bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Class of Ratio‐Cum‐Product‐Type Estimator
Authors: Sisodia B. V. S. , Dwivedi V. K. 
Published: May 2007

AbstractThe 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.
Goodness of Fit of Discriminant Functions from the Vector Space of Fixed Variates
Authors: Kabe D. G. 
Published: May 2007

AbstractAlternative proofs of some of KSHIRSAGAR's (1971) results on testing discriminant functions or canonical variables in the vector space of fixed variates are given. These results are derived in terms of the original variates unlike KSHIRSAGAR (1971) who derives the results by using random orthogonal transformations and triangular decompositions of the original matrix variates.
Multiple Decrement Analysis with Dependent Risks
Authors: Nour EL‐Sayed E. 
Published: May 2007

AbstractIn a competing risks problem where a well‐defined population is exposed simultaneously to several causes of death, interest has centered on the estimation of the probability of death from a given cause when one or more other causes have been eliminated. A basic component of all available procedures for estimating these probabilities is the assumption that the several causes of death act independently—an unrealistic assumption in the context of human and animal populations.This article considers the estimation of these probabilities assuming the existence ofinterdependencies among the various causes of death. A general formula is derived based on a given set of crude probabilities of death as well as the characteristics of the joint distribution of random variables indicating death from the various causes. This formula identifies alternative assumptions, less restrictive than that of independent risks, which may he used for estimation purposes.
Analysis of Detection Processes for Breast Cancer
Authors: Tallis G. M. , O'neill T. J. 
Published: May 2007

AbstractMost existing records of detection processes for breast cancer are in the form of cancer registries or are results of large clinical trials. Statistical modelling can be applied to these data sets to study various properties of breast cancer. In particular we estimate the probability of cure given the size of the tumour at detection, the distribution of tumour growth rates and the distribution of the size of the tumour at detection. There has been a strong recent interest in early detection methods. These consist of giving regular examinations, called screenings. The effect of screening design on the probability of cure is considered. The results of an existing screening trial are used to derive another estimate of the tumour growth rate distribution which agrees well both with our earlier estimate and the most widely used empirical estimate in the literature. The calculation of lead time, which is the time gained in detection when screenings are given, is also discussed.
On Two Measures of Unbalancedness in a One‐Way Model and Their Relation to Efficiency
Authors: Ahrens H. , Pincus R. 
Published: May 2007

AbstractThis 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.
The Estimation of a Multivariate Fitness Function from Several Samples Taken from a Population
Authors: Manly B. F. J. 
Published: May 2007

AbstractThe situation is considered where the multivariate distribution of certain variablesX1, X2, …,Xpis changing with time in a population because natural selection related to theX's is taking place. It is assumed that random samples taken from the population at timest1,t2, …,tsare available and it is desirable to estimate the fitness functionwt(x1,x2,…,xp) which shows how the number of individuals withXi=xi,i= 1, 2, …,pat timetis related to the number of individuals with the sameXvalues 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 estimatingwt.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.
Optimal Allocation, Precision, and Significance Tests
Authors: Finney D. J. 
Published: May 2007

AbstractHORN (1979) queried the recommended ratio where p is the number of treated groups to be compared with a control and n and n0 are the sizes of the treated samples and of the control. The rule was originally stated for maximizing the precision of estimates, and not for optimizing any aspect of significance tests. Although in applied statistics, significance tests are usually of far less importance, it is interesting (but scarcely surprising) that the same rule optimizes power and one or two related characteristics.
Zur „Genauigkeit”︁ bei J. G. Mendel
Authors: Hellmich K. 
Published: May 2007

AbstractWhen taking into account J. G. MENDEL's observed frequencies and comparing them with those noted down by BATESON, CORRENS and DARBISHIRE no „striking”︁ preciseness in accordance with the statement made by F. WELLING is to be noticed statistically. By means of the four‐field table measure K speculations as to a „too precise”︁ indication of frequencies are to be refuted in an easy way.
On the Theory for RYANS Universal Multiple Comparison Procedure with Treatment of Ties in the Ranks of Samples
Authors: Horn M. 
Published: May 2007

