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适用于千以内样本量的符号检验与中位数分布无关置信区间表AI 解读

In 1946 Dixon and Mood published a table of critical values for the sign test with the sample size n, the sum of the two binomial numbers, in the stub and running consecutively from 1 to 100. In 1959 the present writer also published a sign-test table, replacing n by d, the difference between the two binomial numbers, and extending the range of sample sizes to 1,000. However, this second table introduced complicated rules of use and did not facilitate determination of…

一种两样本秩检验：Psi检验及其性质AI 解读

Summary Since the power of the Psi test proposed by Gibbons (1964) compares favourably with that of other one-sided, two-sample rank tests on the equality of two distribution functions, its properties merit further investigation. This paper is devoted to such a study. A table of exact critical values for the test statistic is given for selected small sample sizes, and compared with critical values for the approximate distribution which is a function of Student's t. The…

检验两个分布函数相等的两样本秩检验功效AI 解读

Summary This paper is a comparative study of the power functions of two-sample rank tests of the hypothesis of equal distributions, H 0: H = G. Numerical results are given for the alternative of two extreme distributions, H1:H=1−(1−F)k, G=Fk, with F an unspecified continuous cumulative distribution function, k = 2, 3, 4, sample sizes m = n ≤ 6, significance levels 0·01, 0·05, 0·10. Randomized decision rules are employed when necessary to attain the exact significance level.…

非独立同分布观测的极端次序统计量近似分布AI 解读

The data are n univariate observations that are not necessarily from the same population, from continuous populations, or independent. The problem is to develop an approximate expression for a specified one of the upper (or lower) extremes of this set of observations when a type of m-dependence occurs. General expressions are developed that depend on n, the extreme considered, and the arithmetic average of the cumulative distribution functions (cdf's) for the individual…

非同分布或相关观测的极端次序统计量近似分布AI 解读

The data are n univariate observations that are not necessarily from the same population, from continuous populations, or independent. The problem is to develop an approximate expression for a specified one of the upper (or lower) extremes of this set of observations when a type of m-dependence occurs. General expressions are developed that depend on n, the extreme considered, and the arithmetic average of the cumulative distribution functions (cdf's) for the individual…

若干分布无关离散程度检验的一致性札记AI 解读

In this paper the consistency of the two-sample tests of Sukhatme [6], Ansari and Bradley [1], Siegel and Tukey [5], and Mood [3] is investigated. Each of these tests is a distribution-free analogue of the F-test for testing the equality of the variances of two normal distributions. If the two samples are taken from continuous distributions with the same median (say 0) and distribution functions F(x) and F(x/a) respectively, the hypothesis tested states that a = 1 and the…

正态分布推断的两个定理及其在验收抽样中的应用AI 解读

Two theorems are presented which are useful in making inferences about the univariate normal distribution. Some applications of the theorems are given. It is thought that the theorems will prove useful in other contexts. Theorem 1 represents the normal (0, 1) random variable as a product of two independent random variables in infinitely many ways. Theorem 2 gives the expected value of the cumulative distribution function of the normal (0, 1) distribution, when the argument…

若干分布无关离散程度检验的一致性札记AI 解读

In this paper the consistency of the two-sample tests of Sukhatme [6], Ansari and Bradley [1], Siegel and Tukey [5], and Mood [3] is investigated. Each of these tests is a distribution-free analogue of the F-test for testing the equality of the variances of two normal distributions. If the two samples are taken from continuous distributions with the same median (say 0) and distribution functions F(x) and F(x/a) respectively, the hypothesis tested states that a = 1 and the…

GCL 估计量精确有限样本分布函数在计量统计推断中的应用评述AI 解读

When employed in connection with econometric models that have a sufficiently high degree of cognitive significance (as measured by the extent to which underlying economic premises are actually elucidated into empirically testable implications) qualitative analysis of the exact finite sample distribution functions of GCL estimators of structural parameters finds its paramount use in delimiting the precision with which structural coefficients can be estimated. This kind of…

圆周上的拟合优度检验（二）AI 解读

A statistical analysis is made by use of the null hypothesis test for random samples which have been drawn from a population with the continuous distribution function F(x). It is useful for distributions on a circle since its value does not depend on the arbitrary point chosen to begin cumulating the probability density and the sample points. Sampling experiments on bird flight are plotted by use of an IBM 650 computer.

