反冲塞效应的热弹性理论分析（Ⅰ）──温度场分析

本文对我们新近发现的长脉冲激光束对金属薄片材料的一种新的破坏方式──“反冲塞”效应进行了温度场分析，用Ｈａｎｋｅｌ变换和Ｌａｐｌａｃｅ变换，得到了温度场的精确解，以激光束的空间分布为均匀分布和高斯分布为例对温度场进行了计算，结果表明激光束的空间均匀分布是产生反冲塞效应的主要原因。     

The Exact and Limiting Distributions for the Number of Successes in Success Runs Within a Sequence of Markov-Dependent Two-State Trials

The total number of successes in success runs of length greater than or equal to k in a sequence of n two-state trials is a statistic that has been broadly used in statistics and probability. For Bernoulli trials with k equal to one, this statistic has been shown to have binomial and normal distributions as exact and limiting distributions, respectively. For the case of Markov-dependent two-state trials with k greater than one, its exact and limiting distributions have never been considered in the literature. In this article, the finite Markov chain imbedding technique and the invariance principle are used to obtain, in general, the exact and limiting distributions of this statistic under Markov dependence, respectively. Numerical examples are given to illustrate the theoretical results.     

Distribution of Statistics of Hidden State Sequences Through the Sum-Product Algorithm

We compute exact distributions of statistics of hidden state sequences in general settings. Distributions are computed for undirected and directed graphical models that are represented using conditional random fields and factor graphs. The methods discussed are relevant for graphs with a sparseness of edges that allows exact computation of the normalization constant. The distributions are obtained in an efficient manner by integrating sequential updates of the statistic’s value with the sum-product algorithm. Applications of this work include discrete hidden state sequences perturbed by noise and/or missing values, and state sequences that serve to classify observations. In the case of classification, the methods give a way to quantify the uncertainty in statistics associated with the classifications. The algorithm is applied to model-based false discovery distributions for protein-protein interactions and distributions related to CpG island lengths in DNA sequences.     

Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions

The exact distribution of the likelihood ratio test statistic to test the equality of several variance-covariance matrices has a non-manageable form. On the other hand, the existing asymptotic approximations do not exhibit the necessary precision for many applications. For these reasons, the development of near-exact approximations to the distribution of this statistic, arising from a different method of approximating distributions, emerges as a desirable goal. These distributions, while being manageable are much closer to the exact distribution than the usual asymptotic distributions and opposite to these, are also asymptotic for increasing number of variables and matrices involved. Computational modules to implement the near-exact distributions are made available on a web-site.     

Distribution and moments of the vector of the maximum of two absolutely continuous random vectors

In this paper, we determine the exact distribution of the vector of the componentwise maximum of two absolutely continuous dependent random vectors and we show that it is a finite mixture of particular skew distributions studied in the literature. The results are detailed when the two vectors are elliptically distributed and some particular cases are discussed. The exact expression of the covariance matrix is obtained in the normal case.     

Random walks and a nonparametric criterion for agreement in the problem of comparison of two samples

The exact distributions of Kolmogorov-Smirnov-Gnedenko statistics are obtained on the basis of unbiased estimates. The asymptotic behavior of these distributions is studied.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 106–115, 1988.     

Simple and efficient algorithms for computing exact cumulative discrete probabilities and its inverses

Summary  This paper deals with the computation of exact cumulative probabilities of discrete distributions and its inverses. For the computation of cumulative probabilities an efficient and universal algorithm of 15 lines is presented, which can be applied to the most important discrete distributions (e.g. the binomial, the poisson and the hypergeometric distribution). With a slight modification an algorithm of 20 lines is obtained for the calculation of the respective inverse distributions. The accuracy of both algorithms can be specified. Both algorithms are simple, very fast and numerically stable even if the sample size is one billion.     

The asymptotic expansion fo the Stein estimators for the vector case

Summary Charles Stein established the existence of estimators which dominate the maximum likelihood estimators for the problem of simultanously estimating the means of three or more random variables. Since the exact distributions of the Stein estimators are not known and because the distributions are of great importance for people studying confidence sets, it was the purpose of this note to derive the asymptotic distributions, means and variances of the Stein estimators, as well as that of the quadratic loss functions for the vector case. Financially supported by the CSIR and the University of the OFS Research Fund.     

Near-exact distributions for the independence and sphericity likelihood ratio test statistics

In this paper we show how, based on a decomposition of the likelihood ratio test for sphericity into two independent tests and a suitably developed decomposition of the characteristic function of the logarithm of the likelihood ratio test statistic to test independence in a set of variates, we may obtain extremely well-fitting near-exact distributions for both test statistics. Since both test statistics have the distribution of the product of independent Beta random variables, it is possible to obtain near-exact distributions for both statistics in the form of Generalized Near-Integer Gamma distributions or mixtures of these distributions. For the independence test statistic, numerical studies and comparisons with asymptotic distributions proposed by other authors show the extremely high accuracy of the near-exact distributions developed as approximations to the exact distribution. Concerning the sphericity test statistic, comparisons with formerly developed near-exact distributions show the advantages of these new near-exact distributions.     

精确分布推导的一个基本的方法

寻求统计量的精确分布,在数理统计的理论中是一个重要的问题。然而,在多元统计分析中,往往很不容易得到统计量的精确分布,有些统计量的分布,例如非中心的Wishanrt分布,持续了几十年,还没有获得完满的结果。我国的许宝騄先生早在1939年,就得到了正态总体样本协差阵的特征根的联合分布(参看[1])。据徐钟济先生的回忆,当时R.A.     

Distributions in fuzzy logic

Probability distributions associated with several ‘ply’-operators are discussed. These exact distributions are compared with relevant Gaussian approximations.     

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.     

Exact distributions of MLEs of regression coefficients in GMANOVA-MANOVA model

This paper studies the exact distributions of the MLEs of the regression coefficient matrices in a GMANOVA-MANOVA model with normal error. The unique conditions for linear functions of the MLEs of regression coefficient matrices are presented, and the exact density functions or characteristic functions for these linear functions are derived.     

Probability distributions in fuzzy logic II

Probability distributions associated with several ‘iff’ ply operators are discussed. These exact distributions are compared with relevant normal approximants. Two possible applications are noted.     

Exact inference for a simple step-stress model from the exponential distribution under time constraint

In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special class of accelerated life-tests, allows the experimenter to increase the stress levels at fixed times during the experiment in order to obtain information on the parameters of the life distributions more quickly than under normal operating conditions. In this paper, we consider the simple step-stress model from the exponential distribution when there is time constraint on the duration of the experiment. We derive the maximum likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model with lifetimes being exponentially distributed. The exact distributions of the MLEs of parameters are obtained through the use of conditional moment generating functions. We also derive confidence intervals for the parameters using these exact distributions, asymptotic distributions of the MLEs and the parametric bootstrap methods, and assess their performance through a Monte Carlo simulation study. Finally, we present two examples to illustrate all the methods of inference discussed here.     

On the joint distribution of studentized order statistics

In this paper, the joint distribution of some special linear combinations of the (internally) studentized order statistics are derived for both normal and exponential populations; the exact relationship between their pdf's is also obtained. The exact sampling distributions of studentized extreme deviation statistic, which has been proposed by Pearson and Chandra Sekar (1936,Biometrika,28, 308–320), are derived for these two populations. An application to the most powerful location and scale invariant test is discussed briefly.     

On exceedances of record and order statistics

Exact, limiting distributions along with their rates of convergence of exceedance statistics for both order statistics and record statistics are provided when the underlying distribution is arbitrary. The exact distribution of record statistics for arbitrary underlying distributions is obtained as well.

     

A note on the representation of parametric models for multivariate extremes

In this note, the representations of extremal Dirichlet and logistic distributions are reviewed and extended. These new representations allow exact simulations of the spectral distribution functions and an extension of the extremal logistic case to dimensions higher than two.      

Finite-sample density and its small sample asymptotic approximation

To derive the exact density of a statistic, which can be intractable, is sometimes a difficult problem. The exact densities of estimates of the shift or regression parameters can be derived with the aid of score functions. Moreover, extremely accurate approximations can be obtained by the small sample asymptotics, based on the saddlepoint method. It is of interest to compare these two approaches, at least for small samples. We numerically compare the exact densities of estimates of the shift parameter with their small sample approximations for various parent distributions of the data. For some distributions both methods are in surprising concordance even under very small samples.     

Distributional Properties of Exceedance Statistics

Behaviour of a sequence of independent identically distributed random variables with respect to a random threshold is investigated. Three statistics connected with exceeding the threshold are introduced, their exact and asymptotic distributions are derived. Also distribution-free properties, leading to some common and some new discrete distributions, are considered. Identification of equidistribution of observations and the threshold are discussed. In this context relations between the exponential and gamma distributions are studied and a new derivation of the celebrated Laplace expansion for the standard normal distribution function is given.