POLYA URN MODELS UNDER GENERAL REPLACEMENT SCHEMES
POLYA URN MODELS UNDER GENERAL REPLACEMENT SCHEMES
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一般更换计划下的 POLYA 瓮型号
DOI：
10.14490/jjss1995.31.193
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
S. Aki
中科院分区：
文献类型：
--
作者：
K. Inoue;S. Aki
本文考虑了在一般置换方案下含有m个不同标号球的Polyaurn模型，其特征是一个m × m的整数加法矩阵，除了非负性外，对这m2个整数的值没有限制.该模型包括了一些重要的瓮模型。本文利用概率母函数的方法，研究了n次抽中带有特定标号的球的个数的精确联合分布。作为特例，当m = 2时，精确地导出了一元分布、概率母函数和期望值。我们提出的方法获得的概率生成函数和期望值的所有n正好，这是非常简单，适合于计算机代数系统的计算。本文的结果为Polya瓮模型的研究提供了一个普遍可行的框架，并引起了我们对精确分析的重视。我们的尝试是非常有用的理解非经典瓮模型。最后，数值例子也说明了我们的结果的可行性。
In this paper, we consider a Polya urn model containing balls of m different labels under a general replacement scheme, which is characterized by an m × m ad- dition matrix of integers without constraints on the values of these m 2 integers other than non-negativity. This urn model includes some important urn models treated before. By a method based on the probability generating functions, we consider the exact joint distribution of the numbers of balls with particular labels which are drawn within n draws. As a special case, for m = 2, the univariate distribution, the prob- ability generating function and the expected value are derived exactly. We present methods for obtaining the probability generating functions and the expected values for all n exactly, which are very simple and suitable for computation by computer algebra systems. The results presented here develop a general workable framework for the study of Polya urn models and attract our attention to the importance of the exact analysis. Our attempts are very useful for understanding non-classical urn models. Finally, numerical examples are also given in order to illustrate the feasibility of our results.
与波利亚瓮方案中的模式相关的广义等待时间问题
DOI：
--
发表时间：
2002
期刊：
Annals of the Institute of Statistical Mathematics 54・3
影响因子：
--
作者：
Inoue;K;Aki;S
通讯作者：
S