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似然方程
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  likelihood equation
     This paper studies the quasi likelihood equation ∑ni=1x i(y i-μ(x ′ iβ))=0 with adaptive designs. Under certain conditions, we obtain that there exists solution n to the above equation with probability 1 for sufficently large n, n is the estimator of strong consistency of β 0, and the convergence rate of n-β 0;
     研究自适应设计下的拟似然方程 ∑ni=1xi(yi- μ(x′iβ) ) =0 ,在一定的条件下证明了以概率 1此方程当n充分大时有解^βn,^βn 为β0 的强相合估计 ,且得出了 ^βn- β0的收敛速度 ;
短句来源
     Large Sample Size Property of the Root of Log Likelihood Equation for Cauchy Distribution
     柯西分布族对数似然方程根的大样本性质
短句来源
     The Discussion on the Likelihood Equation of the Parameter Y of Weibull Distribution
     对威布尔分布之参数γ的似然方程的讨论
短句来源
     In this paper,we study the quasi likelihood equation in Generalized Linear Mod-els(GLM) with adaptive design ∑n_i=1x_i(y_i-μ(x′_iβ))=0,where y_i is a q-vector,and x_i is a p×q random matrix. Under some assumptions,it is shown that the Quasi-Likelihood equation for the GLM has a solution which is asymptotic normal.
     本文研究了自适应设计下广义线性回归的拟似然方程∑ni=1xi(yi-μ(xi′β))=0,其中yi是q维向量,xi是p×q阶随机矩阵,在一定条件下证明了方程的解^βn具有渐进正态的性质.
短句来源
     By applying the method of reliability statistics, a parameter iteration of maximum likelihood equation is set up for MIS software with an operation life submitting to minimum distribution.
     应用可靠性统计方法 ,对寿命服从极小值分布的 MIS软件 ,建立最大似然方程的参数迭代法 .
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  “似然方程”译为未确定词的双语例句
     In this paper,we study quasi-likelihood equation sum from i=1 to n X_i(y_i-μ(X_i~1β))= 0 for muttivariate generalized linear models(GLMs).
     本文考虑多维广义线性模型的拟似然方程sum from i=1 to n X_i(y_i-μ(X_i~1β))=0,在一定条件下证明了此方程的解(?)
短句来源
     In this paper, we studied the quasi-likelihood equation forgeneralized linear models y = μ(x'β0) + e. Under mild conditions, we proved that there exists the solution βn to the above equation with probability 1 for sufficently large n, and obtained the strong consistency and the convergence rate of βn.
     本文研究了广义线性模型g=μ(x'β0)+e中形如的拟似然方程,在一定的条件下证明了当n充分大时此方程以概率1有解βn,得到了βn的强相合性和收敛速度.
短句来源
     For the parameter θ in Cauchy distribution,we prove that there exists a strongly consistent and asymptoticly normal estimator_n,which,in probability 1,is the root of the log-likelihood equation when the sample size n is sufficiently large.
     文章针对一类具体的分布族———柯西分布族中参数θ,证明了存在θ的一个强相合且最好渐近正态估计^θ,它以概率1当样本量n充分大时是对数似然方程的根。
短句来源
     The second moment of the least squares estimator in the nonlinear regression model is obtained in this paper in terms of two kinds of curvatures defined by Bates and watts.
     本文从似然方程的二级近似出发,求出了非线性回归模型最小二乘估计量(LSE)的二阶矩与Bates and Watts定义的二种曲率之间的关系。
短句来源
     However, the probability density functions of model (1) and (2) are hard to show directly.
     通常情况下,我们由似然方程来求解参数的极大似然估计,但对于(1)和(2),似然函数难以直接表示。
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  相似匹配句对
     Synthetic Aperture Radar Equations
     合成孔径雷达方程
短句来源
     The simple equation changes into nonlin-ear Schrodinger equation when viscous effect is died away.
     dinger 方程
短句来源
     Consistency Problem of Solution in Quasi Likelihood Equation with Two-Valued Responses
     二值响应变量拟似然方程解的相合性
短句来源
     The Discussion on the Likelihood Equation of the Parameter Y of Weibull Distribution
     对威布尔分布之参数γ的似然方程的讨论
短句来源
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  likelihood equation
The method of statistical estimation of the quantum state from a solution to the likelihood equation and the analysis of the statistical properties of the obtained estimators is developed.
      
The estimates given by this paper also satisfy the maximum likelihood equation.
      
We study the quasi likelihood equation in Generalized Linear Models (GLM) with adaptive design
      
A suggestion for choosing weight function and a method of constructing depth-weighed quasi likelihood equation are given.
      
We point out also that the maximum full likelihood estimator after a simple modification of the likelihood equation provides a good approximation to the maximum partial likelihood estimator.
      
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Based upon the method of statistical testing,this paper analyses and compares the methods of moments, maximum likelihood and curve-fitting in the case of Pearson type Ⅲ distribution. For the curve-fitting method, a comprehensive comparative analysis is made on seven criteria of curve fitting and mainly on the two of them-the least squares criterion φ1 andthe least absolute-values criterion φ2, as well as on the various plotting position formulas.Moreover, the role of historical flood is also examined. The results...