AbstractThe proposal of RYAN (1960) for multiple comparison procedures has not become well known despite of its universal applicability. Only his idea of adjusted levels has been used in a modified manner, cf. EINOT and GABRIEL (1975), WELSCH (1977), RAMSEY (1978). This article re‐introduces the procedure and demonstrates its broad applicability also as a nonparametric method. Above all an exact mathematical foundation is aspired. The case of ties in the ranks of samples has been taken into consideration.
Log‐linear Models for Polytomous Data
Authors: Formann Anton K. 
Published: May 2007

AbstractThe present study discusses two variants of linear logistic models for polytomous variables for „unordered”︁ and for „ordered”︁ categories (polydimensional and one‐dimensional model). The ML‐estimation equations and the possibilities to test the validity of the model are given for both. A test for goodness‐of‐fit (external validity) and a test for equality of the parameter estimates for split data (interval validity) are suggested. In addition, statistical tests for the significance of individual parameters on the basis of the information matrix and likelihood ratio tests for one or more parameters are described. The presentation is completed by an empirical example from the area of audiology.
Bivariate POISSON Binomial Distributions
Authors: Charalambides Ch. A. , Papageorgiou H. 
Published: May 2007

AbstractThree 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.
On Maximum Likelihood Solutions for Exponential Survival Models
Authors: Beck G. J. , Chiang C. L. 
Published: May 2007

AbstractStochastic survival models which adjust for covariate information have been developed by BECK (1979). These models can include one or two living states and several competing death states. The transitions between states are assumed irreversible and the transition intensity functions are assumed to be independent of time but dependent upon the covariates. This paper presents explicit solutions of the maximum likelihood equations for such models when there are only one or two dichotomous covariates. Two applications of these models are discussed where survival in two or four groups are compared.
Über Gausssche MARKOV‐Prozesse als Wachstumsmodelle
Authors: Berg L. 
Published: May 2007

AbstractTo 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.
On the Convergence of an Algorithm of Jones
Authors: Catchpole E. A. 
Published: May 2007

AbstractPearce (1976) proposed the use of the variance matrix for design block experiments. Jones (1976) gave an iterative formula for, but stated that the iteration failed to converge for some block designs. We derive necessary and sufficient conditions for the convergence of JONES' iteration. We also note that a simple modification to JONES' iteration will ensure its convergence.
Explicite Formulae of Exact Tests in Mixed Balanced ANOVA‐models
Authors: Seifert B. 
Published: May 2007

AbstractAs an alternative to SATTERTHWAITE's approximative test strongly unbiased tests of BARTLETT‐SCHEFFÉ 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.
Product Cum Difference Method of Estimation Using two Auxiliary Variables
Authors: Singh R. Karan , Ray S. K. 
Published: May 2007

AbstractProduct method of estimation (MURTHY, 1964) using supplementary information on an auxiliary variable having high negative correlation with the main variable under our study, is well known. In this paper, we propose product‐cum‐difference method of estimation for the population total and the product of population parameters when supplementary information is available on two auxiliary variables. A comparison of product‐cum‐difference method of estimation with the usual product method of estimation using single auxiliary character and the estimators by SINGH (1965) for the estimation of product of population parameters has been made along with an empirical study.
The Classical Assortative Mating Process when more than one Continuous Characteristic is Considered
Authors: Wilson Susan R. 
Published: May 2007

AbstractIn this article we give a general proof for the existence of the equilibrium position for the joint phenotypic distribution of several continuous characteristics, in a population which reproduces assortatively, and wherein generations are overlapping. This model is a more realistic one for human populations, compared with models arising from consideration of a single characteristic. By placing realistic conditions on the assortation process in the equilibrium position it is found that the consequences are even less realistic and less satisfactory compared with conclusions from single (continuous) characteristic models involving assortative mating. This suggests that a different approach to modelling the assortation process may be required, and this is discussed alsewhere (WILSON, 1981).
On a restricted occupancy model and its applications
Authors: Charalambides Ch. A. 
Published: May 2007

AbstractWith the multivariate hypergeometric distribution as a background certain occupancy distributions useful in practical applications are derived. More specifically it is assumed that a sample ofnindividuals is drawn from a population consisting ofmtypes withrindividuals 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 numberZof distinct types observed in the sample are obtained in both cases in terms of the numbers. Assuming, in addition to themequiprobable types of individuals, the existence of a control type, say, withsindividuals, the joint distribution of the numberUof distinct types observed in the sample and the numberVof individuals of the control type present in the sample is obtained in terms of the numbersC(n, k, r) and the marginal distribution ofUin terms of the Gould‐Hopper numbers. Using these distributions minimum variance unbiased estimators of the numbermof types are derived. Moreover small sample tests based on the zero frequency are constructed.
On an Unbiased Variance Estimator for the WILCOXON‐MANN‐WHITNEY‐Statistic Based on Ranks
Authors: Hilgers R. 
Published: May 2007

