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Behrens–Fisher 分布与加权均值AI 解读

SUMMARY (1) The Behrens-Fisher and Welch solutions of the two-means problem are compared, and the former shown to be lacking in sensitivity. (2) Yates’s and the author’s tests for a weighted mean are compared, and the former shown to reject the true value of the mean, in error, more often than is indicated by the nominal significance level (in extreme cases nearly twice as often). (3) A new test for weighted means is put forward which does not neglect the information on the…

卡方分布近似的修正AI 解读

Summary The method of characteristic functions is used to obtain a correction to the usual approximation to the distribution of the chi-squared goodness of fit criterion for a multinomial distribution.

等相关随机变量与多元正态积分AI 解读

Summary An n-dimensional distribution with all correlations equal to p, called an equally correlated distribution, can very simply be constructed from a set of n + 1 one-dimensional variates; these variates are uncorrelated if p is non-negative, and n of them are uncorrelated if p is negative. From this, a general relation is deduced between any problem concerning an equally correlated distribution and an equivalent problem for uncorrelated variates. Applications are (i) to…

概率密度函数的平滑AI 解读

Summary We consider the estimation of a probability density function by linear smoothing of the observed density. A basis for estimation is obtained by assuming that the ordinates of the true density function have a prior distribution such that adjacent ordinates are highly correlated. An equation determining the optimum weighting function under these circumstances is derived, and solved in special cases. The properties of the estimate are discussed and the asymptotic…

去除趋势后的谱密度估计AI 解读

Summary A correction for bias, in the estimate of the spectral density, is derived for the case where a general form of trend has been removed, and a general expression for the bias (to the order n –1) in the serial correlations, due to trend removal, is obtained from this.

平稳时间序列谱密度的一致与渐近有效估计AI 解读

Summary Several general classes of estimates of the spectral density function of a stationary time series are introduced, which are shown to include most estimates previously suggested by various researchers. Asymptotic expressions are given for the mean square error of these estimates. We thus determine, for each estimate, the class of time series for whose spectral density it is a consistent estimate. Further, for a given time series, the minimum integrated mean square…

更新理论及其延伸AI 解读

Summary This is an expository article on the theoretical and some computational aspects of renewal theory. §1 describes basic theory, including Blackwell’s theorem; renewal density theorem; cumulants and asymptotic normality of the number of renewals in (0, t); and the integral equations of renewal theory. §2 is concerned with asymptotic behaviour of processes having an embedded renewal process: regenerative stochastic processes; semi-Markov processes; cumulative processes.…

二元序列的回归分析AI 解读

Summary A sequence of 0’s and 1’s is observed and it is suspected that the chance that a particular trial is a 1 depends on the value of one or more independent variables. Tests and estimates for such situations are considered, dealing first with problems in which the independent variable is preassigned and then with independent variables that are functions of the sequence. There is a considerable amount of earlier work, which is reviewed.

稀释序列：实验操作的统计检验AI 解读

SUMMARY When only the presence or absence of a micro-organism can be ascertained, density can be determined by preparing a dilution series in geometrical progression, setting aside the same number of plates at each level and observing fertile and sterile plates. Sometimes, series of observations appear which suggest that some failure in technique has occurred. An example, in a ten-fold dilution series, with five plates at each level, is given by the following number of…

时间序列相关结构的比较AI 解读

SUMMARY The problem considered is that of comparing two lengths of time-series to test whether their correlation structures are similar. It is pointed out that this may be usefully done only if assumptions are made concerning the type of correlation structure of each series. A test is given depending upon assumed values for a common correlation structure. This test is shown to be insensitive to errors in these assumed values.

