摘要:

AbstractLetX1:n,X2:n,X3:n…,Xn:nbe the order statistics ofnindependent random variables with the common (absolutely continuous strictly increasing) distribution functionF. The main results given in this article are:1For any fixedrand two distinct numberss1ands2(1

ISSN:0323-3847    

DOI:10.1002/bimj.4710210102

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractThe methods of optimal designing of experiments proposed by WALD(1943) are used for determination of anAσ2‐optimal concrete design for estimation of σ2′= (σ a2, σ e2) in case of one‐way analysis of variance. Starting point of definition of the optimality criterion is a quadrati

ISSN:0323-3847    

DOI:10.1002/bimj.4710210103

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractThe standard tables for the KOLMOGOROV‐SMIRNOVtest are valid only in the case of testing whether a set of observations is from a completely specified cumulative distribution,F0(X), with all parameters known. If the parameters are unknown and must be estimated from the sample, then the tables are not valid.A table is given in this paper for use with the KOLMOGOROV‐SMIRNOVstatistic in the case of testing whether a set of observations is from the POISSONdistribution with an unknown mean that must be estimated from the sample. The table is obtained from a Monte Carlo calculat

ISSN:0323-3847    

DOI:10.1002/bimj.4710210104

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractA general algorithm for the factor analysis is developed, which contains the alpha factor analysis, the maximum likelihood method and the minres method as special cases. This algorithm, which is a multidimensional NEWTONalgorithm, uses the partial derivatives of the reproduced communalities with respect to the inserted ones. The partial derivatives are got by means of the perturbation theory.

ISSN:0323-3847    

DOI:10.1002/bimj.4710210105

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractThe relationship between the development of measles and age at immunization and time since immunization is examined using a trichotomous logistic distribution with maximum likelihood estimation of the parameters. The first and second partial derivatives used in the estimation scheme are presented.

ISSN:0323-3847    

DOI:10.1002/bimj.4710210106

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractThe expected error rates associated with using the allocation rule based on logistic regression are derived in the context of two multivariate normal populations with a common covariance matrix and compared with the corresponding error rates of the classical rule based on this normality assumption. It is shown in terms of the actual sizes of the asymptotic expected error rates that the performance of the logistic procedure does not fall far short of the normality based method, even for widely separated populations. This latter result is not obvious from previously available work on the asymptotic relative efficiency of the logistic procedure.

ISSN:0323-3847    

DOI:10.1002/bimj.4710210107

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractAfter general remarks upon the biomathematical tasks of quantitative description or mathematical modelling of biological systems and phenomena on different levels of organization the growth process of body length of human beings serves as illustration of the possibilities of such mathematical treatments. A short survey is given about the attempts of using differential equations for reflecting basic principles of growth processes. Further on analytical functions (as the solutions of growth differential equations) preferably may be used for an objective quantitative reproducing of measured courses of growth variables. The values of parameters contained in such expressions will be calculated by nonlinear fitting procedures. In nearly all cases we got a very high numerical precision in approximating parts of the body length growth process of man which extends from conception until the age of 18. Our attempts of a phenomenologic‐mathematical modelling of this growth process mean a subdividing of the whole process in single growth spurts with a symmetric‐sigmoidal shape of their courses, and describing the single spurt by a hyperbolic tangent function. An advantage of this kind of modelling is the fact that each of the terms is valid for the whole time interval of growth. Within the process of forming the model heuristical hints are taken into consideration arising from biological background and which would supply the possibility of interpretation and verification of the analyzed growth spu

ISSN:0323-3847    

DOI:10.1002/bimj.4710210108

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractIn the presented paper the method of the empirical regression belt is demonstrated. An empirical regression curver(x), which is determined by the realizations (measured points) (x1,y1),i= 1,….,nof a continuous two‐dimensional random variable (X,Y), is enclosed by a belt, the local width of which varies dependent on local frequency and variance of the measured points. This empirical regression belt yields certain information for evaluating the empirical regression curve, providing a useful basis for the biomathematical forming of a model. By giving three examples derived from morphometrics the authors discuss important qualities of the empirical regression b

ISSN:0323-3847    

DOI:10.1002/bimj.4710210109

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractConfigural frequency analysis models are presented for predicting a discrete criterion variable from combining 2 or more discrete predictor variables nonparametrically. Predictions are made via so‐called prediction types which allow to predict a criterion class from combined predictor classes. Prediction types are implicitely defined as cells of a 2‐dimensional contingeney table with rows as predictor combinations and columns as criterion classes. The CFA is extended for two criteria, and for stratified sampl

ISSN:0323-3847    

DOI:10.1002/bimj.4710210110

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY

摘要:

AbstractAugmented designs are frequently used in practice. In this paper, a simplified procedure of analysis of some types of augmented designs is discussed using the concept of efficiency‐balance and partially efficiency‐bala

ISSN:0323-3847    

DOI:10.1002/bimj.4710210111

出版商:WILEY‐VCH Verlag    

年代:1979

数据来源: WILEY