Showing papers in "Biometrical Journal in 1981"
TL;DR: In this paper, a method for the second-order analysis of point processes, and, basing on it, for their orientation analysis, is presented, which has some advantages in comparison to RIPLEY's estimator.
Abstract: The paper presents a method for the second-order analysis of point processes, and, basing on it, for their orientation analysis. For the reduced second moment measure of stationary and of stationary and isotropic point processes a new estimator is given, which has some advantages in comparison to RIPLEY's estimator. Three examples illustrate the use of the statistical techniques.
124 citations
TL;DR: In this article, two measures of unbalanceness in a one-way model are discussed and compared for a given statistical procedure and shown that they may serve as measures of efficiency of a design.
Abstract: This paper discusses two measures of unbalancedness in a one-way model and shows that for a given statistical procedure they may serve as measures of efficiency of a design. They also allow to compare for example estimation methods for variance components in designs with a fixed level of unbalancedness.
94 citations
56 citations
TL;DR: In this paper, finite and asymptotic tests are proposed, which are derived from the (exact conditional) generalized hypergeometrical distribution of the cell frequencies, allowing for considerably more powerful decisions than do the conservative binomial tests.
Abstract: In the Configural Frequency Analysis (CFA) of KRAUTH and LIENERT (1973 a, b), overfrequented (or underfrequented) cells in multivariate contingency tables are identified by simultaneous binomial tests. As an alternative, finite and asymptotic tests are proposed, which are derived from the (exact conditional) generalized hypergeometrical distribution of the cell frequencies. These tests allow for considerably more powerful decisions than do the conservative binomial tests.
54 citations
TL;DR: In this paper, two coefficients, which are normalizations of the mean-squared-error, are proposed as measures of accuracy for the prediction of grassland yield, and a multiplicative model is studied which allows predicting ability to differ over time or over regions.
Abstract: In this paper techniques are presented which allow the evaluation of accuracy of prediction methods, with special reference to the prediction of grassland yield. The more prominent methods of predicting grassland yield are discussed. Two coefficients, which are normalizations of the mean-squared-error, are proposed as measures of accuracy. It is shown that the mean-squared-error partitions into the sum of three meaningful components of error. The distribution of the components is discussed under the assumption that the actual and predicted yields have a bivariate normal distribution. The problem of accuracy analysis is addressed when one is only interested in ranking the yields of grassland areas. The ratio of the mean-squared-error for two competing prediction methods is investigated. Finally, a multiplicative model is studied which allows predicting ability to differ over time or over regions.
32 citations
TL;DR: The negative binomial or the method of inverse sampling (e.g., the authors ) is suggested for prospective studies, which usually has the advantage of fostering an early decision on the statistical significance of some etiological factor in examining successive patient records.
Abstract: The use of the negative binomial, or the method of inverse sampling (e.g. (1), (2)), is suggested for prospective studies. This method usually has the advantage of fostering an early decision on the statistical significance of some etiological factor in examining successive patient records. Several limiting situations for the distribution are discussed regarding the prevalence of a disease. An example illustrates the method.
31 citations
TL;DR: In this paper, a simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v =pk, v=p2k, …, treatments, for k≥p, in incomplete blocks of size k.
Abstract: A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk, v=p2k, …, treatments, for k≥p, in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k+1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for ps being the smallest prime factor of n, ps + 1 for v = n2, ps2+ ps + 1 for v = n3, …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero-one concurrence design. Procedures are described for obtaining additional zero-one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra-block and inter-block analyses are described.
28 citations
TL;DR: In this paper, a multivariate hypergeometric distribution is derived for the number of distinct types observed in a sample of n individuals from a population consisting of m types with r individuals in each type, without replacement and with it another individual of the same type.
Abstract: With the multivariate hypergeometric distribution as a background certain occupancy distributions useful in practical applications are derived. More specifically it is assumed that a sample of n individuals is drawn from a population consisting of m types with r individuals in each type, (i) without replacement and (ii) by returning the selected individual in the population and with it another individual of the same type. The distributions of the number Z of distinct types observed in the sample are obtained in both cases in terms of the numbers. Assuming, in addition to the m equiprobable types of individuals, the existence of a control type, say, with s individuals, the joint distribution of the number U of distinct types observed in the sample and the number V of individuals of the control type present in the sample is obtained in terms of the numbers C(n, k, r) and the marginal distribution of U in terms of the Gould-Hopper numbers. Using these distributions minimum variance unbiased estimators of the number m of types are derived. Moreover small sample tests based on the zero frequency are constructed.
