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Frechet distribution is an important life distribution. In this paper, approximated maximum likelihood estimator for two parameter Frechet distribution under type II censoring is investigated. And the feasibility of this method is obtained through the Monto-Carlo simulation.     

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In this paper, we propose a regime-switching Ornstein-Uhlenbeck (O-U) stochastic mortality model with jumps, in whichthe economic and environment conditions are described by a homogenous, finite-state Markov chain. Using the idea of change of measure, we derive an exponential affine form of the fourier transform of a dampened option-type longevity derivative price.     

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??Comparisons between two samples with multiple endpoints are often encountered in many real applications and Hotelling's T^2 test (HT) may suffer from loss of efficiency when multivariate normality assumption is violated. To overcome this issue, we propose a group Hotelling's T^2 test (GHT) where HT is conducted within each group after inverse normal transformation and then use the maximum value among combined statistics based on $p$-values at the group-level. Extensive simulations show that GHT is more robust than HT and some other existing procedures. Finally, the applications to plasma-renin activity in serum study and the ageing human brain further demonstrate the performance of GHT.     

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This note deals with an insurance company with multiple lines of business. In the context of heavy-tailed heterogeneous claim amounts with the 1st upper-orthant tail dependence, based on the so-called k-out-of-n ruin set, we can exhibit the Radon measure mu and derive the asymptotic ruin probability for some of all lines business to ruin in a finite time. One numerical example is also presented to illustrate our main results.     

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This paper concerns with the estimation of a fixed effects panel data partially linear regression model with the idiosyncratic errors being an autoregressive process. For fixed effects short time series panel data, the commonly used autoregressive error structure fitting method will not result in a consistent estimator of the autoregressive coefficients. Here we propose an alternative estimation and show that the resulting estimator of the autoregressive coefficients is consistent and this method is workable for any order autoregressive error structure. Moreover, combining the B-spline approximation, profile least squares dummy variable (PLSDV) technique and consistently estimated the autoregressive error structure, we develop a weighted PLSDV estimator for the parametric component and a weighted B-spline series (BS) estimator for the nonparametric component. The weighted PLSDV estimator is shown to be asymptotically normal and more asymptotically efficient than the one which ignores the error autoregressive structure. In addition, this paper derives the asymptotic bias of the weighted BS estimator and establish its asymptotic normality as well. Simulation studies and an example of application are conducted to illustrate the finite sample performance of the proposed procedures.     

A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

<正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero.     

KAM Theory for Partial Differential Equations

In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the art in this field.     

Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds

<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.     

傅种孙先生在北京师大附中

1 傅种孙先生简介 1.1 傅先生基本情况介绍 傅种孙先生(1898～1962)1898年2月27日生于江西省高安县.1920年在北京高等师范学校数理部毕业,留母校附中(即现北京师大附中)任教;1921年任母校数理部的讲师;1928年任教授:抗日战争以前,曾先后兼任北京女子师范大学,北平大学女子文理学院,北京大学,辅仁大学教授;1933年当选北平(北京)市数学会理事长秘书;1935年当选中国数学会评议委员兼<数学杂志>编辑;1945年11月至1946年8月在牛津大学、1946年9月至1947年11月在剑桥大学考察;1947～1962年任北京师范大学数学系教授,1956年前曾兼系主任;在1949～1957年间,曾任北京师范大学教务长(3年)及副校长(5年);1952～1957年任北京市人民代表大会代表,中国数学会及其北京市分会常务理事,<中国数学杂志>及其后身<数学通报>总编辑;1962年1月18日病逝于北京.     

Local Unstable Entropy and Local Unstable Pressure for Partially Hyperbolic Endomorphisms*

In this paper, local unstable metric entropy, local unstable topological entropy and local unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. Specially, two variational principles concerning relationships among the above mentioned numbers are formulated.     

Parameter estimation of inverse Lindley distribution for Type-I censored data

In life testing experiments, Type-I censoring scheme has been widely used due to its simplicity and poise with considerable gain in the completion time of an experiment. This article deals with the parameter estimation of inverse Lindley distribution when the data is Type-I censored. Estimates have been obtained under both the classical and Bayesian paradigm. In the classical scenario, estimates based on maximum likelihood and maximum product of spacings coupled with their 95% asymptotic confidence interval have been obtained. Under the Bayesian set up, the point estimate is obtained by considering squared error loss function using Markov Chain Monte Carlo technique and highest posterior density intervals based on these samples are reckoned. The performance of above mentioned techniques are evaluated on the basis of their simulated risks. Further, a real data set is analysed for appraisal of aforementioned estimation techniques under the specified censoring scheme.     