AbstractFor 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.
On HÜHN's Notion of Optimal Sample Size in the χ2 Goodness of Fit Test
Authors: Rayner J. C. W. , Best D. J. 
Published: May 2007

AbstractHühn's notion of optimal sample size for the χ2 goodness of fit test is discussed. It involves minimising the achievable level of the test subject to a given nominal level. This ignores the power of the competing tests and can lead to an ‘optimal’ test that is uniformly less powerful than all the competing tests considered.
Note on a Test for Trend in Binomial Proportions Using Ranks
Authors: Bennett B. M. 
Published: May 2007

AbstractFor a 2xk contingency table when all the k groups fall into a natural order and for which a sequence of k values × may be assigned, ARMITAGE (1955) has suggested a X2(1) test statistic for the hypothesis Ht of a trend in the proportions; This note considers a statistic for Ht based on midrank values for the binary observations. It is shown that the proposed rank‐order test for Ht coincides with that of ARMITAGE (1955).
Stability Investigations of Linearized Systems with Random Structure
Authors: Rademacher P. 
Published: May 2007

AbstractThe relationship between complexity and stability of linearized systems, being characterized by structural parameters like dimension and connectance and interaction strength are investigated by computing relative frequencies of stability. The results are compared with those of other authors. Additionally systems with a special cyclic subsystem structure are investigated. Comparing the stability properties for structured and unstructered systems no increase in stability can be stated if systems are structures in the supposed way.
Application of Fast Fourier Transform in Electroencephalography
Authors: Matthies H. K. , Brödemann R. 
Published: May 2007

AbstractToday the Fourier Transform is also used in the analysis of biological time series with periodical parts. For N = 2M EEG sampling values the Fast Fourier Transform algorithm of COOLEY and TUKEY is applicable. For this a FORTRAN IV program EEG‐FFT has been developed for computation of power spectrum.At the data processing equipment EC 1040 the CPU‐time for 210 = 1024 EEG sampling values is smaller than 1.5 s.The FORTRAN IV program can be applied both in offline and online data processing.
Scale‐independent non‐parametric multivariate tolerance regions and their application in medicine
Authors: Abt K. 
Published: May 2007

AbstractBased on the principles introduced by TUKEY and FRASER, a method is proposed to construct non‐parametric multivariate tolerance regions of irregular multiplanar shape. Contrary to the regions of corresponding shape as constructed by Tukey and Fraser, the tolerance regions constructed according to the proposed method can be shown to be invariant to linear scale transformations. In medical applications, where the concept of multivariate tolerance regions can be used to define “normal” regions for p ≦ 2 variables with measuring units generally differing from each other, the quality of scale‐independency of the regions is essential. With reference to the method proposed, sample size determination and some important aspects of the use of multivariate tolerance regions are discussed.
On Kernel Methods of Estimating Marginal Radial and Angular Probability Density Functions
Authors: Byth Karen 
Published: May 2007

AbstractSpatial point patterns which possess a natural origin are considered. Two ways of estimating the marginal radial and angular probability density functions associated with the stochastic process underlying such a pattern are presented. These methods are based on one and two‐dimensional kernel functions respectively. The angular density estimate can be used to detect angular trend and to test for angular uniformity within a particular sector about the origin. The two methods of estimation produce essentially the same results. That based on the one‐dimensional kernel is recommended because it is computationally simpler.
Bioassay Approach to Prescribe Safe‐limits of Exposure to Non Ionizing Radiation in Ecosystems
Authors: Neelakantaswamy P. S. , Meng Fong Ah 
Published: May 2007

