【摘要】：本文主要利用廣義超幾何級數(shù)得到了廣義幾何分布,第一類廣義Polya Egge-nberger分布,Katz分布,Lagrangian Katz分布高階逆矩的表達(dá)式.同時對廣義超幾何級數(shù)進(jìn)行推廣獲得新的廣義超幾何級數(shù),并利用推廣的超幾何級數(shù)給出了第二類廣義Polya Eggenberger分布,線性負(fù)二項分布,第二類Lagrangian Katz分布的高階逆矩的表達(dá)式,展現(xiàn)出超幾何級數(shù)在逆矩中有著重要的作用.第一章:簡單介紹了組合學(xué),概率論,概率分布逆矩的研究背景及國內(nèi)外研究狀況,并且給出廣義超幾何級數(shù)以及某些離散分布的定義.第二章:利用廣義超幾何級數(shù)得到一些離散分布的高階逆矩及高階階乘逆矩,主要有廣義幾何分布,第一類廣義Polya Eggenberger分布,Katz分布,Lagrangian Katz分布等.第三章:對廣義超幾何級數(shù)進(jìn)行推廣得到新的廣義超幾何級數(shù)的表達(dá)式,并且利用新的廣義超幾何級數(shù)給出一些離散分布的高階逆矩及高階階乘逆矩,如:第二類廣義Polya Eggenberger分布,第二類Lagrangian Katz分布,線性負(fù)二項分布等.
[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.
【學(xué)位授予單位】：內(nèi)蒙古大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O173

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 王春媛;超幾何級數(shù)在概率分布中的應(yīng)用[D];內(nèi)蒙古大學(xué);2014年

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本文編號：2131324