产业结构的统计分析：食品行业应用AI 解读

A stochastic model is used to analyze the changing size distributions of large firms in the food processing and chain store food distributing industries during 1948–1958. The model is shown to have certain predictive usefulness for anticipating changes in these distributions; however, the predictive value of the equilibrium distribution is questioned. An index of size mobility is developed from the model and the value of this index computed for each industry in each year and…

帕累托型稳定随机函数与收入的乘法变化AI 解读

a new family of stable non-gaussian random functions, U(t), and it is intimately connected with random walks of log U(t). Its principal feature is, however, that no use is made of the principle of proportionate effect, the model being rather based upon the fact that there exist certain limits for sums of random functions, upon which the effect of chance in time is multiplicative. (Actually, the result is more general.) This feature provides a new type of motivation for the…

截断分组双曲正割平方分布的位置与尺度参数估计AI 解读

The iterative calculations required to obtain the maximum likelihood estimates of α and β in the distribution function dF(z) = e z /(1 + e z )2 dz, where z = α +βx, are presented for doubly truncated, upper and lower truncated, and untruncated grouped samples. The calculations needed to obtain the maximum likelihood estimator of Pareto's constant are also given for a lower truncated grouped sample with both equal and unequal grouping. Asymptotic variances and covariances are…

两个典型过度识别情形下广义经典线性估计量的精确有限样本分布AI 解读

The asymptotic unbiasedness and normality of alternative statistical estimators θ, θ,1 ··· of a given parameter θ* are generally proved without reference to any explicit knowledge of the exact finite sample distribution functions, F n (x), G n (x) ···. (Here n denotes sample size.) Within the class of asymptotically unbiased and normally distributed estimators of a given parameter it is sometimes possible to demonstrate that one estimator possesses a smaller asymptotic…

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…

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…

收入分布的修匀AI 解读

A FUNCTION representing the distribution of income in a society can serve a number of purposes. It may be used to smooth out irregularities in the observed income distribution caused by the misreporting of income. In this role it is similar to the graduation formulae used in demographic work to correct an age distribution distorted by mistatements of age. An income function may also form the basis of a model explaining how an income distribution is generated. Interest here…

从集中曲线计算恩格尔弹性的方法AI 解读

THIS PAPER PRESENTS, on the assumption of lognormality, a simple graphical method of deriving the Engel elasticities for various items of consumer expenditure from what are known as concentration curves. Usually two types of such curves are distinguished: (a) the Lorenz curve which relates the proportion of total expenditure to the proportion of persons spending up to a given level of total expenditure per capita, and (b) the specific concentration curve which relates the…

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平稳时间序列的统计分析AI 解读

Stationary Stochastic Processes and Their Representations: 1.0 Introduction 1.1 What is a stochastic process? 1.2 Continuity in the mean 1.3 Stochastic set functions of orthogonal increments 1.4 Orthogonal representations of stochastic processes 1.5 Stationary processes 1.6 Representations of stationary processes 1.7 Time and ensemble averages 1.8 Vector processes 1.9 Operations on stationary processes 1.10 Harmonizable stochastic processes Statistical Questions when the…

Normit 分析估计正态分布函数的表格：使用说明与估计方法比较AI 解读

JOSEPH BERKSON; TABLES FOR USE IN ESTIMATING THE NORMAL DISTRIBUTION FUNCTION BY NORMIT ANALYSIS: PART I. DESCRIPTION AND USE OF TABLES: PART II. COMPARISON BET

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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.