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最大与最小次序统计量近似独立所需的样本量AI 解读

Let Xn and X 1 be the largest and smallest order statistics, respectively, of a random sample of size n. Quite generally, Xn and X 1 are approximately independent for n sufficiently large. Minimum n for attaining at least specified levels of independence are developed. Level of independence is measured by the maximum difference between the true values of P(X 1 ≤x 1, Xn ≤xn ) and the corresponding values assuming independence of Xn and X 1. The results apply to all possible…

最大与最小次序统计量近似独立所需的样本量AI 解读

Let Xn and X 1 be the largest and smallest order statistics, respectively, of a random sample of size n. Quite generally, Xn and X 1 are approximately independent for n sufficiently large. Minimum n for attaining at least specified levels of independence are developed. Level of independence is measured by the maximum difference between the true values of P(X 1 ≤x 1, Xn ≤xn ) and the corresponding values assuming independence of Xn and X 1. The results apply to all possible…

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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…

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对《最简单的符号秩检验》的评论AI 解读

In a fundamental contribution, Tukey [5] showed that the Wilcoxon signed-rank test [14, 15, 16, 17] is equivalent to a subclass of some tests presented by Walsh [7, 8]. Since Tukey's memorandum did not explicitly state that only a subclass of Walsh's tests is involved, misunderstandings seem to have arisen concerning the extent of the equivalence between these two classes of tests. This paper points out that a large proportion of Walsh's results are not equivalent to…

伽马分布较低分位点非参数寿命检验的渐近效率AI 解读

This paper does not present new statistical methods. Rather, it shows that a well known nonparametric procedure which is valid under extremely general conditions also has high efficiency and other favorable properties for certain types of life testing situations. This nonparametric method is the sign test and its confidence interval and point estimate analogs. Sign test procedures and methods of applying them have already received extensive coverage in the literature (e.g.,…

伽马分布较低分位点非参数寿命检验的渐近效率AI 解读

This paper does not present new statistical methods. Rather, it shows that a well known nonparametric procedure which is valid under extremely general conditions also has high efficiency and other favorable properties for certain types of life testing situations. This nonparametric method is the sign test and its confidence interval and point estimate analogs. Sign test procedures and methods of applying them have already received extensive coverage in the literature (e.g.,…

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…

正态总体稳定性检验的操作特性AI 解读

This paper presents values of the operating characteristic (OC) function for a common type of stability test and for two possible substitutes for this test. The situation considered is that of small samples from normal populations. The purpose of a test is for deciding whether a sample is from a specified population.

正态总体稳定性检验的操作特征AI 解读

This paper presents values of the operating characteristic (OC) function for a common type of stability test and for two possible substitutes for this test. The situation considered is that of small samples from normal populations. The purpose of a test is for deciding whether a sample is from a specified population.

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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…

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…

已知方差比时 t 检验样本量的最佳选择AI 解读

The situation considered is that of testing the difference of the means of two normal populations on the basis of a sample from each population, where the ratio of the population variances is known. The choice of sample sizes has been restricted to certain pairs which are equally preferable from the viewpoint of practical considerations (cost, difficulty of obtaining sample values, etc.). This note presents an easily applied method of determining which of these pairs of…

方差比已知时 t 检验样本量的最佳选择AI 解读

The situation considered is that of testing the difference of the means of two normal populations on the basis of a sample from each population, where the ratio of the population variances is known. The choice of sample sizes has been restricted to certain pairs which are equally preferable from the viewpoint of practical considerations (cost, difficulty of obtaining sample values, etc.). This note presents an easily applied method of determining which of these pairs of…

总体方差已知时使用 t 检验损失的“信息”AI 解读

This note calls attention to the use of the power function as a means of determining how much “information” is lost by using some other test in place of the most powerful test of a given hypothesis. As an example of the method, the case of using a t-test for the mean of a normal population with known variance is analyzed.

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