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作者：AITKEN, AC
摘要：A lemma due to Siegel is stated and an elegant proof given. It is shown that the lemma may be used to go from the Laplace transform or moment-generating function of the estimates of 2d order moments of a k-variate normal population to the vVishart distr. function. A derivation of the moment-generating function of the estimates is given for the ordinary case and also for the case in which a polynomial rather than a constant is fitted to the variates. In the latter case, it is shown that the Wis...
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作者：JOHNSON, NL
摘要：A variable x is transformed by z = f(x) so that z is a unit normal variable. If the transformation, f(x), depends on a few parameters, a system of frequency curves is generated. In particular, taking z = [image] the parametersV A /'' [gamma] and [delta] determine the shape of the distributions of x while [lambda]and [xi] are scale and location parameters. The three systems, Sl corresponding to the transformation z = [gamma] + [delta] log (x - [xi]), SB with transformation z = [gamma] + [delta]...
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作者：KENDALL, MG
摘要：An attempt is made to reconcile the points of view of the frequentists (von Mises et al.) and the non-frequentists (Keynes, Jeffries et al.) by pointing out that the premises made by each school have counterparts in the structure of the other, that both are compelled to rely on the properties of equi-probable exclusive alternatives for justification of the product rule, P(pq
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作者：KENDALL, MG
摘要：The effect of non-normality on the known relations between Kendall''s [image] and Spearman''s [rho]s rank correlation coeffs. on the one hand and the product moment coeff. [rho] on the other, is investigated. Non-normality is introduced through the Gram-Charlier A series. It is found that the expressions for E(t) and E(rs) in terms of [rho] are independent of odd order product moments and hence, of skewness in the parent population. Corrections to the usual formulas for mean and variance of bo...
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作者：IRWIN, JO
摘要：In an ( r x s) frequency table with observed frequencies aij and expected frequencies apij, where a =[image]> consider the matrix of [image] standardized variables, Xij -[long dash][plus or minus][long dash][long dash][long dash][long dash][plus or minus][long dash][center dot] The result 3 sppir of premultiplying this matrix by a Helmert matrix constructed from the row marginal values and postmultiplying by the transpose of the Helmert column matrix is an (r x s) matrix with zeroes in the 1st...
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作者：GUMBEL, EJ
摘要：For a sample of n from a symmetrical unlimited distribution o (x) of exponential type, u is defined by [image] The [image]asymptotic distr. of the reduced range, R = [alpha] (W-2u), where W is the sample range, is obtained from convolution of the asymptotic distributions of the extremes. Tables of the asymptotic distribution and frequency functions of reduced range are given.
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作者：BATEMAN, GI
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作者：TOCHER, KD
摘要：Equations are derived for an iterative solution for the max. likelihood estimates of mean and variance in the underlying normal distr. of probit data which are mixed but can be assumed to be uniformly distributed within m groupings. A numerical process is given in case the groupings are in equal intervals, and approximations based on the Sheppard corrections are shown to give nearly the same estimates.
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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...
