bluuebunny/crossref_metadata_2025 huggingface dataset:
A generalizing, analytic model for 2‐way cross‐classifications. extensions and ramifications. part 1
Authors: Kannemann K.
Published: May 2007

A generalizing, analytic model is developed for 2‐way cross‐classifications with fixed class sizes The model is expressed in closed form as a simple operator formula, and is readily extended to n‐way cross‐classifications, and to such cases where one or more cells are vacuous or fixed. The model permits easy derivation, by means of simple differential operators, of the exact power moments, product moments, and factorial moments of the cell frequencies. From this, the moments of the exact sampling distribution of the conventional x2‐statistic can be computed, which, in turn, leads to a reappraisal of the Chi‐square approximation for sparse and isotropic contingency tables. Here, the Gamma distribution is considered, and numerical results are presented that would suggest preference of the Gamma approximation over the Chi‐square in such cases.
Efficiencies in multivariate paired experiments
Authors: Jensen D. R.
Published: May 2007

Lower and upper bounds are given for the asymptotic efficiency of the paired T2 test relative to the two‐sample T2 test in comparative multivariate experiments. Consistent estimates for these bounds are illustrated numerically and their relevance to small samples is discussed. Conditions are given such that each procedure dominates the other globally; when these fail the sets of alternatives are characterized at which each procedure dominates the other locally.
Validity of f‐test in a randomized block design with missing data
Authors: Dash S. P.
Published: May 2007

In this paper the first two moments of the test criterion (Treat. S.S.)/(Treat.S.S. + Error S.S.) have been derived assuming that one observation corresponding to the first plot of the first block which is under treatment ‘m’ (say), is missing in a randomized block design with ‘V’ treatments and ‘r’ blocks. To keep the analysis simple the case of one missing observation has been considered. It is concluded that in general the design is not unbiased in YATES (1951) sense and the usual F‐test is satisfactory iff /(vr ‐ r ‐ 1)=(S ‐ S1)/(v ‐ 1) (r‐1), the block errors are homogeneous and (vr ‐ r ‐ 1) is large. The analysis of three unifornity trial data indicates that the first condition is the most important for the F‐test to be satisfactory.

However, if one observation is missing at random from some plot of some block, the F‐test is unbiased. If the block errors are homogeneous and (vr ‐ r ‐ 1) GT96, the F‐test also provides a good approximation to the corresponding randomization test in this case.
A model for the spread of an epidemic
Authors: Längeb H.
Published: May 2007

A temporally continuous and spatially discrete stochastic model for the spread of an epidemic within some set of holdings is constructed. A recursion formula is given for the probability that a certain set of holdings is infected at a certain moment. Moreover, under an additional condition (which will always be satisfied in practice) a formula for the expected value and the variance of the moment when a certain holding is infected the first time is given.
Application of nonlinear estimation in the exploration of dose‐response relationship
Authors: Postelnicu T. , Ursianu E.
Published: May 2007

In this paper a nonlinear model depending of one modifying factor to study the dependence of the PAPOVA virus reduction factor to the irradiant dose. In this model, least squares estimates of the parameters are obtained using the linearization method with the initial guesses values. An extension of the initial exponential model is proposed when the viral material is influenced by some modifying factors.
Probabilities P (Ss) for the friedman statistic
Authors: Likec J. , Laga J.
Published: May 2007

The probabilities P (Ss) for the FRIEDMAN statistic F = 12S/(np (p + 1)) are tabulated for p = 3, n = 14(1)25 and p = 4, n = 9, 10.
Estimation of the restricted variance of a normal population
Authors: Dabli P. V.
Published: May 2007

The maximum likelihood estimator of the variance of a normal distribution when it is known for certain that the variance is greater than or equal to a known positive constant is given and its properties are studied.
Use of prior information in simple random sampling
Authors: Dabli P. V.
Published: May 2007

Is is assumed that the population mean, to be estimated, is less than or equal to a known constant. An estimator is suggested which takes into account this information to advantage. It is also suggested that stratification coupled with the modified estimator can be best suited in such situations.
Measuring pairwise agreement among many observers
Authors: Schouten H. J. A.
Published: May 2007

Weighted kappa is defined as a measure of pairwise inter observer agreement. A weighted intra class kappa coefficient is proposed to measure agreement on a particular response category. An interclass kappa coefficient is proposed for each pair of response categories. Simple estimation procedures are presented for the case where the observers judging one subject are not necessarily the same as those judging another subject. Large sample standard errors are derived and a numerical example is given.
Principal component regression analysis applied in structure‐activity relationships. 2. flexible opioids with unusually high safety margin
Authors: Mager Peter P.
Published: May 2007

Multicollinearities among chemical regressor variables in structure‐activity relationships can be avoided using the principal component regression analysis. An example adapted from drug design (conformationally flexible opioids) shows the working technique.
EEG Feature extraction using parcor coefficients
Authors: Jindra R. H.
Published: May 2007

