Estimating functionals of particle size distributions
Estimating functionals of particle size distributions
复制标题
估计粒径分布的泛函
DOI：
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发表时间：
1971
期刊：
影响因子：
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通讯作者：
G. Watson
中科院分区：
文献类型：
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作者：
G. Watson
由直径分布为G(x)的平面或线性探头与球体场的交点组成的数据通常用于估计线性泛函或它们的比率。结果表明，无分布估计量可能很差，并且它们的分布，即使在大样本中，也依赖于可能无法获得的小x的G知识。参数化方法难度大，对下尾误差的鲁棒性差。当有可行的替代方法时，似乎应该避免这种实验方法。假设粒子群在几何上与大小分布函数G(x)相似，随机分布在空间中。粗略地说，它们的中心将通过泊松过程放置。这个空间可能会以某种方式被探测；我们将只考虑平面和线性探头。在前者中，数据是粒子的交点和探测平面的某一区域。在后者中，数据是探测线某一间隔上的一组和弦。从这些数据中，目标是估计表单的函数
SUMMARY Data consisting of the intersections of a planar or linear probe with a field of spheres, with a diameter distribution G(x), is often used to estimate linear functionals or their ratios. It is shown that distribution-free estimators may be poor and that their distribution, even in large samples, depends on knowledge of G for small x that may be unobtainable. The parametric approach is arduous and not robust against errors in the lower tail. It seems that this experimental method should be avoided when there is a practicable alternative. Suppose that a population of particles, geometrically similar with a size distribution function G(x) are randomly dispersed through space. Roughly, their centres will be placed by a Poisson process. The space may be probed in some way; we will consider only planar and linear probes. In the former the data are the intersections of the particles and some area of the probing plane. In the latter the data are a set of chords on some interval of the probing line. From such data, the object is to estimate functionals of the form