索末菲积分的指数逼近法

指数逼近法解决了被积函数指数项中波数 k 为复数的索末菲积分,该法应用围线定理变换积分路径,把索末菲积分简化为几项解析式的近似和,它具有近似精度高,计算速度快和几乎不受频率限制的特点.     

完备的2-距离空间中的不动点定理

2-距离空间的概念是1964年Gahler给出的,本文把[2]中的一些结果推广到了2-距离空间,得到2-距离空间中的不动点定理。     

Model selection: some generalized distributions

Many models have been used to represent the distributions of random variables in statistics, engineering, business, and the physical and social science. This paper considers two, four-parameter generalized bea distributions that include nearly all the models actually used as special or limiting cases. Properties and the interrelationships among these distributions are considered. Expressions are reported that facilitate parameter estimation and the analysis of associated means, variances, hazard functions and other distributional characteristics.

Estimation procedures corresponding to different data types are considered. Maximum likelihood estimation is used and the value of the likelihood function provides and important criterion for model selection. The relative performance of the various models is compared for several data sets.     

从斯密-杨格定理谈区域一体化和区域协调发展

分工与市场间的互为决定和依赖关系及其循环互动效应,是认识把握区域一体化问题的理论基石.区域一体化的本质特征是地区分工和专业化程度不断加深、产品和要素自由流动的空间不断拓展,也就是分工与市场间形成了反馈互动的正向效应.区域协调发展与区域一体化具有同向性.一切旨在促进区域协调发展的政策行为、制度安排都应着眼于深化地区分工、整合国内市场,加快区域一体化进程是实现区域协调发展的最根本途径.     

Nonparametric test for the homogeneity of the overall variability

In this paper, we propose a nonparametric test for homogeneity of overall variabilities for two multi-dimensional populations. Comparisons between the proposed nonparametric procedure and the asymptotic parametric procedure and a permutation test based on standardized generalized variances are made when the underlying populations are multivariate normal. We also study the performance of these test procedures when the underlying populations are non-normal. We observe that the nonparametric procedure and the permutation test based on standardized generalized variances are not as powerful as the asymptotic parametric test under normality. However, they are reliable and powerful tests for comparing overall variability under other multivariate distributions such as the multivariate Cauchy, the multivariate Pareto and the multivariate exponential distributions, even with small sample sizes. A Monte Carlo simulation study is used to evaluate the performance of the proposed procedures. An example from an educational study is used to illustrate the proposed nonparametric test.     

Efficient score tests for heteroskedasticity in micro-economics

Kruskal's theorem is used to provide simple and elegant alternative derivations of the efficiency of some two step estimators (2SE) for models containing anticipated and unanticipated variables. Several new results are established: 2SE is not efficient for a structural equation with current and lagged values of both anticipated and unanticipated variables; 2SE is always efficient for the parameter associated with the current unanticipated variable, and for the parameter associated with the lagged unanticipated variable if there is no lagged dependent variable in the expectations equation; the inclusion of additional regressors in the structural equation and contemporaneous correlation of the structural and expectations errors can both be analysed in a straightforward manner; the single-equation generalized least squares estimator can be as efficient as the systems maximum likelihood estimator.     

Nonparametric estimation of the canonical measure for infinitely divisible distributions

Infinitely divisible distributions (i.d.d.'s) with a finite variance have a characteristic function of a particular form. The exponent is written in terms of the canonical or Kolmogorov measure. This paper considers a nonparametric estimate of the Kolmogorov measure based on the empirical characteristic function (e.c.f.) and a truncation. The weak convergence of this estimator is studied. The raw form of the estimator is a functional of the e.c.f., but to be useful in a finite sample it requires some additional smoothing. Thus smoothed estimators are considered. A dynamic data dependent method of truncation is given. A simulation study is undertaken to show how the Kolmogorov measure can be estimated, as well as giving an illustration of the numerical stability questions. It is also seen that a large sample size is needed.     

A bimodal flexible distribution for lifetime data

ABSTRACT

A four-parameter extended bimodal lifetime model called the exponentiated log-sinh Cauchy distribution is proposed. It extends the log-sinh Cauchy and folded Cauchy distributions. We derive some of its mathematical properties including explicit expressions for the ordinary moments and generating and quantile functions. The method of maximum likelihood is used to estimate the model parameters. We implement the fit of the model in the GAMLSS package and provide the codes. The flexibility of the model is illustrated by means of three real data sets.     

Some identities among moments of order statistics

Some new identities among the m oments of order statistics are derived. These are more general in nature and are applicable when moments of Some extreme order statistics do not exist.     

Asymptotic properties of the inhomogeneous Lotka‐Von Foerster system

In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution.