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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：KENDALL, DG
摘要：The birth-and-death stochastic process introduced by W. Feller (Acta Biotheoretica, 1939) describes growth of a population under simplified laws of reproduction and mortality. One simplification is that chances of both are completely independent of the previous history of the individual, including elapsed time since his own birth. This assumption implies that the stochastic dependence of population size on time is given by a discontinuous Markoff process. The author claims, however, that this ...
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作者：JONES, AE
摘要：The problem of estimating the mean value of a random variable along a continuous strip of finite length is considered for the case in which the autocorrelations decay exponentially. It is shown that if the serial correlation is appreciable or if the sample is large the best systematic arrangement is a measurement at the centers of equally spaced intervals. The 2d paper points out that this result is valid only in the case considered and that for other autocorrelation schemes, this arrangement ...
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作者：ORCUTT, GH; JAMES, SF
摘要：Prior investigation of 52 economic time series indicated they might have been drawn from a population of series generated by [PSI]t+1=[PSI] t + .3([PSI]t- [PSI]t-1) + [epsilon]t+1, where [epsilon] is random in time with expected value of zero. Using this model, a set of non-related series were constructed and correlations between them were computed. Empirical investigation indicates that significance tests may be devised by computing the approx. variance of the correlation r between 2 unrelate...
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作者：ANSCOMBE, FJ
摘要：Transformations having the effect of approx. normalizing Poisson, binomial and negative-binomial variables are given to within a constant appearing in each transformation. Optimum values of the constants are defined as those which make the variance of the transformed variable most nearly constant, with obvious application in the technique of analysis of variance. Asymptotic formulae are given for the first four moments and for the efficiency in estimation of the original parameters for transfo...
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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：GODWIN, HJ
摘要：A recurrence relation is derived to make possible calculation of the moments of the distribution of the mean deviation from the mean of a sample of n from a normal population. The first 4 moments agree essentially with those reported by Geary; a new 5th moment is given. Two functions of m which are distributed more nearly normally than m itself are obtained and their means and standard deviations given.
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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...
