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作者：HOFFDING, W
摘要：Kendall in 1938 obtained the sampling distribution of [tau] from a universe in which all possible rankings are equally likely and showed that the distribution is asymptotically normal. In terms of the probabilities [rho], that 2 members (x 1, y 1) and (x 2, y 2) of the universe are concordant (they are concordant when (x 1[long dash]x 2) (y 1[long dash]y 2) > 0) and [kappa], that of 3 members one is concordant with the other 2, it is shown that the distribution of [tau] is asymptotically norma...
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作者：GEARY, RC
摘要：Universal normality may be tested by a field of tests for kurtosis given by [alpha](c) = 1/[image] [SIGMA]
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作者：BARNARD, GA
摘要：The note points up the areas of agreement and disagreement between the 2 papers on 2 X 2 tables by Barnard and by Pearson in the same issue of Biometrika.
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作者：PEARSON, ES
摘要：In an effort to end the controversy which has raged since 1941, Pearson, following Barnard, has differentiated between 3 distinct situations in which data may be classed in a 2 X 2 table. The 3 situations produce tables in which (a) both margins are fixed, (b) one is fixed and (c) neither is fixed. Corresponding to the first, the appropriate test is Fisher''s exact distribution. Corresponding to the others, Pearson suggests a compound probability consisting of the probability of the observed m...
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作者：WHITFIELD, JW
摘要：The use of [tau] for tied rankings (Kendall; Biometrika, 1946) is extended to the case where one variable is ranked and the other expressed as a dichotomy, the dichotomy being viewed as a ranking in which all data are tied at two values only. In applying the method to the case of the 2X2 table, a slight discrepancy is noted with the usual x 1 calculation.
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作者：DAVID, FN
摘要：The hypothesis that there is randomness within a sequence of alternatives is to be tested against the field of alternate hypotheses that the dependence is of the type in simple Markoff chains. A conditional power function formula is obtained for sequences of [gamma]1 E''s and [gamma]2''Es arranged in k sets. The function is plotted for a few typical sequences.
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作者：MORAN, PAP
摘要：It is shown that the covariance of 2 time series, each generated by weighted sums of sequences of independent random variables having the same distribution (for each series), is asymptotically normally distributed. The variance of the distribution is calculated in terms of the weights. It is pointed out that the wts. may not be detd. from the sample and used to determine the variance. It is instead necessary to decide first the orders and coeffs. of the stochastic difference equations which ge...
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作者：WISHART, J
摘要：Explicit expressions for the exact cumulants of Fisher''s z-distribution are given. Cumulants for the logarithmic x 2-distribution are first found (the same result was published by Bartlett and Kendall in 1946) and the cumulants of 2 obtained by considering the z-distribution as the difference between two logarithmic x 2-distributions. Cumulants of the logarithmic t-distribution are obtained by specializing the z-distribution.
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作者：WELCH, BL
摘要：A population parameter [eta] is estimated by a statistic [gamma], normally distributed about [eta] with variance [image], where the [sigma]i are positive numbers and the [sigma]2 are unknown variances. If independent estimates of these variances are provided by the observed data, it is possible to make probability statements about [gamma] similar to those Student gave for the mean of a single sample. The form of the exact solution is given and a series solution is developed. The series converg...
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作者：BARNARD, GA
摘要：In considering a significance level as a probability, it is necessary to isolate a class of events having the given probability. Some of the difficulties in this isolation and identification are pointed out in connection with a particular problem.
