{"title":"比例的折叠指数变换","authors":"Hans-Peter Piepho","doi":"10.1046/j.0039-0526.2003.00509.x","DOIUrl":null,"url":null,"abstract":"<p><b>Summary. </b> Several transformations have been suggested for proportions <i>x</i>. Most of these require that 0<<i>x</i><1 and therefore fail when <i>x</i>=0 or <i>x</i>=1, which is quite common in practice. The paper proposes a transformation which allows <i>x</i>=0 and <i>x</i>=1. It is based on an extension of the exponential transformation and works well for moderately skewed unimodal distributions, whereas J-shaped or very skewed unimodel distributions are less well accommodated. Use of the transformation is exemplified with three data sets.</p>","PeriodicalId":100846,"journal":{"name":"Journal of the Royal Statistical Society: Series D (The Statistician)","volume":"52 4","pages":"575-589"},"PeriodicalIF":0.0000,"publicationDate":"2003-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1046/j.0039-0526.2003.00509.x","citationCount":"36","resultStr":"{\"title\":\"The folded exponential transformation for proportions\",\"authors\":\"Hans-Peter Piepho\",\"doi\":\"10.1046/j.0039-0526.2003.00509.x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><b>Summary. </b> Several transformations have been suggested for proportions <i>x</i>. Most of these require that 0<<i>x</i><1 and therefore fail when <i>x</i>=0 or <i>x</i>=1, which is quite common in practice. The paper proposes a transformation which allows <i>x</i>=0 and <i>x</i>=1. It is based on an extension of the exponential transformation and works well for moderately skewed unimodal distributions, whereas J-shaped or very skewed unimodel distributions are less well accommodated. Use of the transformation is exemplified with three data sets.</p>\",\"PeriodicalId\":100846,\"journal\":{\"name\":\"Journal of the Royal Statistical Society: Series D (The Statistician)\",\"volume\":\"52 4\",\"pages\":\"575-589\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1046/j.0039-0526.2003.00509.x\",\"citationCount\":\"36\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Royal Statistical Society: Series D (The Statistician)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1046/j.0039-0526.2003.00509.x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Royal Statistical Society: Series D (The Statistician)","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1046/j.0039-0526.2003.00509.x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The folded exponential transformation for proportions
Summary. Several transformations have been suggested for proportions x. Most of these require that 0<x<1 and therefore fail when x=0 or x=1, which is quite common in practice. The paper proposes a transformation which allows x=0 and x=1. It is based on an extension of the exponential transformation and works well for moderately skewed unimodal distributions, whereas J-shaped or very skewed unimodel distributions are less well accommodated. Use of the transformation is exemplified with three data sets.