This study presents pattern recognition experiments of the electroencephalogram. The components of the feature vector are built up by Parcor coefficients which provide a simple structure of the covariance matrix. The BAYES classifier is implemented which is theoretically best in minimizing the error rate. The MAHALANOBIS classifier is used too by means of an averaged covariance matrix. The performance of the classifier is tested in experiment by computing the error rate.
Test d'ajustement gigogne
Authors: Chamayou J. M. F.
Published: May 2007

Pour dépouiller les résultats d'une expérience de biologie, on a mis au point une série de tests d'ajustement qui s'emboǐtent les uns dans les autres. Le premier test, un test mixte (continu, discret) permet de comparer deux échantillons, le second test permet, à l'aide dun estimateur du maximum de vraisemblance, d'ajuster une loi sur un échantillon à l'aide de l'estimateur défini sur le second échantillon et vice versa, lorsque les deux échantillons sont censés appartenir à la měme population.
A study of the effects of truncation in bivariate normal distribution
Authors: Gupta A. K. , Tracy D. S.
Published: May 2007

The moments of bivariate normal distribution, which is truncated with respect to both the random variables, are obtained by using the orthogonal expansion of the distribution and the properties of HERMITE polynomials. In particular the correlation coefficient of the truncated distribution is derived in terms of the actual correlation coefficient. In order to study the effect of truncation tables have been prepared of this correlation coefficient for certain given values of the actual correlation coefficient and for a few selected values of the points of truncation. A listing of the computer program for this purpose is also given.
Inequalities for estimative and predictive probabilities
Authors: Jensen D. R.
Published: May 2007

LetμEbe the estimative andμPthe predictive measures for assessing Gaussian probabilities. It is shown for convex symmetric setsAthatμE(A)μP(A) and that similar inequalities hold between members of a sequence of predictive measures. An application yields inequalities for generalized indices of atypicality associated with the two methods.
Discriminant functions for linear comparisons of means when covariance matrices are unequal
Authors: Misra R. K.
Published: May 2007

Situations exist, as in the biological example of discriminant analysis for natural hybridization, cited in the text, where (a) not all populations have equal variances, and (b) comparisions based on single degrees of freedom must be planned. This paper presents a statistical methodology of estimating discriminant functions for linear comparisons among k(<2) multivariate normal populations, and of testing their significance, when these populations have unequal covariance matrices.
Note on combining risks using a logistic discriminant function approach
Authors: Lachenbruch P. A.
Published: May 2007

A simple method for combining risks based on repeated observations on an individual is presented. Implications of this model are explored for several special cases, and an example is presented.
Entwicklung eines dynamischen modells der stoffproduktion von zuckerrüben mit hilfe der multiplen regressionsanalyse
Authors: Hoffmann F.
Published: May 2007

If data are available which fulfil sufficiently the demands of statistics, and if physiologically plausible hypotheses can be formulated then it is possible to identify models by means of multiple regression analysis which simulate approximatively the behaviour of a crop within the range of the used data. A statistical as well as a physiological evaluation of the numerical results is necessary at every step of the calculation. The model consists of two equations describing the net assimilation rate and the distribution of the produced dry matter to leaves and roots. Some modification of the model are discussed, one of them with time‐dependent parameters. The following influencing variables are taken into account: leaf area or leaf mass, global radiation, nitrogen content of the leaves, and water stress, the latter being calculated from available soil moisture and potential evaporation. One version of the model together with an algorithm of dynamic optimization was used to control the water status of sugar beet in field trials.
Estimation of Linear Regression Model with Random Coefficients Ensuring Almost Non‐Negativity of Variance Estimators
Authors: Srivastava V. K. , Mishra G. D. , Chaturvedi A.
Published: May 2007

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.
A 2‐step procedure for comparing binomial populations available when given differences are to find out
Authors: Horn M. , Kanka U.
Published: May 2007

A two‐step procedure for comparing two binomial probabilities is presented. The method is compared with the exact test of FISHER. In average it needs essentially smaller sample sizes. In situations like drug screening it is desired to minimize the type II error rates for great differences of the binomial probabilities and to maximize it for small differences, simultaneously. In this point the method is superior to the FISHER test. Examples from drug screening demonstrate the advantages of the method.
A Phenomenologic‐mathematical Model of Growth Dynamics
Authors: Peil J. , Helwin H.
Published: May 2007

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.
Optimal Immunization and Isolation Policies for the GREENWOOD Chain‐Binomial Epidemic Model
Authors: Lefèvre Cl.
Published: May 2007

Optimal control for the GREENWOOD chain‐binomial epidemic model is examined when control action is effected by immunization of susceptibles, isolation of infectives, or a combination of immunization and isolation in a way which minimizes the social cost of the epidemic and the cost of control over a given planning horizon. Optimal policies can be easily found for the deterministic version of the model. For the stochastic version, optimal policies are of much more complicated form and are only described in the situation when the probability of a given susceptible being infected is either small or large. This paper continues and corrects the work of DAYANANDA and HOGARTH (1977, 1978).
On the Use of the Negative Binomial in Epidemiology
Authors: Bennett B. M.
Published: May 2007

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.
On the Determination of Numerical Density of Cell Organelles Using Mitochondria as an Example
Authors: Wassilew G. , Guski H. , Meyer R.
Published: May 2007

Methods of determining the numerical density of cell organelles described in literature were critically reviewed in a morphometrical and stereological study of muscle cell mitochondria (heart muscle cells, diaphragm cells, sceletal muscle cells). A review of the method described by WEIBEL and GOMEZ showed that the numerical density of the mitochondria depends to a great extent on their shape and not so much on their size distribution. For this reason serial sections should be used to determine the shape factor in biological objects of unknown geometric shape.

