{"title":"检验偏离正态性的一种偏度度量","authors":"S. Nakagawa, Hiroki Hashiguchi, N. Niki","doi":"10.17654/TS052010061","DOIUrl":null,"url":null,"abstract":"We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We obtain asymptotic first four moments of the null distribution for this statistic by using a computer algebra system and its normalizing transformation based on the Johnson $S_{U}$ system. Finally the performance of the proposed statistic is shown by comparing the powers of several skewness test statistics against some alternative hypotheses.","PeriodicalId":8446,"journal":{"name":"arXiv: Computation","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2012-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A measure of skewness for testing departures from normality\",\"authors\":\"S. Nakagawa, Hiroki Hashiguchi, N. Niki\",\"doi\":\"10.17654/TS052010061\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We obtain asymptotic first four moments of the null distribution for this statistic by using a computer algebra system and its normalizing transformation based on the Johnson $S_{U}$ system. Finally the performance of the proposed statistic is shown by comparing the powers of several skewness test statistics against some alternative hypotheses.\",\"PeriodicalId\":8446,\"journal\":{\"name\":\"arXiv: Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-02-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17654/TS052010061\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/TS052010061","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A measure of skewness for testing departures from normality
We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We obtain asymptotic first four moments of the null distribution for this statistic by using a computer algebra system and its normalizing transformation based on the Johnson $S_{U}$ system. Finally the performance of the proposed statistic is shown by comparing the powers of several skewness test statistics against some alternative hypotheses.
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