{"id":"https://openalex.org/W6989419490","doi":null,"title":"Approximations to non-central distributions and their applications","display_name":"Approximations to non-central distributions and their applications","publication_year":1974,"publication_date":"1974-01-01","ids":{"openalex":"https://openalex.org/W6989419490"},"language":"en","primary_location":{"id":"pmh:oai:localhost:11427/39016","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11427/39016","pdf_url":"https://open.uct.ac.za/bitstream/11427/39016/1/thesis_sci_1974_carter%20johnson%20p%20c.pdf","source":{"id":"https://openalex.org/S4306402129","display_name":"Open University of Cape Town (University of Cape Town)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I157614274","host_organization_name":"University of Cape Town","host_organization_lineage":["https://openalex.org/I157614274"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Master Thesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://open.uct.ac.za/bitstream/11427/39016/1/thesis_sci_1974_carter%20johnson%20p%20c.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Carter-Johnson, P C","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Carter-Johnson, P C","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":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.5961999893188477,"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":0.5961999893188477,"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":0.3571999967098236,"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/T13141","display_name":"Statistical Methods and Applications","score":0.016100000590085983,"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/noncentral-distributions","display_name":"noncentral distributions","score":0.921999990940094},{"id":"https://openalex.org/keywords/statistical-approximation","display_name":"statistical approximation","score":0.550000011920929}],"concepts":[{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.7217000126838684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6765000224113464},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.6474000215530396},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5472999811172485},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.499099999666214},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4717000126838684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44620001316070557},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C65045869","wikidata":"https://www.wikidata.org/wiki/Q81365","display_name":"Decimal","level":2,"score":0.3573000133037567},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27230000495910645},{"id":"https://openalex.org/C12269589","wikidata":"https://www.wikidata.org/wiki/Q1052990","display_name":"Noncentral chi-squared distribution","level":5,"score":0.25459998846054077}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:localhost:11427/39016","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11427/39016","pdf_url":"https://open.uct.ac.za/bitstream/11427/39016/1/thesis_sci_1974_carter%20johnson%20p%20c.pdf","source":{"id":"https://openalex.org/S4306402129","display_name":"Open University of Cape Town (University of Cape Town)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I157614274","host_organization_name":"University of Cape Town","host_organization_lineage":["https://openalex.org/I157614274"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Master Thesis"}],"best_oa_location":{"id":"pmh:oai:localhost:11427/39016","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11427/39016","pdf_url":"https://open.uct.ac.za/bitstream/11427/39016/1/thesis_sci_1974_carter%20johnson%20p%20c.pdf","source":{"id":"https://openalex.org/S4306402129","display_name":"Open University of Cape Town (University of Cape Town)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I157614274","host_organization_name":"University of Cape Town","host_organization_lineage":["https://openalex.org/I157614274"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Master Thesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W6989419490.pdf","grobid_xml":"https://content.openalex.org/works/W6989419490.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2061058697","https://openalex.org/W2053548740","https://openalex.org/W1997279218","https://openalex.org/W7096188328","https://openalex.org/W1996220639","https://openalex.org/W2007064004","https://openalex.org/W2018837778","https://openalex.org/W2397347086","https://openalex.org/W2515445137","https://openalex.org/W4386195212"],"abstract_inverted_index":{"In":[0,55,91],"testing":[1],"hypotheses":[2],"involving":[3,60],"noncentral":[4,137,214],"distributions":[5,144],"percentage":[6],"points":[7],"are":[8,16,18,36,75,101,105,154,184],"not":[9,19,37,110],"always":[10],"readily":[11],"available":[12],"and,":[13],"if":[14,109],"they":[15,168],"available,":[17,76],"very":[20,102],"well":[21],"tabulated":[22],"except,":[23],"perhaps,":[24],"for":[25,33],"smaller":[26],"degrees":[27],"of":[28,44,58,63,67,70,161,199,227],"freedom":[29],"and":[30,49,73,96,104,142,195,234],"noncentralities.":[31],"Consequently,\u00b7":[32],"values":[34,114,121,233],"that":[35],"tabulated,":[38],"interpolation,":[39],"or,":[40],"more":[41,111],"likely,":[42],"extrapolation":[43],"some":[45],"kind":[46],"is":[47,127,202],"necessary,":[48],"the":[50,56,61,64,68,71,94,136,165,178,193,206,213,220,225,228,231,241],"process":[51],"can":[52,145,243],"become":[53],"tedious.":[54],"case":[57],"calculations":[59],"power":[62,69],"test,":[65],"charts":[66,82],"F-test":[72],"t-test":[74],"but":[77],"readings":[78],"taken":[79],"from":[80,123],"these":[81,200],"may":[83,180],"be":[84,146,181,244],"accurate":[85],"to":[86,135,163],"only":[87],"one":[88],"decimal":[89],"place.":[90],"situations":[92,240],"like":[93],"above,":[95],"in":[97,132,151,157,186,205,238],"other":[98],"cases,":[99,153],"approximations":[100,134,149,194,229,242],"useful":[103],"sometimes":[106],"as":[107],"accurate,":[108],"so,":[112],"than":[113],"obtained":[115],"by":[116],"interpolation":[117],"(or":[118],"extrapolation)":[119],"or":[120],"read":[122],"charts.":[124],"This":[125],"thesis":[126],"chiefly":[128],"concerned":[129],"with":[130,156,176,192,219,230],"applications":[131],"which":[133,177,183,239],"x2":[138],",":[139],"F,":[140],"t":[141],"R":[143],"used.":[147,245],"The":[148],"themselves,":[150],"most":[152],"dealt":[155],"a":[158],"fair":[159],"amount":[160],"detail":[162],"show":[164],"reader":[166,179],"how":[167],"were":[169],"obtained.":[170],"Chapter":[171],"1":[172],"defines":[173],"certain":[174],"terms":[175],"unfamiliar,":[182],"used":[185],"subsequent":[187],"chapters.":[188],"Chapters":[189],"2-5":[190],"deal":[191],"their":[196],"applications.\u00b7":[197],"Each":[198],"chapters":[201],"set":[203],"out":[204],"same":[207],"way,":[208],"section":[209,216,222,235],"I":[210],"am":[211],"defining":[212],"distribution,":[215],"II":[217],"dealing":[218],"approximations,":[221],"III":[223],"comparing":[224],"accuracy":[226],"exact":[232],"IV":[236],"showing":[237]},"counts_by_year":[],"updated_date":"2026-08-25T07:29:55.448023","created_date":"2025-10-10T00:00:00"}
