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正态分布的尺度混合
Summary This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio Z/V where Z and V are independent and Z has a standard normal distribution. This representation is useful in Monte Carlo calculations. It is established that when 1/2V 2 is exponential, X is double exponential; and that when 1/2V has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.
关于数据变换选择的一点说明
Recontly Box & Cox (1964) and Fraser (1967) have proposed likelihood functions as a basis for choosing a transformation of data to yield a simple linear model. Here a simple, exact, test of significance is proposed for the consistency of the data with a postulated transformation within a given family. Confidence sets can be derived from this test. The power of the test may be estimated and used to predict the sharpness of the inferences to be derived from such an analysis.…
基于残差的显著性检验
The known distribution of residuals from linear regression models may be used to construct exact tests of significance. New tests for the presence of one or more outliers are considered in detail. Applications of the theory to other tests are discussed. Exact results are worked out for the normal and exponential error distributions; formulae are given for other nonnormal cases.
关于数据变换选择的一则札记
Recontly Box & Cox (1964) and Fraser (1967) have proposed likelihood functions as a basis for choosing a transformation of data to yield a simple linear model. Here a simple, exact, test of significance is proposed for the consistency of the data with a postulated transformation within a given family. Confidence sets can be derived from this test. The power of the test may be estimated and used to predict the sharpness of the inferences to be derived from such an analysis.…
基于残差的显著性检验
The known distribution of residuals from linear regression models may be used to construct exact tests of significance. New tests for the presence of one or more outliers are considered in detail. Applications of the theory to other tests are discussed. Exact results are worked out for the normal and exponential error distributions; formulae are given for other nonnormal cases.