天线罩覆盖的波束近轴场

本文根据复射线法对通过介质天线罩的高斯波束场进行近轴近似分析。实空间的轴向复射线追综大大简化了计算过程,而复相位差、反射-传输系数和曲面扩散系数的进一步校正则提供了相当精确的结果。所得数字结果表明,在波束的近轴区域内为获得同样的计算精度,近轴近似法所需要的计算机时间远小于复射线追综法的时间。     

Approximations of the critical region of the fbietkan statistic

The Friedman (1937) test for the randomized complete block design is used to test the hypothesis of no treatment effect among k treatments with b blocks. Difficulty in determination of the size of the critical region for this hypothesis is com¬pounded by the facts that (1) the most recent extension of exact tables for the distribution of the test statistic by Odeh (1977) go up only to the case with k6 and b6, and (2) the usual chi-square approximation is grossly inaccurate for most commonly used combinations of (k,b). The purpose of this paper 2 is to compare two new approximations with the usual x² and F large sample approximations. This work represents an extension to the two-way layout of work done earlier by the authors for the one-way Kruskal-Wallis test statistic.     

An approximation of the inverse moments of the positive hypergeometric distribution

The negative moments of the positive hyper geometric distribution are often approximated by the inverse of the positive moments of this distribution. In this paper, a suitable approximation to the positive hypergeometric distribution is used to obtain the negative moments.     

An asymptotic expression for cumulative sum of probabilities of the hermite distribution

An asymptotic approximation of cumulative sum F(s) of probabilities of the Hermite distribution (Kemp C. D. and Kemp A. W. (1965)) and an asymptotic approximation of individual Hemite Probability P_s are given for large s.     

A Generalization of Hotelling's T 2

ABSTRACT

We derive an asymptotic version of Hotelling's T ² for the multivariate proper dispersion models of Jøtrgensen and Lauritzen (2000 Jørgensen , B. , Lauritzen , S. L. ( 2000 ). Multivariate dispersion models . J. Multivariate Anal. 74 : 267 – 281 . [CSA] [CROSSREF]  [Google Scholar]), the main tool being the saddlepoint approximation. Multivariate dispersion models are suitable for positive, directional, compositional, and other non normal data. We illustrate the results by a multivariate gamma model.     

LIKELIHOOD APPROXIMATIONS AND DISCRETE MODELS FOR TIED SURVIVAL DATA

ABSTRACT

Ties among event times are often recorded in survival studies. For example, in a two week laboratory study where event times are measured in days, ties are very likely to occur. The proportional hazards model might be used in this setting using an approximated partial likelihood function. This approximation works well when the number of ties is small. On the other hand, discrete regression models are suggested when the data are heavily tied. However, in many situations it is not clear which approach should be used in practice. In this work, empirical guidelines based on Monte Carlo simulations are provided. These recommendations are based on a measure of the amount of tied data present and the mean square error. An example illustrates the proposed criterion.     

Monte Carlo Approximations of the Quantiles of a Sample Statistic

We consider in this article the problem of numerically approximating the quantiles of a sample statistic for a given population, a problem of interest in many applications, such as bootstrap confidence intervals. The proposed Monte Carlo method can be routinely applied to handle complex problems that lack analytical results. Furthermore, the method yields estimates of the quantiles of a sample statistic of any sample size though Monte Carlo simulations for only two optimally selected sample sizes are needed. An analysis of the Monte Carlo design is performed to obtain the optimal choices of these two sample sizes and the number of simulated samples required for each sample size. Theoretical results are presented for the bias and variance of the numerical method proposed. The results developed are illustrated via simulation studies for the classical problem of estimating a bivariate linear structural relationship. It is seen that the size of the simulated samples used in the Monte Carlo method does not have to be very large and the method provides a better approximation to quantiles than those based on an asymptotic normal theory for skewed sampling distributions.     

Probability computations for an extension of the geometric distribution

An extension of the stochastic process associated with the geometric distribution is presented. Combinatorial arguments are used to derive probabilities for various events of interest. Probabilities are approximated by evaluating truncated series. Bounds on the errors of approximation are developed. An example is presented and some additional applications are noted.     

Inequalities for Expected Current Record Statistics

In this article, we obtain sharp distribution-free bounds for the expected value of the gap between the current records and record values as well as upper sharp bounds for the spacings between any two upper current records. We also present two-sided bounds on the errors in approximating the means of current records by inverse hazard functions.     

Quasi-optimal Bayesian procedures of many hypotheses testing

Quasi-optimal procedures of testing many hypotheses are described in this paper. They significantly simplify the Bayesian algorithms of hypothesis testing and computation of the risk function. The relations allowing for obtaining the estimations for the values of average risks in optimum tasks are given. The obtained general solutions are reduced to concrete formulae for a multivariate normal distribution of probabilities. The methods of approximate computation of the risk functions in Bayesian tasks of testing many hypotheses are offered. The properties and interrelations of the developed methods and algorithms are investigated. On the basis of a simulation, the validity of the obtained results and conclusions drawn is presented.