谱估计中的带宽与方差AI 解读

SUMMARY This paper deals with the uncertainty principle that governs the behaviour of bandwidth and variance in the estimation of the spectrum of a stationary stochastic process. Lomnicki and Zaremba (1957) have tried to show that this principle is not valid. It will be shown below that their reasoning is not correct. Further it will be shown, that not only is the uncertainty principle correct as it was originally stated, but that it can be extended in various directions.…

多元分析中一个检验统计量的精确分布AI 解读

SUMMARY By rearranging the factors of the complicated r th moment of the distribution of a statistic in multivariate analysis and using Mellin’s Transformation it is possible to find the exact distribution of the statistic. This cannot be found easily by other methods.

匹配分布：Poisson 极限形式与近似方法AI 解读

SUMMARY (1) The Matching Problem is reviewed. (2) Stevens’s approach is generalized to yield the explicit results so far known. (3) A continuous range of Poisson limits is derived for the various matching distributions by an elementary method (alternative to Kaplansky’s symbolic proof). (4) The approximations afforded by some of these are improved by orthogonal polynomial fitting. (5) Further Poisson limits are derived for certain general classes of multiple matching…

连续分布的卡方拟合优度检验AI 解读

SUMMARY Suppose that in a chi-squared goodness-of-fit test the unknown parameters are estimated from the likelihood of the continuous observations before grouping. The effect on the distribution of the test criterion is examined.

若干时间序列拟合优度检验的渐近功效AI 解读

SUMMARY The distances, upon which the asymptotic powers of certain goodness of fit tests for stationary time series depend, are expressed in terms of the spectral density functions on the null and alternative hypotheses.

多名维修人员条件下机器干扰问题的正态近似AI 解读

Summary An approximate solution of the machine interference problem with many repairmen is derived in terms of the normal distribution.

简单队列非平衡理论的进一步结果AI 解读

Summary A number of new results are obtained in the non-equilibrium theory of a simple single-server queue with random arrival and departure, involving both the frequency distribution and distribution function of queue length, the derivation of exact and asymptotic expressions for means and variances, and the distribution of the time taken to reach a pre-assigned state.

作为因子分析替代方法的方差分析AI 解读

Summary An analogy between factor analysis and analysis of variance is pointed out, and an approximate test of significance is indicated. It is suggested that considerable simplification in the factor loadings may be made without appreciably affecting the final results. The interactions of factors is discussed, and it is suggested that batteries of tests should be designed so that they can be measured and tested. Some examples are given to illustrate the points made.

修正拉丁方设计AI 解读

Summary The modified latin square design (semi-latin square) is described and discussed. The expectations of the mean squares are derived and, from these, the nature of the bias is developed. Empirical values of the bias are obtained from some corn uniformity data and found to be small. An unbiased estimator of the error of a comparison among treatments is obtained. A formula for obtaining the efficiency of the modified latin square relative to randomized blocks, using…

随机过程处理中正态近似的使用AI 解读

Summary A method of treating nonlinear Markov processes is discussed, based on the assumption that the variates are normally distributed. The method is applied to models of logistic population growth, plant competition, and animal predation. In the preparatory section (§2) an alternative form (9) of the Bartlett relation is deduced, which is relatively convenient if one wishes to derive equations for the cumulants of a Markov process; the relation is particularly useful in…

利用序贯抽样在两个总体间选择的极小极大程序AI 解读

Summary When a choice has to be made in favour of one of two populations the cost of sampling (experimenting) in order to obtain information on which to base the decision must be balanced against the cost of making the wrong choice. Wald’s (1950) minimax procedure is used to determine a sequential method of sampling when a decision is to be made between two normal populations on the basis of their sample means. It is assumed that the cost of making a wrong choice is given by…

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正态回归中纪录值趋势检验的效率AI 解读

Summary A test for trend based on records is found to have asymptotic relative efficiency of zero compared with several other tests against normal regression alternatives, while two other well-known tests have zero efficiency compared even to the records test.

中位数与 U 统计量的联合渐近分布AI 解读

Summary It is shown that under mild restrictions on the density function, the joint distribution of the median and a U statistic is asymptotically normal. This result is extended to random vectors as also to generalised U statistics occurring in the two-sample problem.