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作者：MORAN, PAP
摘要：Exact values of the first 3 moments are obtained for the serial coeff., [image] and for the cyclical coeff., [image] with Xn+1 taken equal to Xi, under the assumption that the Xi are actually uncorrelated and have the same normal distribution. In the case that the mean of the time series is known as well, the definitions of the 2 coeffs. are modified in an obvious manner and the first four moments of each is given. Some mention is made of the serial coeff. when s units separate paired measurem...
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作者：ASPIN, AA
摘要：On the basis of 2 samples of size n1 and n2 drawn from 2 normal populations with true means [alpha]1and [alpha]2 and true variances [sigma]12 and [sigma]2, respectively, it is often necessary to calculate confidence intervals for ( [alpha]l- [alpha]2) from the sample means [image]1 and [image]2 and sample variances s12 and s22. This is a special case of a problem considered by Welch (Biom., 1947). Welch obtained a soln. in the form of a series expansion to terms of the order of 1/ni2; the seri...
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作者：NAIR, KR
摘要：In routine analysis of variance, each of k independent estimates of an unknown variance may be tested against another independent estimate so2. The largest and smallest estimates are most likely to be declared significantly different from So2. With k of the order of 20, at least one of the estimates may be expected to be declared significant. A proper test of significance involves the distr. of the largest (or smallest) variance ratio of a set of k. Both distr. functions are obtained for k est...
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作者：BATEMAN, G
摘要：The distr. of the longest run in a sequence of alternatives, with unequal numbers of elements of each kind, is given for the cases of independent sequences, simple Markoff chains and 2d-order Markoff chains. Numerical results are obtained for sequences of length 10-20. In each case, comparison is made of the power functions of longest run and of number of groups. For the case of independence, it would appear that the test of number of groups is uniformly better.
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作者：JOHNSON, NL
摘要：Four alternative set-ups are considered, according as bi is a constant parameter or a random variable and the cij are independently or dependently distributed where Xij = a + bi + cij, Xij being the jth observation in the ith group. In the most important cases, cij independently distributed, power functions of the significance tests are given. The power function for bi constant and cij independent had been obtained by Tang in 1938; for bi a random variable with the cij independent, the result ...
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作者：HARTLEY, HO
摘要：If a non-linear regression law may be regarded as a soln. of a linear differential equation, data may be fitted directly to the linear equation, the least squares technic giving linear equations for the parameters. In order to fit an empirical series, it is necessary to use an equivalent difference equation. Summing the difference equation gives an equation for the dependent variable in terms of its own repeated sums and the independent variable. Such an equation is called an internal regressi...
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作者：COX, DR
摘要：Three asymptotic distributions, one of which is new, are discussed for the case of samples from a symmetric unimodal distribution. Gumbel''s distribution (Ann. Math. Stat., 1947), in terms of a modified Bessel function of the second kind appears to be least accurate. Cox''s distribution is of the form [image] where [PHI] (x) and [PHI] (x) are the frequency and distribution functions of the basic symmetrical distribution with mean zero, and wn is the sample range. This distribution is obtained ...
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作者：PEARSON, ES; MERRINGTON, M
摘要：Various problems lead to analysis by 2 x 2 tables. The one considered here is that in which two treatments, the old (or no) treatment A and the improved treatment B are each given to half of a sample of N individuals such that X of the N would react favorably if given either treatment, Y if given treatment B, and Z would not react to A or to B. The hypothesis Y = 0 is to be tested against alternatives Y>0. The data are observed in the form of a 2x2 table, [image] The appropriate test is whethe...
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作者：DUMAS, M
摘要：It is shown that the points of discontinuity of the derivative in the Pearson differential equation lie on the curve traced by a biquadratic function of [beta]1 and [beta] 2. Wherever the curve traverses a zone of the B 1, [beta] 2-plane corresponding to a type in Pearson''s system, the functions defined have essentially different kinds of contact at one extreme of the range according as they correspond to points on the curve, on one side or the other. Typical forms of the frequency curves are...
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作者：FINNEY, DJ; STEVENS, WL
摘要：A more detailed table than those previously available is given for max. and min. working probits, ranges and weighting coefficients for use in probit analysis. Table XI in Fisher and Yates: Statistical Tables (1946) gives these values for the range 1-9 by 0.1; this table covers the same range by differences of 0.01 in the argument.