AbstractA biological assay that quantifies hazardous response in living matter to an electromagnetic stimulus, is evolved. Considering the various susceptible aspects of physio‐anatomical systems constituting a living subject, a dominance criterion to determine an optimum all‐or‐none response limit of exposure to electromagnetic pollutions is established. Based on the statistics of proneness and susceptibility of discrete physio‐anatomical parts of living systems (biotic components) to polluting radiations (abiotic environment), the stochastic nature of damage involved is considered to formulate a quantal index which specifies a “safe” intensity‐level of electromagnetic radiation to which living systems can be exposed without encountering any deleterious effects. The locations of vulnerable parts which are affected by radiation are identified through random mosaic modeling of a test subject. Using this model, a susceptance priority sequence of biotic components is constructed. This sequence is then terminated at a point of weightage proportional to the diversity of victim population. The biotic species falling within this limit of truncation are subsequently studied to assay the tolerance (optimum lethal dose) of the test subject to the radiation in question. The possibility of simulating the entire ecological system under consideration by means of a microprocessor is suggested.
Zur Bestimmung des Wanderungsprozesses
Authors: Tziafetas G. N. 
Published: May 2007

AbstractIn this paper we analyse the migration process in connection with the birth and death process. We assume that the populations are distributed spatially and are subject to birth, death and migration to or from neighbouring populations. Furthermore, we distinguish between populations with infinite and finite number of colonies. By this way we calculate the cumulant of first order.First this problem was studied by BAILEY and ADKE for time‐dependent rates. Similarly PURI has specialized the problem for right migration (vij = 0 for i ≢ j). Finally RENSHAW had the same result with other procedures.
Minimum Variance Unbiased Estimation in a Bivariate Modified Power Series Distribution
Authors: Shoukri M. M. 
Published: May 2007

AbstractThe functional form of the class of Bivariate Modified Power Series Distributions is considered. The probabilities are functions of two unknown parameters ϑ1 and ϑ2. The necessary and sufficient conditions for the existence of a minimum variance unbiased estimator for a parametric function of ϑ1 and ϑ2 are given.
The Use of a Symbol Processing Computer Language in Point Estimation of Parameters and in Construction of Confidence Intervals
Authors: Quednau H. D. 
Published: May 2007

AbstractThis paper presents a method to generate automatically computer programs which are necessary for parameter estimation, hypothesis tests and construction of confidence intervals by the maximum likelihood method. The spectral or density function of the random variable is arbitrary, but must be known and given in closed form. The programming language used is the symbol processing language LIBAFORM, whose statements are interpreted by a package of LISP‐routines. The application of the method is illustrated by the analysis of a linear model whose residuals follow a logarithmic F‐distribution, and the analysis of a dose‐response curve.
The Exact Evaluation of 2‐way Cross‐classifications: An Algorithmic Solution
Authors: Kannemann Klaus 
Published: May 2007

AbstractAn algorithm is presented which permits the exact evaluation of sparse cross‐classifications and contingency tables. It may be used to compute the exact point and cumulative probabilities of observed values of the X2‐like test statistic, or even of the observed tables themselves. For sparser cases, it may also be used to generate part or all of the exact distributions. As a corollary, an operational solution is presented to the enumeration problem of rectangular integer matrices with arbitrarily fixed row and column sums. Exact results obtained with the algorithm accompany this presentation, giving, further support to the recommendation that the Gamma distribution be preferred to the Chi‐square in sparse cases.
A FORTRAN Program for the KASTENBAUM‐BOWMAN Test
Authors: Würgler F. E. , Berchtold W. 
Published: May 2007

AbstractThe KASTEITBAUM‐BOWMAN test allows the determination of the significance of a mutation frequency. A simple FORTRAN program for the KASTENBAUM‐BOWMAN test is given. The subroutines may be incorporated easily into larger programs and allow to calculate the exact P value for the test.
The Statistical Significance of Mutation Frequencies
Authors: Würgler F. F. , Graf U. 
Published: May 2007

AbstractTRAUT has proposed a method for determining the statistical significance between a mutation frequency observed after treatment with a potential mutagen and a control frequency. The method is developed further by us for an easier practical use. A table for the minimal sample size in the region of interest for the sex‐linked recessive lethal test in Drosophila melanogaster has been calculated.TRACT'S test is compared with FISHER'S exact test and the KASTENBAUM‐BOWMAN test. TRAUT'S test turns out to be more sensitive than the other tests. This observation strongly supports TRAUT'S conclusion that his test should only be used if very accurate determinations of the spontaneous frequencies are available.