关于不放回抽样和OK-Corral骨灰盒模型
On Sampling without replacement and OK-Corral urn models
摘要：
在这项工作中，我们讨论了两个骨灰盒模型与一般的权重序列$(A,B)$与他们，$A=(α_n)_{n\in\N}$和$B=(β_m)_{m\in\N}$，推广了两个著名的Pólya-Eggenberger骨灰盒模型，即所谓的不放回抽样骨灰盒模型和OK Corral骨灰盒模型。我们推导出简单的显式表达式的白球的数量的分布，当所有的黑色已经画出，并获得作为副产品的Pólya-Eggenberger瓮模型的相应结果。此外，我们还证明了无放回不放回抽样瓮模型和具有一般权值的OK Corral瓮模型在一定意义上是对偶的。我们讨论了高维不放回抽样和OK Corral瓮模型的扩展，分别，在那里我们也得到了明确的结果的概率质量函数，也是一个模拟的对偶关系。最后，我们推导出一个特殊的选择的重量序列的极限定律。
英文摘要：
In this work we discuss two urn models with general weight sequences $(A,B)$ associated to them, $A=(α_n)_{n\in\N}$ and $B=(β_m)_{m\in\N}$, generalizing two well known Pólya-Eggenberger urn models, namely the so-called sampling without replacement urn model and the OK Corral urn model. We derive simple explicit expressions for the distribution of the number of white balls, when all black have been drawn, and obtain as a byproduct the corresponding results for the Pólya-Eggenberger urn models. Moreover, we show that the sampling without replacement urn models and the OK Corral urn models with general weights are dual to each other in a certain sense. We discuss extensions to higher dimensional sampling without replacement and OK Corral urn models, respectively, where we also obtain explicit results for the probability mass functions, and also an analog of the dualitiy relation. Finally, we derive limit laws for a special choice of the weight sequences.
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