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生产函数与英国煤炭开采AI 解读

The method used here represents an attempt to eliminate the influence of unspecified factors on the dependent variate in multiple regression analysis. It is applied in constructing a production function for British coal mining over the period 1943-53 and in estimating the elasticities of output with regard to labour and to horsepower, the latter indicating mechanisation. The statistical and economic significance of the results is examined.

实验推断的随机化理论AI 解读

The paper contains a description of the extent to which the use of randomization in experimental designs permits evaluation of the experimental results. The case considered is that in which the whole population of treatments is used with particular experimental material. A completely general mathematical specification of the design is given and the procedure by which linear models for the experimental results are derived is exemplified by the cases of the completely…

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收入分布：一个新模型AI 解读

This paper endeavours to present a simple model to explain the frequency distribution of income by adding birth and death considerations to the more usual random shock system type of model. The form of this model turns out to be a Gram-Charlier distribution subject to a linear logarithmic transformation, the parameters of which are meaningful and significant. A tentative method of fitting such curves is suggested and the values of the parameters discussed.

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凹函数纵坐标的点估计AI 解读

A method is developed for obtaining maximum likelihood estimates of points on a surface of unspecified algebraic form when ordinates of the points are required to satisfy a set of linear inequalities. A production function with one variable input is considered in some detail. In this case the restrictions follow from the assumption of non-increasing returns. An illustrative computation is worked out using a procedure based on equivalence between the estimation problem and a…

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The purpose of this paper is to show the geometrical significance of the maments of order statistic derived from normal populations. It appears that these, as well as the moment-generating function of the sqare of any order statistic, are intimately related to the contents of the members of a class of hyperspherical simplices. Further geometrical interpretations, together with the extension of the present results to bivariate moments and other properties, will be provided in…

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实验设计中检验 Student 假设的若干非参数方法AI 解读

In experimental designs the quantities investigated are often grouped into blocks as a method of obtaining a higher precision for the experiment. This grouping may result in high correlation among observations within the same block. If the positions of the treatments within a block are assigned at random, the amount of correlation is difficult to determine and may vary greatly between treatments and from block to block. Also for many experiments the variances of the…

实验设计中检验 Student 假设的若干非参数方法AI 解读

In experimental designs the quantities investigated are often grouped into blocks as a method of obtaining a higher precision for the experiment. This grouping may result in high correlation among observations within the same block. If the positions of the treatments within a block are assigned at random, the amount of correlation is difficult to determine and may vary greatly between treatments and from block to block. Also for many experiments the variances of the…

Charts are presented which can be used to simplify estimation of μ and σ in the case of sampling from a singly truncated normal distribution when (a) the point of truncation and the number of observations in the truncated portion are known, (b) the number of observations in the truncated portion is not known. A somewhat different iteration procedure for case (a) than given by other writers is suggested and an example is given.

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