Tolerance Bounds for Log Gamma Regression Models
Finding lower confidence bounds for the quantiles of Weibull populations has received much attention in recent literature. An accurate procedure (based on solving a quadratic equation) is presented in (1.17). It is, in fact, more accurate than the currently available Monte Carlo tables. It extends t...
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| Veröffentlicht in: | Technometrics 1985-05, Vol.27 (2), p.109-118 |
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| container_end_page | 118 |
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| container_title | Technometrics |
| container_volume | 27 |
| creator | Jones, Robert A. Scholz, F. W. Ossiander, Mina Shorack, Galen R. |
| description | Finding lower confidence bounds for the quantiles of Weibull populations has received much attention in recent literature. An accurate procedure (based on solving a quadratic equation) is presented in (1.17). It is, in fact, more accurate than the currently available Monte Carlo tables. It extends to any location-scale family; this article shows that it is accurate for all members of the log gamma (K) family with ½ ≤ K ≤ ∞. The procedure is shown to work well for censored data. It also extends naturally to regression data. An even more accurate procedure (an approximation to the Lawless conditional procedure, in which the "configurations" are replaced by an approximation of their expected values) is presented in (3.1). It involves numerical integration, but the tables are independent of the data. It extends easily to the censored case. |
| doi_str_mv | 10.1080/00401706.1985.10488028 |
| format | Article |
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It extends easily to the censored case.</description><identifier>ISSN: 0040-1706</identifier><identifier>EISSN: 1537-2723</identifier><identifier>DOI: 10.1080/00401706.1985.10488028</identifier><identifier>CODEN: TCMTA2</identifier><language>eng</language><publisher>Legacy CDMS: Taylor & Francis Group</publisher><subject>Applied sciences ; Approximation ; Bar stock ; Censored data ; Censoring ; Censorship ; Closed form approximation ; Covariance matrices ; Exact sciences and technology ; Linear regression ; Log gamma distribution ; Maximum likelihood estimation ; Operational research and scientific management ; Operational research. Management science ; Regression analysis ; Reliability theory. Replacement problems ; Sample size ; Standard deviation ; Statistics And Probability ; Tables for approximate conditional approximation ; Tolerance bounds</subject><ispartof>Technometrics, 1985-05, Vol.27 (2), p.109-118</ispartof><rights>Copyright Taylor & Francis Group, LLC 1985</rights><rights>Copyright 1985 The American Statistical Association and the American Society for Quality Control</rights><rights>1985 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c336t-d1411be5b3bcd38e8e501a9c9e129a3863d41c95ebdb6cbdb3c5d88104d5d9933</citedby><cites>FETCH-LOGICAL-c336t-d1411be5b3bcd38e8e501a9c9e129a3863d41c95ebdb6cbdb3c5d88104d5d9933</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/1268759$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/1268759$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27924,27925,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=9203464$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Jones, Robert A.</creatorcontrib><creatorcontrib>Scholz, F. W.</creatorcontrib><creatorcontrib>Ossiander, Mina</creatorcontrib><creatorcontrib>Shorack, Galen R.</creatorcontrib><title>Tolerance Bounds for Log Gamma Regression Models</title><title>Technometrics</title><description>Finding lower confidence bounds for the quantiles of Weibull populations has received much attention in recent literature. An accurate procedure (based on solving a quadratic equation) is presented in (1.17). It is, in fact, more accurate than the currently available Monte Carlo tables. It extends to any location-scale family; this article shows that it is accurate for all members of the log gamma (K) family with ½ ≤ K ≤ ∞. The procedure is shown to work well for censored data. It also extends naturally to regression data. An even more accurate procedure (an approximation to the Lawless conditional procedure, in which the "configurations" are replaced by an approximation of their expected values) is presented in (3.1). It involves numerical integration, but the tables are independent of the data. It extends easily to the censored case.</description><subject>Applied sciences</subject><subject>Approximation</subject><subject>Bar stock</subject><subject>Censored data</subject><subject>Censoring</subject><subject>Censorship</subject><subject>Closed form approximation</subject><subject>Covariance matrices</subject><subject>Exact sciences and technology</subject><subject>Linear regression</subject><subject>Log gamma distribution</subject><subject>Maximum likelihood estimation</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Regression analysis</subject><subject>Reliability theory. Replacement problems</subject><subject>Sample size</subject><subject>Standard deviation</subject><subject>Statistics And Probability</subject><subject>Tables for approximate conditional approximation</subject><subject>Tolerance bounds</subject><issn>0040-1706</issn><issn>1537-2723</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1985</creationdate><recordtype>article</recordtype><sourceid>CYI</sourceid><recordid>eNqFkE1LxDAQhoMouK7-A5EexFvXSdKmyVHFL1gRRM8hTbJSaRvNdBH_val11ZuXDIRn3nd4CDmisKAg4RSgAFqBWFAly_RVSAlMbpEZLXmVs4rxbTIboXykdske4gsA5UxWMwKPofXR9NZn52HdO8xWIWbL8Jxdm64z2YN_jh6xCX12F5xvcZ_srEyL_uB7zsnT1eXjxU2-vL--vThb5pZzMeSOFpTWvqx5bR2XXvoSqFFWecqU4VJwV1CrSl-7Wtj0cFs6KdP1rnRKcT4nJ1Puawxva4-D7hq0vm1N78MaNStkoUBAAsUE2hgQo1_p19h0Jn5oCnoUpDeC9ChIbwSlxePvBoPWtKvRQoM_24oBL0SRsMMJ6w0a3Q8Rv3IABBNU_Ka84BDi327GodKUCVmVKmFnE9b0SXBn3kNsnR7MRxvippn_c_AnbrSMIw</recordid><startdate>19850501</startdate><enddate>19850501</enddate><creator>Jones, Robert A.</creator><creator>Scholz, F. 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W. ; Ossiander, Mina ; Shorack, Galen R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c336t-d1411be5b3bcd38e8e501a9c9e129a3863d41c95ebdb6cbdb3c5d88104d5d9933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1985</creationdate><topic>Applied sciences</topic><topic>Approximation</topic><topic>Bar stock</topic><topic>Censored data</topic><topic>Censoring</topic><topic>Censorship</topic><topic>Closed form approximation</topic><topic>Covariance matrices</topic><topic>Exact sciences and technology</topic><topic>Linear regression</topic><topic>Log gamma distribution</topic><topic>Maximum likelihood estimation</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Regression analysis</topic><topic>Reliability theory. Replacement problems</topic><topic>Sample size</topic><topic>Standard deviation</topic><topic>Statistics And Probability</topic><topic>Tables for approximate conditional approximation</topic><topic>Tolerance bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jones, Robert A.</creatorcontrib><creatorcontrib>Scholz, F. W.</creatorcontrib><creatorcontrib>Ossiander, Mina</creatorcontrib><creatorcontrib>Shorack, Galen R.</creatorcontrib><collection>NASA Scientific and Technical Information</collection><collection>NASA Technical Reports Server</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Technometrics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jones, Robert A.</au><au>Scholz, F. W.</au><au>Ossiander, Mina</au><au>Shorack, Galen R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Tolerance Bounds for Log Gamma Regression Models</atitle><jtitle>Technometrics</jtitle><date>1985-05-01</date><risdate>1985</risdate><volume>27</volume><issue>2</issue><spage>109</spage><epage>118</epage><pages>109-118</pages><issn>0040-1706</issn><eissn>1537-2723</eissn><coden>TCMTA2</coden><abstract>Finding lower confidence bounds for the quantiles of Weibull populations has received much attention in recent literature. An accurate procedure (based on solving a quadratic equation) is presented in (1.17). It is, in fact, more accurate than the currently available Monte Carlo tables. It extends to any location-scale family; this article shows that it is accurate for all members of the log gamma (K) family with ½ ≤ K ≤ ∞. The procedure is shown to work well for censored data. It also extends naturally to regression data. An even more accurate procedure (an approximation to the Lawless conditional procedure, in which the "configurations" are replaced by an approximation of their expected values) is presented in (3.1). It involves numerical integration, but the tables are independent of the data. It extends easily to the censored case.</abstract><cop>Legacy CDMS</cop><pub>Taylor & Francis Group</pub><doi>10.1080/00401706.1985.10488028</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
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| ispartof | Technometrics, 1985-05, Vol.27 (2), p.109-118 |
| issn | 0040-1706 1537-2723 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_24849060 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; NASA Technical Reports Server |
| subjects | Applied sciences Approximation Bar stock Censored data Censoring Censorship Closed form approximation Covariance matrices Exact sciences and technology Linear regression Log gamma distribution Maximum likelihood estimation Operational research and scientific management Operational research. Management science Regression analysis Reliability theory. Replacement problems Sample size Standard deviation Statistics And Probability Tables for approximate conditional approximation Tolerance bounds |
| title | Tolerance Bounds for Log Gamma Regression Models |
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