21 citations
TL;DR: Whenever optimal estimates of variance components can be made attractive to users, it is thought that MINQUE or related estimates should be started and it would be a good deal to work on more effective ways of its computation.
Abstract: Standard methods for estimating variance components, such as HENDERSON's methods are based on equating well-known sums of squares to expectation. These methods are computationally simple and therefore widely used.
From a theoretical point of view we are not that happy about these methods. There is lack of theoretical background, there is no unique description of these methods and finally, we know very little about optimal properties of HENDERSON's estimates unless the model is totally balanced.
It was mainly this trouble which caused statisticians to develop an extensive theory on optimal estimation of variance components and among the mostly known contributors to this line of research was C. E. RAO. We believe that his MINQUE principle gave a new idea to statistical theory. It provides some kind of optimality and does not refer to the normal assumption which is in difference to the majority of alternative proposals made in literature. And even if one thinks of its theoretical background as being not much better than that of HENDERSON's method one has to accept the advantage of having a unique estimation procedure.
A difficulty is its calculation. The computational advice given by RAO requires inversion of matrices as high in dimension as the total number of observations is. This is, we believe, the main reason for its neglect by most of the people working on such kind of data. But among all estimates which perform any kind of optimality MINQUE seems still to be among the simplest to calculate. That is why we think, whenever optimal estimates of variance components can be made attractive to users, we should start with MINQUE or related estimates and it would be a good deal to work on more effective ways of its computation.
One way is to present explicit and easy handable formulae under several standard ANOVA models of which the simplest one is going to be studied in this paper. Analog results for more complicated cases are given in KLEFFE (1980). Having solved this major problem we may proceed by comparing new and traditional methods to find out about what estimate is to be recommended.
19 citations
TL;DR: In this paper, the efficiency of synthetic retrospective designs relative to that of the full cohort analysis when the association is studied using the logistic or proportional hazards model is examined. And the efficiencies of matched vs. unmatched designs are also examined.
Abstract: In many large cohort studies of association between a disease and a concommitant variable, only a small fraction of subjects develope the disease. Substantial computational expense can be avoided by restricting the analysis to the diseased cases and a random sample of disease-free controls. This paper examines the efficiency of such synthetic retrospective designs relative to that of the full cohort analysis when the association is studied using the logistic or proportional hazards model. Within this context the efficiencies of matched vs. unmatched designs are also examined.
15 citations
TL;DR: In this paper, the influence of outliers in one of the samples on Hotelling's generalized T10 is investigated by considering the directional derivate of the expected value with respect to the proportion of outlier in the disturbed population at the proportion zero.
Abstract: The influence of outliers in one of the samples on Hotelling's generalized T10 is investigated by considering the directional derivate of the expected value with respect to the proportion of outliers in the disturbed population at the proportion zero. To make the problem tractable, the estimate of the covariance matrix thereby is replaced by its expected value under the altered distributional assumptions. For the two sample case the influence of outliers on the variance of the test criterion is also investigated. The analytical findings are confirmed by simulation results.
Abstract: A modification of the numbers of degrees of freedom which makes the F ratio test of the equality of two variances applicable also in the paired case with incomplete data is suggested. Monte Carlo simulation studies indicate that the suggested test is reasonably powerful in many cases.
TL;DR: In this paper, an alternative to SATTERTHWAITE's approximative test strongly unbiased tests of BARTLETT-SCHEFFE type are considered to test hypotheses about fixed and random effects in mixed and random ANOVA-models with equal cell frequencies.
Abstract: As an alternative to SATTERTHWAITE's approximative test strongly unbiased tests of BARTLETT-SCHEFFE type are considered to test hypotheses about fixed and random effects in mixed and random ANOVA-models with equal cell frequencies. Explicite formulae are given to test hypotheses in the usual two- and three-way classifications and the four-way cross-classification. These formulae also can be used in the multivariate case.
TL;DR: In this paper, a model of the body length increase of a human reaching from the time of conception up to the end of adolescence is presented, where the whole growth process can be subdivided into independent partial processes for succeeding time periods of the individual's development each of which produces a more or less marked growth spurt.
