负相关二元泊松变量的生成方法研究

发布时间：2017-12-30 22:21

本文关键词：负相关二元泊松变量的生成方法研究　出处：《上海交通大学》2015年硕士论文　论文类型：学位论文

【摘要】：泊松分布是一种应用非常广泛的随机变量分布形式,很多研究都要求生成指定参数和相关性的多元泊松变量,尤其是二元泊松变量。但是目前,该问题只有当指定的相关系数为正的时候,才得到了很好的解决,对于相关系数为负数的情况,比较好的方法如NORTA、Inbal's method,只是得到了近似结果,而且计算复杂度很大。本文利用伯努利分布与泊松分布的混合分布,借鉴Trivariate Induction的思想,提出了两种新的产生二元泊松分布随机变量的算法：伯努利-泊松法和伯努利-泊松-迭代法。当在某一特定范围内指定负相关系数值时,伯努利-泊公法能精确地产生服从该负相关系数的二元泊松变量,如果被指定的二元泊松量参数比较小,伯努利-泊松法能生成负相关系数为任意值的二元泊松变量,且该算法的时间复杂度为O(1)。在相关系数超出了该指定的负数区间时,可采用本文提出的伯努利-泊松迭代法。这部分,文章首先研究了对于各自服从任意离散分布的两个随机变量-迭代法,该算法对区间内指定的任何负数都能近似生成服从该负相关系数的二元泊松变量。
[Abstract]:The Poisson distribution is random variable distribution form a very wide range of applications, multivariate Poisson variables in many studies required to generate the specified parameters and the correlation, especially the two yuan Poisson variables. But at present, the problem only when the correlation coefficient is specified for the time, to be a very good solution, the correlation coefficient is negative the good method, such as NORTA, Inbal's method, just got similar results, but the computational complexity greatly. By using Bernoulli distribution and Poisson mixture distribution, using Trivariate Induction, we proposed two kinds of algorithms of two yuan Poisson distributed random variables to generate new: Bernoulli Poisson and Bernoulli Poisson - iterative method. When the specified correlation value in a certain range, Bernoulli Bo law can accurately produce to two yuan Poisson variables the negative correlation coefficient, Two yuan if the Poisson parameter is specified amount is relatively small, two yuan Poisson variables Bernoulli Poisson method can generate negative correlation coefficient for arbitrary values, and the time complexity of the algorithm is O (1). The correlation coefficient exceeded the specified interval can be negative when using the proposed Poisson and Bernoulli iteration method. In this part, the article has been studied for two random variables obey arbitrary discrete distribution of each iteration, the algorithm can generate approximately two yuan to obey Poisson variables the negative correlation coefficient of any negative range specified.

【学位授予单位】：上海交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211.5

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