AN EMPIRICAL BAYES TWO-SIDED TEST PROBLEM FOR CONTINUOUS ONE-PARAMETER EXPONENTIAL FAMILIES

An empirical Bayes（EB）two-sided test problem about the continuousone-parameter exponential family has been discussed.We construct the EB test decisionrule and prove its asymptotical optimality.Further,we get its convergence ratesO(n-（λ（s-2））/（2s+1）under suitable conditions,where 0【λ【2,and s】2 is a given natural number.Finally,some examples about the result of the convergence rates are given.

A Family of the Exponential Attractors and the Inertial Manifolds for a Class of Generalized Kirchhoff Equations

In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.

The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations

In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space E0 to Ek, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.

Asymptotically Optimal Empirical Bayes Estimation of Parameter for Scale-exponential Family under PA Samples

The Bayes estimator of the parameter is obtained for the scale exponential family in the case of identically distributed and positively associated（PA） samples under weighted square loss function.We construct the empirical Bayes（EB） estimator and prove it is asymptotic optimal.

A Family of Exponential Attractors and Inertial Manifolds for a Class of Higher Order Kirchhoff Equations

In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained.

GEOMETRY OF EXPONENTIAL TYPE REGRESSION MODELS AND ITS ASYMPTOTIC INFERENCE

In this paper, exponential type regression models are considered from geometric point of view. The stochastic expansions relating to the estimate are derived and are used to study several asymptotic inference problems. The biases and the covariances relating to the estimate may be calculated based on the expansions. The information loss of the estimate and a limit theorem connected with the observed and expected Fisher informations are obtained in terms of the curvatures.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

The Modi Exponentiated Exponential Distribution

In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.

The Family of Exponential Attractors and Random Attractors for a Class of Kirchhoff Equations

To prove the existence of the family of exponential attractors, we first define a family of compact, invariant absorbing sets Bk. Then we prove that the solution semigroup has Lipschitz property and discrete squeezing property. Finally, we obtain a family of exponential attractors and its estimation of dimension by combining them with previous theories. Next, we obtain Kirchhoff-type random equation by adding product white noise to the right-hand side of the equation. To study the existence of random attractors, firstly we transform the equation by using Ornstein-Uhlenbeck process. Then we obtain a family of bounded random absorbing sets via estimating the solution of the random differential equation. Finally, we prove the asymptotic compactness of semigroup of the stochastic dynamic system;thereby we obtain a family of random attractors.

Generalized Weighted Exponential-Gompertez Distribution

Statistical analysis of lifetime data is a significant topic in social sciences, engineering, reliability, biomedical and others. We use the generalized weighted exponential distribution, as a generator to introduce a new family called generalized weighted exponential-G family, and apply this new generator to provide a new distribution called generalized weighted exponential gombertez distribution. We investigate some of its properties, moment generating function, moments, conditional moments, mean residual lifetime, mean inactivity time, strong mean inactivity time, Rényi entropy, Lorenz curves and Bonferroni. Furthermore, in this model, we estimate the parameters by using maximum likelihood method. We apply this model to a real data-set to show that the new generated distribution can produce a better fit than other classical lifetime models.

Maximum Likelihood Estimator of the Parameter for a Continuous One-Parameter Exponential Family Under the Optimal Ranked Set Sampling

This paper studies a maximum likelihood estimator(MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling(RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed(iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice,are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.

UMVUE OF POLYNOMIALS OF (EX)^(-1) FOR SEVERAL NATURAL EXPONENTIAL FAMILIES ON THE POSITIVE LINE

In this paper, we obtain the UMVUE gn(1) of a polynomial of 1/m, say g(1/m), for several NEFs on [0, +∞), where m = E(X) and gn(1) is a polynomial of 1 with the same degree as g(1/m). These estimators are asymptotically normal and asymptotically efficient. The NEFs are the Gamma, the Inverse Gaussian and the Ressel as well as the Abel families.

ON CONSTRUCTING THE NATURAL EXPONENTIAL FAMILIES WITH POLYNOMIAL VARIANCE FUNCTIONS

In this paper,we discuss the regular exponential family(REF),a natural exponentialfamily with minimum dimension and with the mean function m=E_θX taken as a new parameter.Wepoint out the importance of the REF with polynomial variance function(PVF-REF).When m is asingle factor of PVF and the left end of its defined domain is zero,the corresponding REF is givenas the single-side lattice distribution family;other PVF-REFs can be obtained by a limit process.As an illustration,the results for all seven cases of polynomial variance functions of third degreeare given.

Efficiency and superefficiency in one-parameter two-sided truncated distribution families

whereθis an unknown parameter, φ(θ) is a continuous differentiable function such that θ【φ(θ), s(θ)=dφ(θ)/dθ】0, θ∈R, and f(x;θ) is a positive continuous density func-tion on [θ,φ(θ)]. The one-parameter two-sided truncated distribution families (1)

Marshall-Olkin Exponentiated Fréchet Distribution

In this paper, a new distribution called Marshall-Olkin Exponentiated Fréchet distribution (MOEFr) is proposed. The goal is to increase the flexibility of the existing Exponentiated Fréchet distribution by including an extra shape parameter, resulting into a more flexible distribution that can provide a better fit to various data sets than the baseline distribution. A generator method introduced by Marshall and Olkin is used to develop the new distribution. Some properties of the new distribution such as hazard rate function, survival function, reversed hazard rate function, cumulative hazard function, odds function, quantile function, moments and order statistics are derived. The maximum likelihood estimation is used to estimate the model parameters. Monte Carlo simulation is used to evaluate the behavior of the estimators through the average bias and root mean squared error. The new distribution is fitted and compared with some existing distributions such as the Exponentiated Fréchet (EFr), Marshall-Olkin Fréchet (MOFr), Beta Exponential Fréchet (BEFr), Beta Fréchet (BFr) and Fréchet (Fr) distributions, on three data sets, namely Bladder cancer, Carbone and Wheaton River data sets. Based on the goodness-of-fit statistics and information criteria values, it is demonstrated that the new distribution provides a better fit for the three data sets than the other distributions considered in the study.

Gumbel-Exponentiated Weibull {Logistic} Lifetime Distribution and Its Applications

A new generalized exponentiated Weibull model called Gumbel-exponentiated Weibull {Logistic} distribution is introduced and studied. The new distribution extends the exponentiated Weibull distribution with additional parameters and bimodal densities. Some new and earlier distributions formed the sub-models of the proposed distribution. The mathematical properties of the new distribution including expressions for the hazard function, survival function, moments, order statistics, mean deviation and absolute mean deviation from the mean, and entropy were derived. Monte Carlo simulation study was carried out to assess the finite sample behavior of the parameter estimates by maximum likelihood estimation approach. The superiority of the new generalized exponentiated Weibull distribution over some competing distributions was proved empirically using the fitted results from three real life datasets.

贝叶斯统计中共轭先验分布的教学研究

先验分布在贝叶斯统计中扮演着关键角色,而共轭先验则是其中最为重要的一种。学生对共轭先验分布的理解和掌握程度直接影响他们对贝叶斯统计方法的学习效果。目前的大多数教材通常是先介绍一些常见分布的共轭先验,然后再证明其共轭性质。然而,这种教学方法缺乏深度和灵活性。为了解决这个问题,本文提出在更广泛的指数族分布下,给出参数共轭先验的一般表达形式。接着,针对一些常见分布,通过从指数分布族结构推导出其待估参数的共轭先验,使得学生不仅能深刻理解共轭先验的本质,还能学到一种更为灵活的共轭先验选择策略。这种从一般到具体的教学方法有助于提高学生对贝叶斯统计的理解深度,并培养学生灵活运用共轭先验的能力。

稠油主要族组分对其粘度的影响

对稠油主要族组分的含量与粘度关系进行了定量的实验研究。结果表明,饱和烃、芳烃、中性非烃、酸性非烃、胶质和沥青质的质量分数分别与稠油的粘度呈指数函数关系。稠油的粘度随饱和烃和芳烃质量分数的增加而呈指数函数关系降低,随中性非烃、酸性非烃、胶质和沥青质质量分数的增加而呈指数函数关系升高,对稠油粘度影响重要程度的顺序为:胶质和沥青质>酸性非烃>中性非烃。其中,胶质和沥青质的质量分数是影响稠油粘度的最主要因素,这与其它实验研究结果是一致的。降低稠油中的中性非烃、酸性非烃、胶质和沥青质质量分数,将有效降低稠油的粘度。

刻度指数族参数的经验Bayes估计的收敛速度

本文对刻度指数族在加权平方损失下获得了参数的Bayes估计,并构造了相应的经验Bayes（EB）估计,证明了所提出的EB估计是渐近最优的且有收敛速度,其中1/2≤λ<1,s≥3是一给定的整数.最后,给出了刻度指数族EB估计的两个应用.

刻度指数族参数的渐近最优的经验Bayes估计

对刻度指数族在加权平方损失下获得了刻度参数的Bayes估计 ,并构造了相应的经验Bayes估计 。