Abstract: Starting point of the modelling procedure are measured courses of the body length increase of man (inverse problem) reaching from the time of conception up to the end of adolescence. First assumption: The whole growth process can be subdivided into independent partial processes for succeeding time periods of the individual's development each of them producess a more or less marked growth spurt. 2. Superposition of these partial processes means addition of the portions of body length which are generated by the spurts yielding in this manner the measured course of body length increase. 3. There is no change in dynamics for producing the several growth spurts, and this dynamics will be described by the differential equation of the logistic law of growth. These steps will be interpreted in control-theoretical terms. In this sense growth is a follow-up control process which is governed by the genetically fixed “biological program of growth” in form of a step function of reference values.
TL;DR: In this paper, three bivariate generalizations of the POISSON binomial distribution are introduced and the probabilities, moments, conditional distributions and regression functions for these distributions are obtained in terms of bipartitional polynomials.
Abstract: Three bivariate generalizations of the POISSON binomial distribution are introduced. The probabilities, moments, conditional distributions and regression functions for these distributions are obtained in terms of bipartitional polynomials. Recurrences for the probabilities and moments are also given. Parameter estimators are derived using the methods of moments and zero frequencies and the three distributions are fitted to some ecological data.
TL;DR: The correlated bivariate inverted beta distribution as discussed by the authors is constructed from the bivariate mixture of two independent gamma random variables whose scale parameters follow Kibble's correlated gamma distribution, and explicit expressions have been derived for the form of the joint probability density function, the joint cumulative distributive function and other statistical properties of interest.
Abstract: The correlated bivariate inverted beta distribution is constructed from the bivariate mixture of two independent gamma random variables whose scale parameters follow Kibble's correlated gamma distribution. Explicit expressions have been derived for the form of the joint probability density function, the joint cumulative distributive function and other statistical properties of interest. These results confirm and extend some of the conjectures of HUTCHINSON in connection with generalizations of probabilistic models of severity distribution arising from injuries sustained in two-vehicle head on collison.
TL;DR: In this paper, a linear regression model with random coefficients is considered and the estimation of the mean of the coefficient vector is considered, in turn involving the variances of random coefficients.
Abstract: For a linear regression model with random coefficients, this paper considers the estimation of the mean of coefficient vector which, in turn, involves the estimation of variances of random coefficients. The conventional estimation methods for it sometimes provides negative estimates. In order to circumvent this kind of difficulty, a proposal is forwarded and is examined in the light of existing ones.
TL;DR: In this article, it was shown that 3-point response curves from N individuals imply a second order correlation (triplet correlation) between the 3 series of repeated measurements if the curves are clustered as to their shapes.
Abstract: It is shown that 3-point response curves from N individuals imply a second order correlation (triplet correlation) between the 3 series of repeated measurements if the curves are clustered as to their shapes. Coefficients are defined and tests are suggested for triplet correlations. Nonparametric alternatives to ANOVA are discussed for repeated measurement designs involving shapeclustered response curves.
TL;DR: In this article, a discrete POISSON-inverse GAUssian distribution is obtained by compounding the poisson distribution with the inverse-GAUssians distribution.
Abstract: The discrete POISSON-inverse GAUssian distribution is obtained by compounding the POISSON distribution with the inverse-GAUssian distribution. The maximum likelihood of the parameter is discussed. Comparison with the POISSON, negative binomial, POISSON-LINDLEY and the generalized WARING distribution when fitting a distribution to accident statistics data is given.
TL;DR: In this paper, a class of ratio-cum-product-type estimators is proposed and its bias and variance to the first order of approximation are obtained for an appropriate weight ‘a' and good range of α-values, it is found that the proposed estimator is superior than a set of estimators (i.e., sample mean, usual ratio and product estimators, SRIVASTAVA's (1967) estimator, CHAKRABARTY's (1979) estimators) which are the particular cases of it.
Abstract: The problem of estimating the population mean using an auxiliary information has been dealt with in literature quite extensively. Ratio, product, linear regression and ratio-type estimators are well known. A class of ratio-cum-product-type estimator is proposed in this paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and good range of α-values, it is found that the proposed estimator is superior than a set of estimators (i.e., sample mean, usual ratio and product estimators, SRIVASTAVA's (1967) estimator, CHAKRABARTY's (1979) estimator and a product-type estimator) which are, in fact, the particular cases of it. At optimum value of α, the proposed estimator is as efficient as linear regression estimator.
