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作者：KENDALL, DG
摘要：Fisher''s logarithmic series, developed as a limiting case of the negative binomial distr. for small intrinsic probabilities, has been used successfully in graduating data of a great var. of biological problems. The apparently basic nature of the distr. suggests the attempt to provide a theoretical interpretation. A stochastic process is defined, specifying birth and death rates and a constant rate of immigration. General solns. are obtained and 3 special cases are considered. In each case, th...
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作者：PATNAIK, PB
摘要：A system of contours in the p1 P2-plane, depending only on the ratio of ni-n2, determines similar regions for the power function of the test for the difference between 2 proportions in samples of ni and n2. Tables based on a normal approximation are provided for determining the power against a specified alternative with known sample sizes or for determining the sample sizes to produce a specified power against a specified alternative.
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作者：FOG, D
摘要：The purpose of this paper is to show how in some cases the geometrical method for the detn. of exact sampling distrs. may be translated into analytical form without any knowledge of multidimensional geometry. Three examples are given, each of which is treated in 2 ways, in a geometrical and in an analytical manner, the latter being the translation of the former into analytical language.
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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：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.
