{"title":"均方加权偏差的统计分布","authors":"I. Wendt, C. Carl","doi":"10.1016/0168-9622(91)90010-T","DOIUrl":null,"url":null,"abstract":"<div><p>The probability distribution of the mean squared weighted deviation (MSWD) is derived and its dependence on degrees of freedom f is shown. The expectation (or mean) value of MSWD=1 and is not a function of f. However, the +1σ range of the expectation value of the MSWD decreases with increasing f. The standard deviation of the MSWD is σ = ±(2/f)<sup>1/2</sup>. If MSWD 1+2(2/f)<sup>1/2</sup>, there is only <5% probability that the data define an isochron. Use of MSWD as a criterion for accepting or rejecting the assumption of an isochron may be applied only if analytical errors σ<sub>x<sub>i</sub></sub> and σ<sub>y<sub>i</sub></sub> are well known.</p></div>","PeriodicalId":100231,"journal":{"name":"Chemical Geology: Isotope Geoscience section","volume":"86 4","pages":"Pages 275-285"},"PeriodicalIF":0.0000,"publicationDate":"1991-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0168-9622(91)90010-T","citationCount":"658","resultStr":"{\"title\":\"The statistical distribution of the mean squared weighted deviation\",\"authors\":\"I. Wendt, C. Carl\",\"doi\":\"10.1016/0168-9622(91)90010-T\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The probability distribution of the mean squared weighted deviation (MSWD) is derived and its dependence on degrees of freedom f is shown. The expectation (or mean) value of MSWD=1 and is not a function of f. However, the +1σ range of the expectation value of the MSWD decreases with increasing f. The standard deviation of the MSWD is σ = ±(2/f)<sup>1/2</sup>. If MSWD 1+2(2/f)<sup>1/2</sup>, there is only <5% probability that the data define an isochron. Use of MSWD as a criterion for accepting or rejecting the assumption of an isochron may be applied only if analytical errors σ<sub>x<sub>i</sub></sub> and σ<sub>y<sub>i</sub></sub> are well known.</p></div>\",\"PeriodicalId\":100231,\"journal\":{\"name\":\"Chemical Geology: Isotope Geoscience section\",\"volume\":\"86 4\",\"pages\":\"Pages 275-285\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0168-9622(91)90010-T\",\"citationCount\":\"658\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chemical Geology: Isotope Geoscience section\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/016896229190010T\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chemical Geology: Isotope Geoscience section","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/016896229190010T","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The statistical distribution of the mean squared weighted deviation
The probability distribution of the mean squared weighted deviation (MSWD) is derived and its dependence on degrees of freedom f is shown. The expectation (or mean) value of MSWD=1 and is not a function of f. However, the +1σ range of the expectation value of the MSWD decreases with increasing f. The standard deviation of the MSWD is σ = ±(2/f)1/2. If MSWD 1+2(2/f)1/2, there is only <5% probability that the data define an isochron. Use of MSWD as a criterion for accepting or rejecting the assumption of an isochron may be applied only if analytical errors σxi and σyi are well known.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
