随机独立

In this paper we generalize Bernstein inequality of t he sequence of independent random variables to the martingale difference s, then we give an application of this inequality.

本文将独立随机变量序列的Bernstein型不等式推广到鞅差序列情形，给出该不等式的一个应用，并在一定条件下证明了非参数回归中函数估计的强相合性。

Using projection theory and a decomposition in canonical form, a new recursive reduced-order filter for descriptor discrete-time stochastic linear systems with correlated noises is given by transferring system with correlated noised to that with independent noises.

基于广义系统典范型分解，应用射影理论，对带相关噪声的广义离散随机线性系统，通过将带相关噪声系统转化为带独立噪声系统给出一种新的递推降阶滤波器。

Most of them rely on the central limit theorem, that states that the mean of N independent realizations of a random variable with mean u and variance d^2 approaches a normal distribution with mean u and variance d^2/N .

在蒙特卡罗评估框架内大量的各种选择性算法已经被推出，他们中的大部分依赖于中心极限定理，一个均值为U方差为D^2的随机变量的N次独立实现的平均值接近于一个均值为U方差为D^2/N的正态分布。

Therefore, in this article,we first discussed the compound negative binomial, it able to simultaneously fitthe claim size and the claim number. At the same time, we studied the sum of themutually independent compound negative binomial and the sum of the mutuallyindependent compound negative binomial with discount factor and the sum of themaximal compound negative binomial; Next, for the claim data to be better fitted, this article has establishedthe superposition distributed model about the weighted average of the discreterandom and has discussed the estimation method of the parameters of thesuperposition distribution; Once more, we in detail elaborated the NCD which based on the claim numberand the NCD which based on the claim size and the claim number. Besides, weestablished an applied NCD model which also based on the claim size and the claimnumber; At last, we introduced the rewards and punishment coefficient of automobiletravel region into the applied NCD model, availably consummated the present NCD.

因此，本文首先讨论了能拟合索赔额大小和索赔次数的复合负二项分布，并对相互独立的复合负二项分布的和、带有折现因子的相互独立的复合负二项分布的和以及最大复合负二项分布进行了研究；其次，为了更好地拟合索赔数据，本文建立了离散随机变量加权平均的叠加分布模型，并讨论了其中的权数的估计方法；再次，本文详细阐述了基于索赔次数的无赔款优待系统、考虑索赔次数和索赔额大小的无赔款优待系统以及应用型的同时考虑索赔次数和索赔大小的无赔款优待系统；最后，本文在无赔款优待系统中引入了汽车行驶区域奖惩系数，对现行的无赔款优待系统进行了完善。

The concept and definition of linear process with independent increments were presented. Then the regression model and analysis method for linear process with independent increments were established. Furthermore, the regression equation and confidence limit curves were given.

提出了线性独立增量随机过程的概念和定义，建立了线性独立增量过程回归模型及其分析方法，给出了回归方程和高置信度、高可靠度的置信上、下限曲线。

Based on the previous works, we study Markov chains in random environments, especially random walk in random environments in this dissertation.

在前人的研究的基础上，本文研究了随机环境中的马氏链的有关问题，主要讨论了独立环境中的随机游动这个具体的模型。

Acquired conclusion was that the sample mean value submitted to normal distribution, and the sample variance was composed of a number of linear sum of random variable submitted to Chi-Squared distr.

得出的结论是：样本均值服从正态分布，样本方差由若干个服从卡方分布的随机变量的线性之和组成；样本均值的期望等于各管落点期望的算术平均值，方差为各管方差的算术平均值；样本方差是各管落点总体平均方差的无偏估计，方差与各管落点散布的差异相关；样本均值与方差相互独立的充要条件是：各管落点属于独立同分布样本。

Control layer and parameter layer represent the available number of rows and the concrete value of the available rows of separation matrix respectively. Non-Gaussian was used to measure the independence of the stochastic signals. The kurtosis was maximized/minimized by searching a linear combination of observation signals, and then the independent variables were separated.

用控制层、参数层分别表示分离阵有效行数和有效行数的具体数值，将非高斯性作为随机信号相互独立的度量，通过寻求观测信号的一个线性组合，使其峭度最大化或最小化来分离独立分量。

In this paper, a new random algorithm is introduced for the classical problem of estimating the cardinality of a union of sets, which only needs pair -wise independent random input.

仅用成对独立的随机变量作为输入，得到了一个关于估计并集的基的问题的随机算法。

These subnets are independently evaluated and then are substituted by the nonprimitive transitions as performance equivalence in the original model to achieve a state space reduc tion.

这篇论文提供了一种将大型随机高级Petri网模型构造成独立子网的方法和技术这些子网可以独立地进行性能评价，在原模型中子网可由非基本变迁进行性能等效替代，以达简化状态空间的目的。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。