摘要:

AbstractMany multivariate non‐null distributions and moment formulas can be expressed in terms of hypergeometric functionspFqof matrix arqument. Muirhead [6] and Constantine and Muirhead [2]gave partial differential equations for the functions of2F1of one argument matrix and two argument matrices, respectively. Such differential equations have been used to obtain asymptotic expansions of the functions (Muirhead [7], [8], [9], Sugiura [10]). The purpose of this paper is to derive partial differential equations for the functions3F2(a1a2, a3; b1, b2, R) and3F2(a1, a2, a3; b1, b2; R, S). Differential equations for2F2are also obtaine

ISSN:0319-5724    

DOI:10.2307/3315276

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractLet (X, Y) have a (p+q)‐dimensional normal distribution and let C, K be convex symmetric sets of dimensions p, q respectively. Under certain restrictions on the mean vector it is shown that P(X ε C, Y ε K) is a monotonically increasing function of the first canonical correlation coefficient between X and Y, provided the remaining coefficients are z

ISSN:0319-5724    

DOI:10.2307/3315277

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractA two‐sample problem for rank‐order data is formulated as a two‐decision problem. Using the general Bayes solution, Bayes procedures are derived for several configurations of the set of states of nature including some for which the problem is distribution‐free. It is shown that for certain prior distributions these procedures reduce to classical LMP rank tests. Some devices for selection of prior distributions are suggested. It is shown that the Bayes risk of these procedures tends to zero as sample sizes i

ISSN:0319-5724    

DOI:10.2307/3315279

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractThe problem of estimating the effects in a balanced two‐way classification with interaction\documentclass{article}\pagestyle{empty}\begin{document}$$y_{ijk} = \mu + r_i + c_j + t_{ij} + e_{ijk}$$\end{document}\documentclass{article}\pagestyle{empty}\begin{document}$i = 1, \ldots ,I;j = 1, \ldots ,J;k = 1, \ldots ,K$\end{document}using a random effect model is considered from a Bayesian view point. Posterior distributions ofri,cjandtijare obtained under the assumptions thatri,cj,tijandeijkare all independently drawn from normal distributions with zero meansand variances\documentclass{article}\pagestyle{empty}\begin{document}$\sigma _r^2 ,\sigma _c^2 ,\sigma _t^2 ,\sigma _e^2$\end{document}respectively. A non informative reference prior is adopted for\documentclass{article}\pagestyle{empty}\begin{document}$\mu ,\sigma _r^2 ,\sigma _c^2 ,\sigma _t^2 ,\sigma _e^2$\end{document}. Various features of thisposterior distribution are obtained. The same features of the psoterior distribution for a fixed effect model are also obtained. A numerical example is give

ISSN:0319-5724    

DOI:10.2307/3315280

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractThe photographic emulsion is not a pure energy detector. For either very high or very low intensities of the incident light, the efficiency of an emulsion in terms of resulting photographic density is not as great as intermediate levels of intensity. Such behaviour is called reciprocity law failure.In this article a simple probabilistic model for reciprocity failure is presented which incorporates both high and low intensity failure. The flexibility of the model inherent in its simplicity allows more sophisticated models to be constructed.

ISSN:0319-5724    

DOI:10.2307/3315281

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractEfficient numerical algorithms are developed to evaluate several probabilities related to multinomial trials.In the first part of the paper, the probability distribution of the number of trials until the alternatives j, j = 1,… m, have occurred at least ijtimes is computed. The multinomial trials involve the m alternatives l,…, m, with positive probabilities Pl‐Pmof occurrence.In the second part, several aspects of a multinomial subset selection problem, discussed by S. S. Gupta and K. Nagel, are investi

ISSN:0319-5724    

DOI:10.2307/3315282

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractAn alternative to the criteria proposed by King [9] for clustering correlation matrices is explored. Several simple examples examined by total enumeration employing our criterion indicate that the criterion yields clusters with high within group correlation. A step‐wise routine is suggested for problems of realistic size and is applied to the examples presented in King's article. Additional evidence in the form of several Monte Carlo experiments indicates that the routine performs satisfactorily in determining the optimal separation of variables into two group

ISSN:0319-5724    

DOI:10.2307/3315283

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractDistance between two probability densities or two random variables is a well established concept in statistics. The present paper considers generalizations of distances to separation measurements for three or more elements in a function space. Geometric intuition and examples from hypothesis testing suggest lower and upper bounds for such measurements in terms of pairwise distances; but also in Lpspaces some useful non‐pairwise separation measurements always lie within these bounds. Examples of such separation measurements are the Bayes probability of correct classification among several arbitrary distributions, and the expected range among several random variable

ISSN:0319-5724    

DOI:10.2307/3315284

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractIt is assumed that a large random sample of fixed size n is drawn from a logarithmic series distribution with parameter $tH and that it is desired to estimate e by means of two‐sided confidence interval. Using asymptotic results, charts of confidence intervals are prepared for n = 50, 100, 200, 500 and 1,000, and confidence coefficients 0.90 and 0.9

ISSN:0319-5724    

DOI:10.2307/3315278

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY

摘要:

AbstractIn this paper a method of constructing group‐divisible incomplete block designs has been suggested. A series of balanced incomplete block designs has also been obtaine

ISSN:0319-5724    

DOI:10.2307/3315286

出版商:Wiley‐Blackwell    

年代:1975

数据来源: WILEY