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首页> 外文期刊>Statistica neerlandica >Multinomial distributions applied to random sampling of particulate materials
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Multinomial distributions applied to random sampling of particulate materials

机译：多项式分布应用于颗粒材料的随机采样

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摘要

When sampling a batch consisting of particulate material, the distribution of a sample estimator can be characterized using knowledge about the sample drawing process. With Bernoulli sampling, the number of particles in the sample is binomially distributed. Because this is rarely realized in practice, we propose a sampling design in which the possible samples have a nearly equal mass. Expected values and variances of the sample estimator are calculated. It is shown that the sample estimator becomes identical to the Horvitz–Thompson estimator in the case of a large batch-to-sample mass ratio and a large sample mass. Simulations and experiments were performed to test the theory. Simulations confirm that the round-off error due to the discrete nature of particles is negligible for large sample sizes. Sampling experiments were carried out with a mixture of PolyPropylene (PP) and PolyTetraFluorEthylene (PTFE) spheres suspended in a viscous medium. The measured and theoretical variations are in good agreement.
机译：在对由颗粒物质组成的批次进行采样时，可以使用有关样本抽取过程的知识来表征样本估算器的分布。对于伯努利采样，样本中的粒子数量是二项分布的。由于这在实践中很少实现，因此我们提出了一种采样设计，其中可能的采样质量几乎相等。计算样本估计量的期望值和方差。结果表明，在批次与样品的质量比大且样品质量大的情况下，样本估计量与Horvitz-Thompson估计量相同。进行了仿真和实验以验证该理论。仿真证实，由于颗粒的离散性而导致的舍入误差对于大样本量而言可以忽略不计。使用悬浮在粘性介质中的聚丙烯（PP）和聚四氟乙烯（PTFE）球的混合物进行采样实验。测得的和理论上的变化非常吻合。

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