A modified Kolmogorov-Smirnov test for a rectangular distribution with unknown parameters: Computation of the distribution of the test statistic

A recursive scheme for the calculation of the distribution of the test statistic of a modified Kolmogorov-Smirnov-test for a rectangular distribution with unknown parameters is given.     

Bayesian estimation for the Pareto income distribution

The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function. This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized for the doubly truncated gamma prior distribution. Now deceased.     

伽马分布的形状参数的一种估计

本文利用服从伽马分布的随机变量 X 与其逆 X~(-1)的协方差只与形状参数有关这一性质,给出伽马分布形状参数的所谓自逆协方差估计,进而构造了相应的无偏估计,并证明了这类估计的大样本性质:强相合性以及渐近正态性。     

单李代数不可约表示的标记

对于n秩单李代数g,当采用Dynkin关于素根的分类时,其不可约表示可以用n个非负整数Λ_(αi)标记,也可通过初等表示的权用数组li来标记。利用Cartan逆矩阵,我们给出了计算Λ_(α_i)与li之间关系的方法。对于B_n、C_n、D_n和F_4,利用Cartan逆矩阵证明了这些li是与采用Cartan关于素根的分类时的Λi是一致的。     

光谱法测量等离子体离子温度和再循环粒子流速

利用多道光学分析仪（OSMA）测量HT-6M托卡马克限制器前Hα线形分布,通过高斯拟合由多普勒展宽和多普勒频移分别得出等离子体离子温度和再循环粒子流速。     

广东普通工科高等教育的办学效益分析研究

对广东普通工科高等教育的办学效益问题,从结构布局效益、层次与规模效益进行了讨论,提出了提高办学效益的基本对策。     

RECENTERED AND RESCALED INSTRUMENTAL VARIABLE ESTIMATION OF TOBIT AND PROBIT MODELS WITH ERRORS IN VARIABLES

Since Durbin (1954) and Sargan (1958), instrumental variable (IV) method has long been one of the most popular procedures among economists and other social scientists to handle linear models with errors-in-variables. A direct application of this method to nonlinear errors-in-variables models, however, fails to yield consistent estimators.

This article restricts attention to Tobit and Probit models and shows that simple recentering and rescaling of the observed dependent variable may restore consistency of the standard IV estimator if the true dependent variable and the IV's are jointly normally distributed. Although the required condition seems rarely to be satisfied by real data, our Monte Carlo experiment suggests that the proposed estimator may be quite robust to the possible deviation from normality.     

Order statistics from non-identical right-truncated Lomax random variables with applications

In this paper, we derive some recurrence relations for the single and the product moments of order statistics from n independent and non-identically distributed Lomax and right-truncated Lomax random variables. These recurrence relations are simple in nature and could be used systematically in order to compute all the single and product moments of all order statistics in a simple recursive manner. The results for order statistics from the multiple-outlier model (with a slippage of p observations) are deduced as special cases. We then apply these results by examining the robustness of censored BLUE's to the presence of multiple outliers. Received: November 30, 1998; revised version: March 8, 2000     

Statistical Analysis of Marginal Count Failure Data

Manufacturers want to assess the quality andreliability of their products. Specifically, they want to knowthe exact number of failures from the sales transacted duringa particular month. Information available today is sometimesincomplete as many companies analyze their failure data simplycomparing sales for a total month from a particular departmentwith the total number of claims registered for that given month.This information—called marginal count data—is, thus,incomplete as it does not give the exact number of failures ofthe specific products that were sold in a particular month. Inthis paper we discuss nonparametric estimation of the mean numbersof failures for repairable products and the failure probabilitiesfor nonrepairable products. We present a nonhomogeneous Poissonprocess model for repairable products and a multinomial modeland its Poisson approximation for nonrepairable products. A numericalexample is given and a simulation is carried out to evaluatethe proposed methods of estimating failure probabilities undera number of possible situations.     

Non-parametric Estimation of the Residual Distribution

Consider a heteroscedastic regression model Y = m ( X ) +σ( X )ε, where the functions m and σ are smooth, and ε is independent of X . An estimator of the distribution of ε based on non-parametric regression residuals is proposed and its weak convergence is obtained. Applications to prediction intervals and goodness-of-fit tests are discussed.