论文标题
无需替代的采样下订单统计数据的分布
The distribution of order statistics under sampling without replacement
论文作者
论文摘要
本文研究了从没有替换的简单范围采样（SRSWOR）的有限种群中，值为1，...，n。该分布是以特定方式进行参数化的β-二元分布的变化版本。我们得出分布，并显示了与单位间隔中均匀分布的IID采样下订单统计分布之间的关系。我们检查分布的特性，包括力矩和渐近结果。我们还将分布概括为采样，而无需替代任意有限人群的订单统计数据。我们研究了关于未知人口规模（称为德国坦克问题）的订单统计属性的特性，并根据观察一组任意订单统计数据的观察来得出相关的估计结果。我们还引入了一种算法，该算法在不替换任意有限人群的订单统计的情况下模拟采样，而无需生成整个样本。
This paper examines the distribution of order statistics taken from simple-random-sampling without replacement (SRSWOR) from a finite population with values 1,...,N. This distribution is a shifted version of the beta-binomial distribution, parameterised in a particular way. We derive the distribution and show how it relates to the distribution of order statistics under IID sampling from a uniform distribution over the unit interval. We examine properties of the distribution, including moments and asymptotic results. We also generalise the distribution to sampling without replacement of order statistics from an arbitrary finite population. We examine the properties of the order statistics for inference about an unknown population size (called the German tank problem) and we derive relevant estimation results based on observation of an arbitrary set of order statistics. We also introduce an algorithm that simulates sampling without replacement of order statistics from an arbitrary finite population without having to generate the entire sample.
