摘要:

A sample of sizeNis taken from an equiprobablet-category multinomial distribution. The precise values of Pearson'sX2and the likelihood ratio statistic A were computed fort= 3(1)6,N= 3(1)12;t= 6(1)14,N= 6(1)2t;t=15(1)18,N= 6(1)28. The logarithms of the tail areas were smoothed and fitted by means of quadratic expressions. Much information is given concerning the accuracy of the chi-squared fits to the distributions ofX2and A. A table of −log10P(χ2>a) is given, fora= 1(1)50, and d.f. = 1(1)20. The distribution of the total number of repeats within cells is also discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481078

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The problem of the measurement of association between two attributes is of importance in social sciences [5]. Following Hotelling [6, 7], Lancaster [9], and Kendall [8], the canonical structure of a two-way classification is obtained. Based on the canonical correlations, three measures of association are suggested. Their metric properties are summarized. One of the measures is shown to reduce to the measure suggested by Cramér [1]. Their large sample distributions are approximated on the null hypothesis of independence between the two attributes.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481079

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

A decision theoretic approach to the design of a clinical trial is considered for the situation in which a total ofNpatients with a disease receive one of two treatments and the responses to the treatments are dichotomous. Two costs are considered: The cost of treating a patient with the inferior treatment and the cost of conducting the trial. Minimax and Bayes procedures are used to determine the optimum size of a fixed sample trial. Bayes solutions for the optimum sample size are given for a variety of beta prior distributions and various values ofN.Minimax solutions are given for a variety of regions over which the minimaxing was performed, and for various values ofN. The optimum sample sizes are found to be asymptotically proportional toN1/2using the Bayes procedure andN2/3using the minimax procedure. The consequences of erring in specifying the value ofNare explored.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481080

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

The theory of uniformly most accurate upper tolerance limits is presented for families of discrete distributions having monotone likelihood ratios. Explicit formulae are derived for binomial, negative-binomial and Poisson distributions. The relationship to systems of uniformly most accurate upper confidence limits is exposed.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481081

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

This study is concerned with the extension of the Bradley-Terry model for paired comparisons to situations which allow an expression of no preference. A new model is developed and its performance compared with a model proposed by Rao and Kupper. The maximum likelihood estimates of the parameters are found using an iterative procedure which, under a weak assumption, converges monotonically to the solution of the likelihood equations. It is noted that for a balanced paired comparison experiment the ranking obtained from the maximum likelihood estimates agrees with that obtained from a scoring system which allots two points for a win, one for a tie and zero for a loss. The likelihood ratio test of the hypothesis of equal preferences is shown to have the same asymptotic efficiency as that for the Rao-Kupper model. Two examples are presented, one of which introduces a set of data for an unbalanced paired comparison experiment. Initial applications of the test of goodness of fit suggest that the proposed model yields a reasonable representation of actual experimentation.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481082

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

In this article the minimal cut lower bound on the reliability of a coherent system, derived in Esary-Proschan [6] for the case of independent components not subject to maintenance, is shown to hold under a variety of component maintenance policies and in several typical cases of component dependence. As an example, the lower bound is obtained for the reliability of a “two out of three” system in which each component has an exponential life length and an exponential repair time. The lower bound is compared numerically with the exact system reliability; for realistic combinations of failure rate, repair rate, and mission time, the discrepancy is quite small.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481083

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

A method is developed for the design of experiments with mixtures in which the mixture components are categorized (acids, bases, etc.), and each category of components contributes a fixed proportion to the total mixture. The number of categories of mixture components is general(q< ∞), and each category is represented in every mixture by one or more of its member components.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481084

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

A result which follows from a general Bayes solution is that the inverse estimator [4] is Bayes with respect to a particular informative prior.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481085

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

Coefficients for computing ordered linear unbiased minimum variance (OLUMV) estimators of the location and scale parameters have been obtained for selected members of a class of symmetric power distributions which includes the normal, double exponential, and as a limiting case, the rectangular. Two examples are given illustrating how these coefficients may be used to study the sensitivity of inferences concerning location parameters to departure from normality. The first example involves a single location parameter while the second extends the method to linear contrasts of several location parameters. Other uses of the coefficients are indicated, and a comparison of the efficiencies of the OLUMV estimators with several commonly used estimators of location is given.

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481086

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor

摘要:

This article suggests a distribution-free signed rank test for the parallelism of two regression lines. Pitman efficiency comparisons of the signed rank test and a normal theoryt-test are presented. Monte Carlo sampling is used to compare the signed rank test with a nonparametric test proposed by Potthoff [7].

ISSN:0162-1459    

DOI:10.1080/01621459.1970.10481087

出版商:Taylor & Francis Group    

年代:1970

数据来源: Taylor