概率母函数

First, in Chapter 1, we provide some exact, elegant formulae of the transition distribution of immigration-birth-death process by moment generating function.

第一章我们利用矩母函数给出了三个精确而优美的转移概率公式。

By the method of supplemental variable, some important performance measures and queues generating function of this system have been attained.

运用补充变量法列出稳态下系统的状态偏微积分方程组，从而求得了系统主要排队指标及稳态队长的概率母函数的随机分解结果。

We obtain the risk process involved in this model,the statistical properties of the surplus process,and statistical features of the claim numbers and the probability distribution of the total amount of compensation.The three types of business of the risk model is given when the number of claims obey Poisson distribution and negative binomial distribution.We make a comparison between the risk model built in the thesis and the classic risk models with independent claim numbers when the amount of claims obey Weillbull distribution and Exponential distribution.The results have a good practical significance.

其次，考虑不同险种间的相互关系，建立了一种含有主副理赔的风险分析模型；借助随机过程和经典风险理论，对该风险模型所涉及的风险过程、盈余过程的统计特性以及理赔总额的概率分布、数字特征和矩母函数进行解析研究，给出了主理赔次数服从泊松分布和负二项分布的这种风险模型的具体实例，并在理赔额变量服从Weillbul分布和Exponential分布的情况下，把文中所建风险模型和理赔次数相互独立的风险模型作了比较，所得结果有很好的现实意义。

By solving the probability equation,generating function and in-degree distribution was deduced.

构建一个加速生长网络，根据主方程建立了概率方程，应用母函数方法求解概率方程，获得了加速生长网络模型的母函数及入度表达式。

After studying the MAC protocol of Ad hoc network and by modifying the Wireless Token Ring Protocol, a new uncontested Distributed Parallel Wireless Polling Access Protocol that can provide MAC QoS guarantees for Ad hoc network is presented, and the mathematical model is established by the embedded Markov chain theory and the probability generating function method. Based on it, the mean value of queue length and message waiting time are explicitly obtained.

摘要该文对Ad hoc网络的MAC层协议进行了研究，通过对无线令牌环协议进行改进，提出了一种新的具有QoS保障的无竞争的分布式并行无线轮询访问协议，并采用嵌入Markov链和概率母函数的分析方法，用限定服务规则进行了系统建模，在系统模型的基础上得到了系统的平均排队队长以及平均等待时间的解析结果。

By using complementary variable method to analyze the state-changing equations of this queueing system, the generating function of stationary probablity distribution of retrial queue length, some performance indexes such as three different stationary state probablity,stationary availability, and stationary failure frequence of the transfer-unit are derived.

研究通信网络中交换单元的可修模型M1，2，3/G/1，呼叫的到达是重试性的，利用补充变量法对排队系统的状态转移方程作了分析，求得了重试队列稳态队长概率分布的母函数以及交换单元的处于三种不同状态下的稳态概率、稳态可用度及稳态故障频度等性能指标。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。