{"title":"用k矩估计的光滑经验概率密度函数代替直方图","authors":"Demetris Koutsoyiannis","doi":"10.3390/sci4040050","DOIUrl":null,"url":null,"abstract":"Whilst several methods exist to provide sample estimates of the probability distribution function at several points, for the probability density of continuous stochastic variables, only a gross representation through the histogram is typically used. It is shown that the newly introduced concept of knowable moments (K-moments) can provide smooth empirical representations of the distribution function, which in turn can yield point and interval estimates of the density function at a large number of points or even at any arbitrary point within the range of the available observations. The proposed framework is simple to apply and is illustrated with several applications for a variety of distribution functions.","PeriodicalId":10987,"journal":{"name":"Decis. Sci.","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Replacing Histogram with Smooth Empirical Probability Density Function Estimated by K-Moments\",\"authors\":\"Demetris Koutsoyiannis\",\"doi\":\"10.3390/sci4040050\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Whilst several methods exist to provide sample estimates of the probability distribution function at several points, for the probability density of continuous stochastic variables, only a gross representation through the histogram is typically used. It is shown that the newly introduced concept of knowable moments (K-moments) can provide smooth empirical representations of the distribution function, which in turn can yield point and interval estimates of the density function at a large number of points or even at any arbitrary point within the range of the available observations. The proposed framework is simple to apply and is illustrated with several applications for a variety of distribution functions.\",\"PeriodicalId\":10987,\"journal\":{\"name\":\"Decis. Sci.\",\"volume\":\"23 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Decis. Sci.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/sci4040050\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Decis. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sci4040050","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Replacing Histogram with Smooth Empirical Probability Density Function Estimated by K-Moments
Whilst several methods exist to provide sample estimates of the probability distribution function at several points, for the probability density of continuous stochastic variables, only a gross representation through the histogram is typically used. It is shown that the newly introduced concept of knowable moments (K-moments) can provide smooth empirical representations of the distribution function, which in turn can yield point and interval estimates of the density function at a large number of points or even at any arbitrary point within the range of the available observations. The proposed framework is simple to apply and is illustrated with several applications for a variety of distribution functions.