Stochastic monotonicity of the MLE of exponential mean under different censoring schemes

In this paper, we present a general method which can be used in order to show that the maximum likelihood estimator (MLE) of an exponential mean θ is stochastically increasing with respect to θ under different censored sampling schemes. This propery is essential for the construction of exact confidence intervals for θ via “pivoting the cdf” as well as for the tests of hypotheses about θ. The method is shown for Type-I censoring, hybrid censoring and generalized hybrid censoring schemes. We also establish the result for the exponential competing risks model with censoring.     

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The hybrid censoring scheme is a mixture of type-I and type-II censoring schemes. It is a popular censoring scheme in the literature of life data analysis. Mixed exponential distribution (MED) models is a class of favorable models in reliability statistics. Nevertheless, there is no much discussion to focus on parameters estimation for MED models with hybrid censored samples. We will address this problem in this paper. The EM (Expectation-Maximization) algorithm is employed to derive the closed form of the maximum likelihood estimators (MLEs). Finally, Monte Carlo simulations and a real-world data analysis are conducted to illustrate the proposed method.     

Pareto�ֲ�����II������ɾʧ�µIJ�������

??In this paper, we concern with the estimation problem for the Pareto distribution based on progressive Type-II interval censoring with random removals. We discuss the maximum likelihood estimation of the model parameters. Then, we show the consistency and asymptotic normality of maximum likelihood estimators based on progressive Type-II interval censored sample.     

并联压力—强度模型可靠性研究

In this paper,the reliability of a parallel stress-strength model of exponentiated Pareto distribution is discussed.Different point estimations and interval estimations are proposed.The point estimators obtained are maximum likelihood and Bayesian estimators.The interval estimations obtained are approximate,exact,bootstrap-p and bootstrap-t confidence intervals and Bayesian credible interval.Different methods and the corresponding confidence intervals are demonstrated using some simulation studies.     

Bayesian inference using record values from Rayleigh model with application

In this article, based on a set of upper record values from a Rayleigh distribution, Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameter, and some lifetime parameters such as the reliability and hazard functions. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. These estimators are derived using the informative and non-informative prior distributions for σ. We compare the performance of the presented Bayes estimators with known, non-Bayesian, estimators such as the maximum likelihood (ML) and the best linear unbiased (BLU) estimators. We show that Bayes estimators under the asymmetric loss functions are superior to both the ML and BLU estimators. The highest posterior density (HPD) intervals for the Rayleigh parameter and its reliability and hazard functions are presented. Also, Bayesian prediction intervals of the future record values are obtained and discussed. Finally, practical examples using real record values are given to illustrate the application of the results.     

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-II hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size, we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively, and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.     

定时截尾数据缺失场合下Weibull分布的Bayes分析

本文研究了定时截尾数据缺失场合下的两个参数与可靠度的Bayes估计.利用数值计算的方法,获得了两个参数与可靠度的Bayes估计的近似结果.大量的Monte-Carlo数值模拟试验表明了所给方法是可行的.     

Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density

In the context of semi-functional partial linear regression model, we study the problem of error density estimation. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance a constant parameter. This mixture error density has a form of a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, is estimated by the ordinary least squares and functional Nadaraya–Watson estimators. The estimation accuracy of the ordinary least squares and functional Nadaraya–Watson estimators jointly depends on the same bandwidth parameter. A Bayesian approach is proposed to simultaneously estimate the bandwidths in the kernel-form error density and in the regression function. Under the kernel-form error density, we derive a kernel likelihood and posterior for the bandwidth parameters. For estimating the regression function and error density, a series of simulation studies show that the Bayesian approach yields better accuracy than the benchmark functional cross validation. Illustrated by a spectroscopy data set, we found that the Bayesian approach gives better point forecast accuracy of the regression function than the functional cross validation, and it is capable of producing prediction intervals nonparametrically.     

Exact inference for joint Type-I hybrid censoring model with exponential competing risks data

Assuming that the failure time under different risk factors follows the independent exponential distribution, a joint model under Type-I hybrid censoring is addressed in detail. Based on the Maximum likelihood estimates (MLEs) of unknown parameters, we obtain exact distributions of MLEs by using the moment generating function (MGF). Confidence intervals (CIs) of parameters are constructed through both the exact method and the parametric bootstrap method. Then we compare the performances of different methods by Monte Carlo simulations. Finally, the validity of the proposed models and methods are demonstrated by a numerical example.