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队首优先排队系统的时变解AI 解读

SUMMARY The method of supplementary variables has been used to obtain the Laplace transform of the time-dependent probabilities in a head-of-the-line priority queue characterized by Poisson arrivals and general service-time distributions. An explicit solution has, however, been obtained under exponential service-time distributions with equal mean rates. The queue length probabilities, under steady-state conditions, have been evaluated and are found to be different from those…

大样本中的有效估计与最优推断程序AI 解读

SUMMARY The concept of efficiency in estimation is linked with closeness of approximation to the derivative of log likelihood, which plays an important role in statistical inference in large samples. Various orders of efficiency are defined depending on degrees of closeness, and properties of estimates satisfying these criteria are studied. Such measures of efficiency appear to be more appropriate than the one related to asymptotic variance of an estimate for judging the…

非平衡设计下组间方差的二次估计AI 解读

SUMMARY The optimum properties of the popular estimate of the interclass variance in components of variance models are known if there are an equal number of observations in the subclasses. In contrast to this, it is shown that unbiased quadratic estimates having uniformly minimum variance do not exist if the design is not balanced.

一种最大似然估计方法AI 解读

SUMMARY Knowledge of one or more of the parameters in a maximum-likelihood problem sometimes results in a very considerable simplification, the analysis becoming almost trivial. A method of obtaining maximum-likelihood estimates and their asymptotic covariance matrix is given which makes it possible to capitalize on simplifications of this sort when they arise. Application is mainly in the field of regression, but other examples are mentioned. A numerical example of…

样本分位数与中程统计量的渐近方差性质AI 解读

SUMMARY In this paper, some properties of the asymptotic variance of the sample quantiles and the derived mid-ranges are studied and the role of the sample median is critically discussed. It is shown that among the class of sample quantiles, the sample median will have asymptotically the smallest variance only under somewhat restrictive regularity conditions; while among the class of sample mid-ranges, the sample median (being the central mid-range) has asymptotically the…

相依随机变量情形下最大似然法的一则说明AI 解读

SUMMARY The validity of certain statistical procedures depends on the “classical” properties of the method of maximum-likelihood, viz., its consistency and the fact that it leads to an estimator whose asymptotic variance can be derived easily from the likelihood function. These properties are well established for the case where successive observations are independent. Here it is shown that their extension to the dependent case involves suitable behaviour of two…

破坏性测试中利用分位数估计参数AI 解读

SUMMARY The estimation of mean and standard deviation from the values of two quantiles dividing the specimens into three groups has, by previous authors, been made the basis of a quality control system of gauging specimens at two levels. When a specimen may be gauged once only, single gauging, different specimens must be gauged at each level, and the efficiency of the method is reduced. For a variate normally distributed with mean, μ, and standard deviation, σ, the…

若干具有吸收边界的随机过程AI 解读

SUMMARY Models for growth distributions of biological organisms are investigated in this paper. They are specializations of the birth–death equations with two absorbing barriers. The solutions we seek are the distributions of the time to grow from an initial dose to an infective dose. Equations for these functions are simply obtained from the birth–death equations. Two main cases of interest are then examined. In the first case the birth and death rates are proportional to…

受限备择下的均值齐性检验AI 解读

SUMMARY Suppose that observations x1, x2, …, xk have been obtained from normal populations with unknown means μ1, μ2, …, μk and known standard deviations σ1, σ2, …, σk. The paper discusses tests of the hypothesis μ 1, μ 2, … = μk when prior information is available about the μ‘s under the alternative hypothesis. A generalized form of the χ 2-test, denoted by x2¯, has been developed for use when this information takes the form of order restrictions between some or all of the…

截断多元正态分布的矩母函数AI 解读

SUMMARY In this paper the moment generating function (m.g.f.) of the truncated n-dimensional normal distribution is obtained. From the m.g.f., formulae for E(Xi) and E(Xi Xj) are derived, and are used to investigate certain special cases. Some applications of these results to statistical genetics are also discussed.

有序方差的同质性检验AI 解读

SUMMARY Suppose that an estimate of variance is available from each of a set of normal populations. The situation in which there is a definite trend in the magnitude of the population variances is considered, and this is represented by assuming the ith variance to be inversely proportional to λ + iμ. A uniformly most powerful unbiased test is developed for the hypothesis μ = 0, and methods for estimating μ and λ are considered.

不准确性与统计推断AI 解读

SUMMARY The idea of uncertainty, as developed in communication theory, is generalized to “inaccuracy”. The applications of this inaccuracy to the problems of statistical inference are discussed.

线性函数关系的参数估计AI 解读

SUMMARY A variety of consistent estimators of the parameters of a linear functional relation have been proposed over the years. Some find their basis in least-squares procedures, some in the methods of analysis of variance, some in the method of grouping, and some in diverse other methods. In this paper we generalize a class of estimators suggested originally by the method of grouping, and consider the asymptotic variance of a number of different types of estimators. As a…

算术平均数幂的无偏估计量AI 解读

SUMMARY An unbiased estimator for integral powers of the arithmetic mean, when sampling with replacement, is given, together with a formula for its variance and an unbiased estimator for this variance. Similar results are given for functions which can be expressed as a series in powers of the mean.

Daniels广义相关系数的渐近效率AI 解读

SUMMARY The asymptotic efficiency of the generalized correlation coefficient devised by Daniels, used as a test of association in the bivariate function H(x, y) = F(x) G(y) {1 + αA(x) B(y)}, is shown to depend in a simple way on the score-matrices used to define the coefficient. Two coefficients for which the corresponding row sums of the two score-matrices, written in a standard form, are proportional are shown to have the same asymptotic efficiency. In particular, this is…

用半马尔可夫过程求解排队与库存模型AI 解读

SUMMARY In this paper we set forth an approach to queueing and inventory problems which is based on the theory of semi-Markov processes. The method is applicable to a wide variety of models in continuous or discrete time. After developing two basic theorems, we illustrate the method by determining the limiting distribution of a “batch service” queue, in which K customers are always served at a time. The batch service queue is also shown to be equivalent to a classical…

随机过程在道路交通中的应用：双车道道路的延误AI 解读

SUMMARY A theoretical formula is found for the average speed achieved over a long journey by a vehicle travelling along a road according to certain rules governing overtaking, when the other traffic on the road is postulated to be of a particularly simple kind. Except for the vehicle whose behaviour is studied, vehicles in each direction travel at the same speed, and are spaced at random, but with a certain minimum distance between vehicles. The vehicle being studied wishes…

统计推断与决策中的一致性AI 解读

SUMMARY It is suggested that the strength of a person’s beliefs may be tested by finding at what odds he is prepared to bet on them. This leads to a system of numerical “medial personal probabilities” obeying the classical laws of probability. However, these do not have precisely defined values, but are contained within specified intervals. The appropriate method of inference is Bayes’s Theorem. This leads to generally accepted statistical procedures in large samples, except…

序贯抽样后应用同质性检验的说明AI 解读

SUMMARY It is pointed out that tests based on permutation theory can often be validly used to test the homogeneity of results obtained in a sequential trial.

关于 Pistimetric 推断的若干札记AI 解读

SUMMARY The Pistimetric method, in which the probability distribution of parameters is determined by means of a pivotal quantity as soon as the number of observations permit, and posterior probability distributions are subsequently deduced by Bayes’s theorem, is here applied in outline to a variety of situations. These include cases where the variate is discrete, where it is continuous, and when events occur in continuous time.

截断与删失样本下多元正态总体参数的估计AI 解读

SUMMARY This paper is concerned with the problem of estimation of means and variances of a k-variate normal distribution from a sample doubly truncated or censored on s-variates (s ≤ k), when variates are uncorrelated. Maximum likelihood equations are derived which, with the help of normal probability tables, can readily be solved by iteration. The information matrix is given from which the asymptotic variances and covariances of the estimates can be determined. to…

论Lindley提出的若干贝叶斯推断扩展AI 解读

SUMMARY Critical comments are given on an extension of Bayesian inference proffered by Lindley (1957, 1958). The process is applied to the combination of two normal samples.

群体遗传学中的离散随机过程AI 解读

SUMMARY The application to population genetic models of the approximate treatment of a non-linear discrete stochastic process by linearizing near an equilibrium point is discussed. The value of the dominant characteristic root for approximate linear changes near an initial equilibrium can be used to estimate the chances of survival of newly occurring genotypes. These methods are illustrated on the classic population genetic model for a balanced polymorphism and also on a…

单变量随机过程的Green型近似解AI 解读

SUMMARY A study is made of approximations of Green's type (often called W.K.B. approximations) to the solution of equations governing univariate stochastic processes. After considering some specific processes, the general homogeneous process in continuous time is discussed. A numerical comparison is made between the approximate and exact probabilities for the multiplicative birth and death process. Diffusion processes are briefly examined. The method is applied to the…