摘要:

In this paper methods for obtaining approximations and bounds for the moments of order statistics from a continuous parent distribution are discussed. These bounds and approximations depend on the distribution function only through certain moments of order statistics in small samples. It is shown that for the Cauchy distribution bounds and approximations of all finite moments can be obtained. Some numerical calculations for normal and Cauchy distributions are also given.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501081

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501082

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Several approximations to the binomial distribution were compared in 1956 by Raff [9], including the normal, arcsine, normal Gram-Charlier, Camp-Paulson, Poisson, and Poisson Gram-Charlier approximations. The closeness of these approximations is judged by the maximal error which can arise in evaluating any sum of consecutive binomial terms. Borges [3] investigated a general class of approximations (which includes some of the above) and showed that a certain beta-transformation of a binomially distributed variable is the unique member of this class which is approximately normal with error 0(1/n). In 1963, Bol'shev [2] gave two new Poisson-Type approximations. In this paper, some of Raff's tables are extended and tables for the error of these newer approximations are added. As a consequence of the numerical results obtained, the Poisson Gram-Charlier approximation is recommended for small values ofpwhile the Camp-Paulson and Borges' approximations should generally be preferred for largep.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501083

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A set of observations may be partitioned into two clusters to maximize the ratio of between sum of squares to within sum of squares. This maximum ratio is the likelihood ratio test statistic for the observations to come from two normal populations, with different means but the same variance. A table of percentage points of the statistic is given under the null hypothesis, that the observations are a sample from a single normal population.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501084

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A table is presented containing critical points for the non-centralFwith non-centrality of one-half for type one error .05, .10, .25 and .50 and numerator and denominator d.f. including 1–30, 40, 60, 120, 200, 400, 1000. The critical points may be used to test the hypothesis that a set of exact linear restrictions imposed on the parameters of a linear model yield estimators that are better in generalized MSE than the unrestricted, o.l.s., estimators. Tabulation is discussed and some examples are presented on how the tables may be used.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501085

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

A nomogram is given for estimating the probability (P) for a given value of the “Student”-Fisherttest (tranging from 1 to 65) for values of degree of freedom from 1 to infinity). Values ofPfrom 0.5 to 0.00001 are given.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501086

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Decision Analysis: Introductory Lectures on Choices under Uncertainty.Howard Raiffa.Reading, Massachusetts: Addison-Wesley, 1968. 309 pp. $4.95. Reviewed by J. J. McCall

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501087

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501088

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

This article has no abstract

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501040

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor