{"title":"一种新的Shannon熵估计及其在正态分布拟合优度检验中的应用","authors":"M. Madukaife","doi":"10.9734/arjom/2023/v19i10735","DOIUrl":null,"url":null,"abstract":"In this paper, a new estimator of the Shannon entropy of a random variable X having a probability density function \\(\\mathit{f}\\)(\\(\\mathit{x}\\)) is obtained based on window size spacings. Under the standard normal, standard exponential and uniform distributions, the estimator is shown to have relative low bias and low RMSE through extensive simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"2135 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Estimator of Shannon Entropy with Application to Goodness-of-Fit Test to Normal Distribution\",\"authors\":\"M. Madukaife\",\"doi\":\"10.9734/arjom/2023/v19i10735\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a new estimator of the Shannon entropy of a random variable X having a probability density function \\\\(\\\\mathit{f}\\\\)(\\\\(\\\\mathit{x}\\\\)) is obtained based on window size spacings. Under the standard normal, standard exponential and uniform distributions, the estimator is shown to have relative low bias and low RMSE through extensive simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.\",\"PeriodicalId\":281529,\"journal\":{\"name\":\"Asian Research Journal of Mathematics\",\"volume\":\"2135 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Research Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.9734/arjom/2023/v19i10735\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Research Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.9734/arjom/2023/v19i10735","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A New Estimator of Shannon Entropy with Application to Goodness-of-Fit Test to Normal Distribution
In this paper, a new estimator of the Shannon entropy of a random variable X having a probability density function \(\mathit{f}\)(\(\mathit{x}\)) is obtained based on window size spacings. Under the standard normal, standard exponential and uniform distributions, the estimator is shown to have relative low bias and low RMSE through extensive simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.