Based upon the method of statistical testing,this paper analyses and compares the methods of moments, maximum likelihood and curve-fitting in the case of Pearson type Ⅲ distribution. For the curve-fitting method, a comprehensive comparative analysis is made on seven criteria of curve fitting and mainly on the two of them-the least squares criterion φ1 andthe least absolute-values criterion φ2, as well as on the various plotting position formulas.Moreover, the role of historical flood is also examined. The results of calculation indicate that the quantity Xp derived from the moment method has a much smaller expected value EXP than the true value xp?of the population and that this is on the unsafe side. The maximum likelihood method yields somewhat better result but it cannot be accepted as a universal method because it yields no solution to Pearson Ⅲ .curve when Cs≥2. For the curve fitting method, it is found that the result is substantially affected by the criterion used for curve fitting.In general, φ2 criterion associated with Weibull formula ( abbr. in φ2-W ) may give slightly greater EXP than xpo and smaller root-mean-square error σXp. Consequently, φ2-W curve-fitting method proves to be the better one among all the methods available. The use of historical flood would usually increase EXP and decrease σXp and is, therefore, an important means to improve the computational results.

本文采用统计试验方法,对于P-Ⅲ型曲线分析对比了矩法、极大似然法和适线法.在适线法中分析比较了七种不同的适线准则,并着重比较了其中的平方准则φ_1和绝对值准则φ_2,同时也分析比较了各种不同的经验频率公式.另外,还研究了历史洪水的作用.大量计算结果表明:矩法所得的设计值X_p,其期望值EX_p比总体真值x_p~0偏小较多,不够安全;极大似然法虽具有较好性质,但由于P-Ⅲ曲线在C≥2时似然方程无解,因此无法普遍使用;在适线法中发现适线准则对结果的影响很大,φ_2准则配合期望值公式(简记为φ_2-W)一般能使EX_p,稍大于x_p~0,较小(与矩法接近),因此φ_2-W适线法是较好的一种估计方法,应予采用.考虑历史洪水一般使EX_p增大、σx_p降低,因此是提高计算成果质量的重要措施.给出了历史洪水折算长度的参照数值,计算了历史洪水误差的影响.并修正了计算设计洪水安全改正值用的B值图.

In the hydrological calculation for bridge design, the treatment of extremesis an important problem. Yet, it is difficult to determine the values of the extremes and sometimes they are missing. As yet, no method has been set up to solvethe frequency problems on occasions such as these.This thesis, based on the theory of truncated order statistics, proposes a method to estimate the parameters for the problem. In the thesis, amathematical model for the new method is set up, the maximum likelihood equations for...

In the hydrological calculation for bridge design, the treatment of extremesis an important problem. Yet, it is difficult to determine the values of the extremes and sometimes they are missing. As yet, no method has been set up to solvethe frequency problems on occasions such as these.This thesis, based on the theory of truncated order statistics, proposes a method to estimate the parameters for the problem. In the thesis, amathematical model for the new method is set up, the maximum likelihood equations for the truncated samples based on Pearson Type Ⅲ are then derived. The equations aresolved with an electronic computer, and a set of tables for calculating parameters X, C_s are made. Compared with the actual design values on ten rivers, the results by the proposed method is reasonable, practicable, and a little more on the safe side.

在桥梁设计的水文统计中,特大值的处理是一个重要的问题。但特大值往往难于定量,现行统计方法无法对此类资料直接计算。本文依据数理统计学中缺项顺序统计量理论,对特大值难定量的频率计算问题提出估计参数的新方法。文内建立了新方法的数学模型,推导了皮尔逊Ⅲ型缺项样本的极大似然方程。并将利用电子计算机求解的结果,编出一套皮尔逊Ⅲ型分布参数C_s估计值的表格,可供实用。通过十条河流的实例验证,本计算方法合理可行,稍偏于安全。

The second moment of the least squares estimator in the nonlinear regression model is obtained in this paper in terms of two kinds of curvatures defined by Bates and watts. The variance matrix of LS estimator in our results consists of the usual Cramer-Rao lower bound and two curvature terms determined by the model and the parameterization of the model respectively. The formulas in our results are simple and clear, so that the Clarke's results are fairly improved. Some well known formulas are also derived conveniently,...

The second moment of the least squares estimator in the nonlinear regression model is obtained in this paper in terms of two kinds of curvatures defined by Bates and watts. The variance matrix of LS estimator in our results consists of the usual Cramer-Rao lower bound and two curvature terms determined by the model and the parameterization of the model respectively. The formulas in our results are simple and clear, so that the Clarke's results are fairly improved. Some well known formulas are also derived conveniently, and an useful example is discussed to illustrate the general results.

本文从似然方程的二级近似出发,求出了非线性回归模型最小二乘估计量(LSE)的二阶矩与Bates and Watts定义的二种曲率之间的关系。LS估计的方差矩阵由三项组成:一项为通常的CR下界,即分布族Fisher信息阵的逆阵;一项由模型的固有曲率所决定,这是一个不变量,它取决于模型本身的性质与参数的选择无关;另一项由模型的参数效应曲率所决定,常常可通过参数变换使之为零。本文给出的公式形式简单,统计意义和几何意义清楚,从而改进了Clarke 1980年给出的结果([4])。本文还给出了其他一些有关的公式,并且讨论了二个具有广泛应用价值的例子。

 
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