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作者：PATNAIK, PB
摘要：Approximations are derived for the probability integrals of non-central X2 and of non-central F, i.e., the ratio of a non-central X2 to an independent central X 2. The simplest approximation for non-central X2 with n d.f, interpolatesin the table of centralX2 with n +[image] d.f. and multiplies then + 2 Xinterpolate by 1 + [image], where [image] andX2 =[image]. The corresponding approximation for non- central F uses [image] and V2 d.f. for numerator and denominator, respectively and multiplies...
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作者：HARTLEY, HO
摘要：A test of significance based on the maximum harmonic intensity is given under the usual null hypothesis that the observations are independent normal deviates with common variance. The power of the test is then investigated against alternative hypotheses that the series is composed of (i) a systematic harmonic series with random remainders and (ii) a general systematic component with random remainders. For the first case, the chance of being misled by a significant result of the test is compute...
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作者：LANCASTER, HO
摘要：It is shown that, corresponding to the expression of a multinomial probability law as a product of binomial probability laws,there is a partition of the total X 2 into individual parts with one degree of freedom. The same is true for an r x s contingency table with known marginal totals. For both cases, approximations to the individual values of X 2 may be made by use of the Stirling approximation. Examples of some applications are given.
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作者：QUENOUILLE, MH
摘要：When the purpose of determining a trend line is to eliminate trend in order to study the residuals, it is in general not advantageous to insist upon smoothness in the trend line. A method of rapid calculation is given for eliminating trend using a series of consecutive polynomials of the same degree, subject to the restriction that the observed series is circularly related. Methods are also given for relaxing this restriction.
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作者：THOMAS, M
摘要：The Poisson situation is generalized by considering a no. of primary points distributed over an area and a random no. of secondary points associated with each primary point. The area is divided into squares and the probabilities that a square contains 0, 1, 2, ... points are calculated, assuming that the nos. of primary points per square and of secondary points per primary point are independently Poisson distributed. Estimates are obtained for the two parameters by the method of moments and by...
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作者：HUZURBAZAR, VS
摘要：For a distribution with probability density function [image] and likelihood function L, it is shown that [image] where both evaluations are made at [theta]j the maximum likelihood estimates of the [theta]j This property is used to simplify calculations of the variances and covariances of the maximum likelihood estimates for large samples. In case the [theta] are linearly independent, it follows that the likelihood equations have a unique maximizing solution for samples of any size.
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作者：WISHART, J
摘要：Cumulant recurrence relations given by Guldberg (Skandinavisk Aktuarietidskrift, 1935) for the univariate Bernoulli and Pascal distrs. are generalized to the multivariate case. The results are then used to obtain cumulants to the 4th order.
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作者：GREENWOOD
摘要：Several statistical models of the mechanism of infection of measles are tested by the frequency distributions of multiple cases of the disease in families. Attempts are also made to dissect the distributions of intervals between successive cases in families in order to estimate the distribution of length of the incubation period.
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作者：WHITFIELD, JW
摘要：For the problem of intra-class correlation when only ranks are available, a solution is given for the case of pairs. The general procedure recommended is calculation of the mean correlation using Kendall''s coefficient over all possible arrangements. In the case of pairs, the computation is effected by taking [image] where S is a score counted by arranging the pairs as (a1, b1, (a2, b2), ..., (an/2, bn/2) so that each a1
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作者：GODWIN, HJ
摘要：A linear systematic estimate of the standard deviation of a distribution, F(x), is a linear combination of the order statistics x1[less than or equal] X2 [less than or equal]...[less than or equal]Xn in a sample of n, and may be expressed in the form [image] where yi = Xi+1[long dash]Xi . First and 2d moments of the yi are expressed as linear combinations of [image]and [image]. It is shown that the efficiency of the linear systematic statistic, d, may always be maximized. Two applications are ...
