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首页> 外文期刊>Statistica neerlandica >Estimators for particulate sampling derived from a multinomial distribution
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Estimators for particulate sampling derived from a multinomial distribution

机译：从多项式分布推导的颗粒采样估算器

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Counting the number of units is not always practical during the sampling of particulate materials: it is often much easier to sample a fixed volume or fixed mass of particles. Hence, a class of sampling designs is proposed which leads to samples that have approximately a constant mass or a constant volume. For these sampling designs, estimators were derived which are a ratio of arbitrary sample totals. A Taylor expansion was used to obtain a first-order approximation for the expected value and variance in the limit of a large batch-to-sample size ratio. Furthermore, a π-estimator for a ratio of batch totals was found by deriving expressions for the first- and second-order inclusion probabilities. Practical application of the π-estimator is limited because it requires inaccessible batch information. However, when the denominator of the estimated batch ratio is the batch size, the π-estimator becomes equal to a sample total divided by the sample size in the limit of a large sample-to-particle size ratio. As a consequence, the obtained sample ratio becomes an unbiased estimator for the corresponding batch ratio. Retaining unbiasedness, the Horvitz–Thompson estimator for the variance, which also contains inaccessible batch information, is replaced by an estimator containing sample information only. Practical application of this estimator is illustrated for the sampling of slag, produced during the production of steel.
机译：在采样颗粒物质期间，计算单位数量并不总是可行的：通常更容易对固定体积或固定质量的颗粒进行采样。因此，提出了一类采样设计，其导致样品具有近似恒定的质量或恒定的体积。对于这些抽样设计，得出了估计数，该估计数是任意样本总数的比率。泰勒展开用于获得预期值的一阶近似值，并且在大批量与样品大小之比的极限范围内具有方差。此外，通过推导一阶和二阶包含概率的表达式，找到批总数的比率的π估计量。 π估计器的实际应用受到限制，因为它需要不可访问的批处理信息。但是，当估计的批处理比率的分母为批处理大小时，在大的样本粒径比的范围内，π估计器等于样本总数除以样本大小。结果，所获得的样本比率成为相应批次比率的无偏估计量。为了保持公正，方差的Horvitz-Thompson估计量（也包含不可访问的批次信息）被仅包含样本信息的估计量所取代。说明了该估计器在钢生产过程中产生的炉渣采样中的实际应用。

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