用k矩估计的光滑经验概率密度函数代替直方图

Decis. Sci. Pub Date : 2022-12-12 DOI:10.3390/sci4040050
Demetris Koutsoyiannis
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引用次数: 1

摘要

虽然有几种方法可以提供几个点的概率分布函数的样本估计,但对于连续随机变量的概率密度,通常只使用直方图的粗略表示。结果表明,新引入的可知矩(k -矩)概念可以提供分布函数的平滑经验表示,从而可以在大量点甚至在可用观测范围内的任意点上对密度函数进行点和区间估计。所提出的框架易于应用,并通过对各种分布函数的几个应用进行了说明。
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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.
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