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比较两个正态方差或两个伽马均值的统计表AI 解读

Tables for constructing the uniformly most accurate unbiased confidence interval of level 1 − α for σ1 2/σ2 2, where σ1 2 and σ2 2 are the variances of two normal distributions, and for tests of level α of hypotheses specifying the value of σ1 2/σ2 2 are given for α = .1, .05, .01, .001, n 1,n 2 = 1(1)20(2)30, 36, 45, 60, 90, 180, ∞, where ni is the degree of freedom of the estimate of σi 2. The present tables, more accurate than previous ones, may also be applied to make…

可接受性与统计推断AI 解读

The likelihood principle is criticized and the acceptability principle is enunciated. Most acceptable estimates are defined and some techniques for their calculation are developed. In the one-parameter case the most acceptable estimator is, under some conditions, median unbiased. Conditions for the strong consistency and asymptotic normality of the estimators are obtained. These are less stringent than those for the maximum likelihood estimator. An example is given where the…

可接受性与统计推断AI 解读

The likelihood principle is criticized and the acceptability principle is enunciated. Most acceptable estimates are defined and some techniques for their calculation are developed. In the one-parameter case the most acceptable estimator is, under some conditions, median unbiased. Conditions for the strong consistency and asymptotic normality of the estimators are obtained. These are less stringent than those for the maximum likelihood estimator. An example is given where the…

用于检验正态分布球形性的统计量分布AI 解读

The joint distribution of the sum of the rth powers (r = 1, …, p−1) and the product of all the latent roots of a p × p Wishart matrix is obtained and used to derive the null distributions of the likelihood ratio test criterion and the locally most powerful invariant test criterion for detecting deviations of the variances and covariances of a p-variate normal distribution from proportionality to specified numbers. The sphericity of the distribution is a special case.…

检验正态分布球形性的统计量分布AI 解读

The joint distribution of the sum of the rth powers (r = 1, …, p−1) and the product of all the latent roots of a p × p Wishart matrix is obtained and used to derive the null distributions of the likelihood ratio test criterion and the locally most powerful invariant test criterion for detecting deviations of the variances and covariances of a p-variate normal distribution from proportionality to specified numbers. The sphericity of the distribution is a special case.…

多变量比率与乘积估计量AI 解读

Olkin (1958) proposed a multivariate generalization of the ratio estimator and Singh (1967) proposed a multivariate generalization of the product estimator of Murthy (1964). This note considers an alternative multivariate generalization of the ratio estimator for an arbitrary sampling design and shows that, to a first order of approximation, it has the same variance as Olkin's estimator. The multivariate ratio estimators are compared with the multivariate product and…

多元比率估计量与乘积估计量AI 解读

Olkin (1958) proposed a multivariate generalization of the ratio estimator and Singh (1967) proposed a multivariate generalization of the product estimator of Murthy (1964). This note considers an alternative multivariate generalization of the ratio estimator for an arbitrary sampling design and shows that, to a first order of approximation, it has the same variance as Olkin's estimator. The multivariate ratio estimators are compared with the multivariate product and…

多元正态分布的中心容忍区域AI 解读

Summary In a multivariate normal distribution the probability density takes any particular value at all points on the surface of an ellipsoid whose centre is the mean of the distribution. Among such ellipsoids there is one, R, say, that contains 100α per cent of the individuals in the population. The paper deals with the problem of determining from a random sample a region which contains R with prescribed probability β. In the univariate case, R reduces to an interval with…

多元正态与 t 分布下凸多面体概率的计算AI 解读

Summary It is noted that probabilities of convex polyhedra in p-dimensional space can be expressed in terms of a function V(h1, h2, …, hp), if the distribution is normal, and in terms of a function Vn(h1, h2, …, hp), if the distribution is the t-distribution with n degrees of freedom. Formulae expressing V(h1, h2, …, hp) and Vn(h1, h2, …, hp) in terms of similar functions of lower order are obtained. An asymptotic expansion of Vn(h1,…, hp) in powers of n-1 is also included.…

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