超几何级数在特殊离散分布逆矩中的应用
发布时间：2018-07-18 08:26
【摘要】：本文主要利用广义超几何级数得到了广义几何分布,第一类广义Polya Egge-nberger分布,Katz分布,Lagrangian Katz分布高阶逆矩的表达式.同时对广义超几何级数进行推广获得新的广义超几何级数,并利用推广的超几何级数给出了第二类广义Polya Eggenberger分布,线性负二项分布,第二类Lagrangian Katz分布的高阶逆矩的表达式,展现出超几何级数在逆矩中有着重要的作用.第一章:简单介绍了组合学,概率论,概率分布逆矩的研究背景及国内外研究状况,并且给出广义超几何级数以及某些离散分布的定义.第二章:利用广义超几何级数得到一些离散分布的高阶逆矩及高阶阶乘逆矩,主要有广义几何分布,第一类广义Polya Eggenberger分布,Katz分布,Lagrangian Katz分布等.第三章:对广义超几何级数进行推广得到新的广义超几何级数的表达式,并且利用新的广义超几何级数给出一些离散分布的高阶逆矩及高阶阶乘逆矩,如:第二类广义Polya Eggenberger分布,第二类Lagrangian Katz分布,线性负二项分布等.
[Abstract]:In this paper, the generalized geometric distribution is obtained by means of generalized hypergeometric series. The first kind of generalized Polya Egge-nberger distribution Katz distribution and Lagrangian Katz distribution are used to obtain the expression of higher order inverse moments. At the same time, we generalize the generalized hypergeometric series to obtain a new generalized hypergeometric series. By using the generalized hypergeometric series, we give the expressions of the higher order inverse moments of the generalized Polya Eggenberger distribution, the linear negative binomial distribution, the second Lagrangian Katz distribution, and the generalized hypergeometric series. It is shown that the hypergeometric series play an important role in the inverse moment. Chapter 1: the research background of combinatorial theory, probability theory, inverse moment of probability distribution and the research status at home and abroad are briefly introduced, and the definitions of generalized hypergeometric series and some discrete distributions are given. Chapter 2: by using generalized hypergeometric series, we obtain some higher order inverse moments and higher order factorial inverse moments of discrete distribution, mainly generalized geometric distribution, the first kind of generalized Polya Eggenberger distribution / Katz distribution and Lagrangian Katz distribution, etc. In chapter 3, we generalize the expression of generalized hypergeometric series, and give some discrete higher order inverse moments and higher order factorial inverse moments by using new generalized hypergeometric series. For example: generalized Polya Eggenberger distribution of the second kind, Lagrangian Katz distribution of the second kind, linear negative binomial distribution and so on.
【学位授予单位】：内蒙古大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O173
本文编号：2131324
[Abstract]:In this paper, the generalized geometric distribution is obtained by means of generalized hypergeometric series. The first kind of generalized Polya Egge-nberger distribution Katz distribution and Lagrangian Katz distribution are used to obtain the expression of higher order inverse moments. At the same time, we generalize the generalized hypergeometric series to obtain a new generalized hypergeometric series. By using the generalized hypergeometric series, we give the expressions of the higher order inverse moments of the generalized Polya Eggenberger distribution, the linear negative binomial distribution, the second Lagrangian Katz distribution, and the generalized hypergeometric series. It is shown that the hypergeometric series play an important role in the inverse moment. Chapter 1: the research background of combinatorial theory, probability theory, inverse moment of probability distribution and the research status at home and abroad are briefly introduced, and the definitions of generalized hypergeometric series and some discrete distributions are given. Chapter 2: by using generalized hypergeometric series, we obtain some higher order inverse moments and higher order factorial inverse moments of discrete distribution, mainly generalized geometric distribution, the first kind of generalized Polya Eggenberger distribution / Katz distribution and Lagrangian Katz distribution, etc. In chapter 3, we generalize the expression of generalized hypergeometric series, and give some discrete higher order inverse moments and higher order factorial inverse moments by using new generalized hypergeometric series. For example: generalized Polya Eggenberger distribution of the second kind, Lagrangian Katz distribution of the second kind, linear negative binomial distribution and so on.
【学位授予单位】：内蒙古大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O173
【参考文献】
相关硕士学位论文 前1条
1 王春媛;超几何级数在概率分布中的应用[D];内蒙古大学;2014年
，本文编号：2131324
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