.org/W2025483504","https://openalex.org/W2045317950","https://openalex.org/W2048353963","https://openalex.org/W2069353545","https://openalex.org/W2091242615","https://openalex.org/W2165112171","https://openalex.org/W2165261674","https://openalex.org/W2907233437","https://openalex.org/W2921767717","https://openalex.org/W4230238214","https://openalex.org/W4248568024","https://openalex.org/W6638873773"],"related_works":["https://openalex.org/W4256284424","https://openalex.org/W1964921333","https://openalex.org/W2547792281","https://openalex.org/W2971192015","https://openalex.org/W4223609019","https://openalex.org/W1991526242","https://openalex.org/W2009246008","https://openalex.org/W1997459874","https://openalex.org/W4226383454","https://openalex.org/W1969306233"],"abstract_inverted_index":{"The":[0,32,55,71,99,104,126],"biased":[1,17,33],"transformation":[2,18,34,57],"is":[3,10,48,78,87,97,137],"introduced":[4],"for":[5,20,36,61,65,89,107,119,133],"continuous":[6,38],"random":[7],"variables.":[8],"It":[9],"proved":[11],"in":[12,116,139],"this":[13,47],"article":[14],"that":[15],"the":[16,21,24,29,41,51,62,66,74,90,94,117,120,130],"works":[19,35],"generalized":[22,25],"Pareto,":[23],"extreme":[26],"value,":[27],"and":[28,68],"normal":[30],"distribution.":[31,70],"important":[37],"distributions":[39],"of":[40,53,73,129,142],"exponential":[42],"family":[43],"as":[44],"an":[45,140],"approximation;":[46],"demonstrated":[49,138],"with":[50,123],"aid":[52],"simulations.":[54,81],"new":[56,75,131],"can":[58],"be":[59],"used":[60],"Anderson\u2013Darling":[63],"test":[64,76,86,106,132],"gamma":[67],"beta":[69,91,121,135],"power":[72,95,115],"procedure":[77],"validated":[79],"by":[80],"Finally,":[82],"a":[83,108],"first":[84],"powerful":[85],"available":[88],"distribution":[92,111,122,136],"although":[93],"function":[96],"poor.":[98],"\u03c72-test":[100],"has":[101,112],"lower":[102],"power.":[103],"Kolomogorov\u2013Smirnov":[105],"fully":[109],"specified":[110],"almost":[113],"no":[114],"application":[118],"estimated":[124],"parameters.":[125],"practical":[127],"relevance":[128],"he":[134],"analysis":[141],"meteorological":[143],"data.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
