ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1969.tb00070.x

出版商:Blackwell Publishing Ltd    

年代:1969

数据来源: WILEY

摘要:

Summary In these days some sportsmen are given dangerous drugs in order to stimulate them into still higher efforts. The present paper wants to add some poison to the classical approximation of a binomial by a Poisson distribution. The relatively harmless drug of a little extra calculation shall be seen to result in a much better accuracy.This paper reports both on theoretical considerations, following from series expansions of Poisson‐type parameters, and on extensive numerical investigations of accuracy by means of an Electrologica X8 computer. The main conclusion is that the probability of at mostksuccesses innBernoulli trials with success probabilityp5 one should makep5. In section 5 a series expansion for the exact Poisson parameter is derived. Two new parameters, among which is ζ, are introduced in section 6, where the series expansions for parameters given in table 4 lead to conclusions about the various approximations, summarized in table 6. The final section 7 gives some numerical results, which confirm to a large extent the conclusions from the asym

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1969.tb00071.x

出版商:Blackwell Publishing Ltd    

年代:1969

数据来源: WILEY

摘要:

Summary This paper considers tests of exponentiality against unspecified alternatives. The test functions are modifications of those given by Kac, Kieferand Wolfowitz[Ann. Math. Stat., Vol. 26 (1955) 189–211]. The distributions of these statistics are obtained with the aid of the Monte Carlo method, and the tables may serve to apply a test of exponentiality for the usual levels of significance (sample sizesn≥ 10).A Monte Carlo comparison is also made with competing tests for exponentiality, namely with criteria arising from probability plotting and due to Shapiroand Wilk[(1964) in an unpublished manuscript, but recently described in “Statistical Models in Engineering” by Hahnand Shapiro(Wiley, 1967)], and with tests based on the conditional distribution of total lives and on a likelihoo

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1969.tb00072.x

出版商:Blackwell Publishing Ltd    

年代:1969

数据来源: WILEY

摘要:

Summary The use of vectors and vector spaces for the representation of the fixed‐effects models for the analysis of variance (ANOVA) is well‐known. This representation gives a clear understanding of the estimation and hypothesis testing problems.A similar representation can be used for the random‐effects models and some mixed models. As a result the distribution and the expectation of the mean squares in the ANOVA table can easily be de

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1969.tb00073.x

出版商:Blackwell Publishing Ltd    

年代:1969

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1969.tb00074.x

出版商:Blackwell Publishing Ltd    

年代:1969

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1969.tb00075.x

出版商:Blackwell Publishing Ltd    

年代:1969

数据来源: WILEY

摘要:

Summary The purpose of this paper is to present some corrections and supplements to the second author's papers [2] and [3]in this journal. It is a result of a discussion of the first author's criticism, which was directed against two points, viz. first the presentation of the paradoxes of Zeno from Elea ([3], § 2) and second some technical aspects of the introduction of probability by means of the notion of randomizer ([3], § 5

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1969.tb00076.x

出版商:Blackwell Publishing Ltd    

年代:1969

数据来源: WILEY

摘要:

Book reviewed in this article:Decision Rules in Markovian Decision Processes with incompletely knownm Transition Probabilities, J. Wesels.An Introduction to Probability Theory and Its Applications, Volume I, Third Edition, W. Feller.S. S. Willks: Collected Papers. Contributions to Uathematical Statistics, edited by T. W. Anderson.The Theory of Random Clumping; S. A. Roach.The Theory of Gambling and Statistical Logic, RichardA. Epstein.Handbook of Methods of Applied Statistics, vol. I and II, J. M. Chakravarti, R. G. Lahaand J. Roy.Input‐output experiments, The Netherlands 1948–1961., C. B. Tila

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1969.tb00077.x

出版商:Blackwell Publishing Ltd    

年代:1969

数据来源: WILEY