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三参数对数正态分布的最大似然参数估计AI 解读

This paper is concerned with the three-parameter logarithmic normal distribution; i.e., the general distribution in which the terminus is unknown. Maximum likelihood equations for estimating population parameters from random samples are derived, and an iterative method for their solution is outlined. Variances and covariances of these estimates are obtained from the information matrix. An illustrative example is included.

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Kolmogorov–Smirnov 拟合优度检验AI 解读

The test is based on the maximum difference between an empirical and a hypothetical cumulative distribution. Percentage points are tabled, and a lower bound to the power function is charted. Confidence limits for a cumulative distribution are described. Examples are given. Indications that the test is superior to the chi-square test are cited.

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本科统计教育AI 解读

As WE ENTER the second half of the twentieth century one of the most .tl. serious long-range problems confronting the world of statistics is that of establishing a sound pattern of statistical education for college undergraduates.The uses of statistics and statistical methods have become so widespread throughout business, industry, government, and scientific research in recent years that this matter concerns not only the professional statisticians themselves, but many…

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对非随机性不敏感的大样本 t 统计量AI 解读

Most of the well known significance tests and confidence intervals for the population mean are based on the assumption of a random sample. This paper considers how the significance levels and confidence coefficients of the commonly used class of tests and intervals based on the standard Student t-statistic are changed when the random sample requirement is violated and the number of observations is large. It is found that even a slight deviation from the random sample…

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统计决策函数AI 解读

The foundations of a general theory of statistical decision functions, including the classical non-sequential case as well as the sequential case, was discussed by the author in a previous publication [3]. Several assumptions made in [3] appear, however, to be unnecessarily restrictive (see conditions 1-7, pp. 297 in [3]). These assumptions, moreover, are not always fulfilled for statistical problems in their conventional form. In this paper the main results of [3], as well…

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1944—1948年年收入低于500美元人群的分来源收入估计说明AI 解读

This paper derives estimates of money income received by persons making less than $500 per annum for the years 1944–1948. The estimates are classified by source of income and are obtained by adjusting basic census data for various types of understatement.

极大似然法计算剂量反应曲线的若干新方面AI 解读

The estimation of the parameters of dosage response curves by the standard probit method is an iterative process beginning with approximations to the parameters and using one or more cycles of computations to “improve” these estimates until they converge. The present paper gives a table and method for computing the maximum likelihood solution which converges more rapidly than the standard probit method. A procedure is presented for obtaining more accurate initial…

是否存在两条回归线？AI 解读

If, in sampling from an existent population, we wish to know the regression of u on v, a line is fitted by least squares, minimizing the sum of the squared residuals of v (or y). If there is no error in measuring the independent variate u, regardless of whether the dependent variate has been measured without error as v or with error as y, the regression is an estimate of the true regression. If, however, the independent variate is measured with error in x, the regression…

死亡率的大样本检验与置信区间AI 解读

In computing mortality rates from insurance data, the unit of measurement used is frequently based on number of policies or amount of insurance rather than on lives. Then the death of one person may result in several units of “death” with respect to the investigation; moreover, the number of units per individual may vary noticeably. Thus the usual large sample methods of obtaining significance tests and confidence intervals for the true value of the mortality rate are not…

In computing mortality rates from insurance data, the unit of measurement used is frequently based on number of policies or amount of insurance rather than on lives. Then the death of one person may result in several units of “death” with respect to the investigation; moreover, the number of units per individual may vary noticeably. Thus the usual large sample methods of obtaining significance tests and confidence intervals for the true value of the mortality rate are not…

卡方拟合优度检验中组数与组宽的选择AI 解读

This article describes in non-mathematical fashion the technique suggested by H. B. Mann and A. Wald for selecting the number and width of class intervals for the chi-square test of goodness of fit when the null hypothesis distribution is continuous and completely specified. The number of classes is selected by means of a formula depending upon the sample size and the level of significance and the class limits are chosen such that each class contains the same number of items…