Distributions of random partitions and their applications
Distributions of random partitions and their applications
复制标题
DOI：
10.1007/s11009-007-9018-6
复制
发表时间：
2007-06-01
影响因子：
0.9
通讯作者：
Charalambides, Charalambos A.
中科院分区：
文献类型：
--
作者：
Charalambides, Charalambos A.
假设一个大小为m的随机样本是从包含可数个元素（个体）类（子群体）的总体中选择的。将样本元素的集合划分为（无序的）子集，其中每个子集包含属于相同类的元素，这引起样本大小m的随机划分，其中部分大小{Z（1），Z（2），.，Z（N）}是正整数值随机变量。或者，如果N-j是样本中由j个元素表示的不同类别的数量，对于j= 1，2，.，m，则（N-1，N（2），...，N-m）表示相同的随机划分。给出了（N-1，N-2，…，N-m）以及N =Sigma（m）（j=1）N-j的分布在统计推断中是特别感兴趣的。从推断的观点来看，希望关于总体的所有信息包含在（N-1，N（2），.，N-m）。这就要求人口类别的实际标签不具有任何物理、遗传或其他意义。本文综述了组合抽样、概率抽样和复合抽样模型。此外，抽样模型与人口类的随机权重（比例），特别是Ewens和皮特曼抽样模型，其中许多出版物都致力于广泛介绍。
Assume that a random sample of size m is selected from a population containing a countable number of classes (subpopulations) of elements (individuals). A partition of the set of sample elements into (unordered) subsets, with each subset containing the elements that belong to same class, induces a random partition of the sample size m, with part sizes {Z(1),Z(2),...,Z(N)}being positive integer-valued random variables. Alternatively, if N-j is the number of different classes that are represented in the sample by j elements, for j=1,2,...,m, then (N-1,N (2),...,N-m) represents the same random partition. The joint and the marginal distributions of (N-1,N-2,...,N-m), as well as the distribution of N =Sigma(m)(j=1) N-j are of particular interest in statistical inference. From the inference point of view, it is desirable that all the information about the population is contained in (N-1, N (2),...,N-m ). This requires that no physical, genetical or other kind of significance is attached to the actual labels of the population classes. In the present paper, combinatorial, probabilistic and compound sampling models are reviewed. Also, sampling models with population classes of random weights (proportions), and in particular the Ewens and Pitman sampling models, on which many publications are devoted, are extensively presented.