统计与数据科学学院知识库

在当今信息错综复杂、社会不断进步的新时代，人们对事物的认知能力也在 不断加强，仅仅使用单一的模型已经远远不能够有效地解决我们所面临的许多问 题。混合模型作为一种灵活又高效的数据分析建模工具，能够用来解决很多复杂 的实际问题。近年来寿命分布的产生吸引了越来越多的海内外学者对混合模型进 行研究。据此本文给出了一个新的寿命分布：由 N  2个元件构成的系统，它们 之间相互独立，若随机变量 N 服从于二重或多重泊松分布，元件的寿命服从二 重或多重指数分布，那么该系统寿命就服从二重或多重混合指数－泊松分布。本 文基于以上考虑，最终选择使用二重及多重混合模型来解决这类问题。 本文首先用 EM 算法对二重和多重混合泊松-指数分布模型的参数进行估 计，然后运用二重混合泊松-指数分布模型验证 EM 算法的收敛性和有效性；其 次用改进的 EM 算法对多重混合泊松-指数分布进行参数估计；最后通过 R 软件 进行随机模拟，得出结论：在有限次迭代下，二重混合泊松-指数分布和多重混 合泊松-指数分布通过给定一定数量的初始值，选用不同的初始值对模型进行模 拟，当样本容量n 增大时，其最终值也随之变化，样本容量越大，最终值越逼近 真实值。进而验证了该模型的收敛性和有效性。

In today's new era of intricate information and continuous social progress, people's cognitive ability to things is also constantly strengthening. Using only a single model is far from being able to effectively solve many of the problems we face. As a flexible and efficient data analysis modeling tool, the hybrid model can be used to solve many complex practical problems. The generation of life distribution in recent years has attracted more and more scholars at home and abroad to study mixture models. According to this paper, a new life distribution is given: a system consisting of individual components, which are independent of each other. If the random variable N is subject to a double or multiple Poisson distribution, the life of the component obeys a double or multiple exponential distribution. Then the life of the system is subject to a double or multiple mixed exponential-Poisson distribution. Based on the above considerations, this paper finally chooses to use double and multiple hybrid models to solve these problems.In this paper, EM algorithm is used to estimate the parameters of the double and multiple mixed Poisson-exponential distribution model, and then the convergence and effectiveness of EM algorithm are verified by using the double mixed Poisson-exponential distribution model;Secondly, the improved EM algorithm is used to estimate the parameters of the muti-mixed Poisson-exponential distribution;Finally, the random simulation is performed by R software, and the conclusion is as follows: Under a finite iteration, the double-mixed Poisson-exponential distribution and the muti-mixed Poisson-exponential distribution are modeled by giving a certain number of initial values. When the sample size is increased, the final value also changes, and the larger the sample size, the closer the final value is to the true value. Furthermore, the convergence and effectiveness of the model are verified.