TL;DR: In this article, the authors considered the situation where the multivariate distribution of certain variables X1, X2, Xp is changing with time in a population because natural selection related to the X's is taking place.
Abstract: The situation is considered where the multivariate distribution of certain variables X1, X2, …, Xp is changing with time in a population because natural selection related to the X's is taking place. It is assumed that random samples taken from the population at times t1, t2, …, ts are available and it is desirable to estimate the fitness function wt(x1, x2,…,xp) which shows how the number of individuals with Xi = xi, i = 1, 2, …, p at time t is related to the number of individuals with the same X values at time zero.
Tests for population changes are discussed and indices of the selection on the population dispersion and the population mean are proposed. The situation with a multivariate normal distribution is considered as a special case. A maximum likelihood method that can be applied with any form of population distribution is proposed for estimating wt.
The methods discussed in the paper are illustrated with data on four dimensions of male Egyptian skulls covering a time span from about 4500 B.C. to about 300 A.D. In this case there seems to have been very little selection on the population dispersion but considerable selection on means.
TL;DR: In this paper, a sequence of independent and identically distributed random values with continuous cumulative distribution function F(x) is considered and a record value of this sequence is defined if Xj ≤ max (X1, X2, X3, X4, X5, X6, X7, X8, X9, Xj−1).
Abstract: A sequence {Xn, n≤1} of independent and identically distributed random values with continuous cumulative distribution function F(x) is considered. Xj is a record value of this sequence if Xj ≤ max (X1, X2, …, Xj−1). We define
L(n)=min.(j!j>L(n−1.), Xj
TL;DR: In this article, the probabilities of cycles and components and their numerical distribution were derived for large random networks by computer experiments and combinatorical considerations. But the probability of cycles was not considered.
Abstract: Formulae for the probabilities of components and cycles and of their numerical distribution are obtained for large random networks by computer experiments and combinatorical considerations. Probability considerations are made and formulae for the occurrence and distribution of cycles and of components of certain number, size and structure are received for random networks.
TL;DR: An algorithm and the corresponding FORTRAN-program for the computation of the MANN-WHITNEY U-Test test statistic are introduced in this article, which is simpler than the familiar procedure using ranks.
Abstract: An algorithm and the corresponding FORTRAN-program for the computation of the MANN-WHITNEY U-Test test statistic are introduced which are simpler than the familiar procedure using ranks.
TL;DR: In this article, an unbiased variance estimator is proposed which as only information uses the ranks of the data with the additional property that it is unbiased for the finite variance, and its applicability is not confined to quantitative data but can be applied to ordinal data just as well.
Abstract: For some applications of the WILCOXON-MANN-WHITNEY-statistic its variance has to be estimated. So e.g. for the test of POTTHOFF (1963) to detect differences in medians of two symmetric distributions as well as for the computation of approximate, confidence bounds for the probability P(X1 ≥ X2), cf. GOVINDARAJULU (1968). In the present paper an easy to compute variance estimator is proposed which as only information uses the ranks of the data with the additional property that it is unbiased for the finite variance. Because of its invariance under any monotone transformation of the data its applicability is not confined to quantitative data. The estimator may be applied to ordinal data just as well. Some properties are discussed and a numerical example is given.
TL;DR: The exact generalization of GEHAN's (1965) two-sample test for arbitrarily censored survival data has been overlooked by subsequent work on the multisample problem as mentioned in this paper.
Abstract: The exact generalization of GEHAN's (1965) two-sample test for arbitrarily censored survival data has been overlooked by subsequent work on the multisample problem. We give this general covariance matrix and show how it may be used in test procedures. While this permutation test is less powerful than its competitors in cases where both apply, it may be used on types of data not previously discussed.
TL;DR: In this paper, all non-singular Gaussian Markov processes were determined and two simple specializations for them were given. And the parameters appearing in this context are estimated by the maximum likelihood principle, whereas the numerical calculation of them is done by help of the Gauss-Newton algorithm.
Abstract: To find appropriate models for growth processes we determine firstly all non-singular Gaussian Markov processes and give later on two simple specializations for them. The parameters appearing in this context are estimated by the maximum likelihood principle, whereas the numerical calculation of them is done by help of the Gauss-Newton algorithm. Final remarks concern the evaluation of a start vector for this algorithm with respect to the GOMPERTZ-function and the introduction of a simple simulation model.