Generally, the numerical densities of mitochondria determined by using the method proposed by DEHOFF and RHINES were higher than those obtained with the method described by WEIBEL and GOMEZ. This is attributed to certain corrections used in the former method.

Elaborate computations are generally involved and the geometric shapes of the object examined must be known in order to determine the numerical density of cell organelles or of other biological structures. The numerous sources of error involved in these methods give this parameter the character of an objective estimate. For this reason it is recommended that the value obtained should be checked by determining a two‐dimensional parameter. Our examinations of heart muscle mitochondria showed good agreement between the two parameters.
An Algorithm for the Mann‐Whitney U‐Test
Authors: Pittner P. M.
Published: May 2007

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.
Defining and Detecting Second Order Correlations in Repeated Measurements Designs
Authors: Lienert G. A.
Published: May 2007

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.
A Model for Censored Survival Data When There is an Intervening Event
Authors: Higgins J. E.
Published: May 2007

A model is discussed for incorporating information from a time‐dependent covariable (an intervening event) and covariables independent of time into the analysis of survival data. In the model, it is assumed that individuals are potentially subject to two paths to failure, one including the intervening event and the other not. Additional assumptions are that failure times associated with the two paths are independent and that the time to failure subsequent to the intervening event is dependent on the intervening event time. Allowing the underlying hazard rates for the model to follow a WEIBULL form, use of the model and methods for fitting and hypothesis testing are illustrated by application to a follow‐up study involving industrial workers where disability retirement was the intervening event. Extensions of the model to accommodate grouped survival data are presented.
A Stochastic Model for Oviposition Tactics in the Bean Weevil
Authors: Janardan K. G. , Srivastava R. C. , Taneja V. S.
Published: May 2007

In a recent paper, MITCHELL (1975) experimentally investigated the oviposition behavior of weevils on mung beans. In this paper, we develop a stochastic model to study the oviposition tactics of the female weevils on beans.
Formulas for the Computation of the WILCOXON Test and other Rank Statistics
Authors: Kummer G.
Published: May 2007

A simple program for the computation of the WILCOXON test is introduced, which is suitable for implementation on a programmable desk computer. The allocation of ranks Ri is not necessary (see BERCHTOLD, 1979).

In an analogous manner any ranks respectively rank sums also can be calculated, so that any test criterion or statistical estimate called rank statistic, may be completely constituted by computer programs without explicitely ranging of values.
On Some Nuisance Parameter Free Uniformly Most Powerful Tests
Authors: Kabe D. G. , Laurent A. G.
Published: May 2007

TAKEUCHI (1969) provides a uniformly most powerful (UMP) one side test for testing the location parameter of the two parameters exponential model when the scale parameter is unknown. The power of his similar size α test depends, however, on the unknown scale parameter. In this case and in more general situations when there exists a sufficient statistic for the nuisance parameter, the theory of generalized THOMPSON's distributions, more specifically, the Thompsonization of a test statistic, LAURENT (1959, 1972) provides a UMP test whose power does not depend on the nuisance parameter. Examples of application of the general nuisance parameter free test procedure include here the truncated exponential, the inverse Gaussian, and the geometric distributions.
A Test for the Equality of Variances in the Paired Case with Incomplete Data
Authors: Ekbohm G.
Published: May 2007

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.
Some New Aspects of 2 × 2 Table Measures and Their Applications
Authors: Börzsönyi L.
Published: May 2007

The paper deals with the analysis of 2 × 2 table measures and describes several new possibilities for applying them. An estimate is given for HELLMICH's asymmetric K‐measure and a possible extension of the contingency concept in a special 2×2 case is presented. The concept introduced and the recommended computer application of the 2×2 table measures is supported by new results obtained for the relationship between jaw joint pains and noises examined earlier by F. SCHMID and C. ZSCHEGE. With a larger number of observations the opportunity arises for a deeper analysis of this dental problem using path analysis. The plan of evaluation and the conncetion between the variables examined is illustrated by a path‐diagram.

The association tables determined on the basis of the (C) values introduced during the examination of jaw joint disturbances using association analysis draw attention to the special role of the left side of mastication. The paper raises ideas for further generalisations and indicates where further research is needed.
On the Discrete POISSON‐Inverse GAUSSian Distribution
Authors: Shaban S. A.
Published: May 2007

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.
Mean Square Error Comparison for MINQUE, ANOVA and Two Alternative Estimators Under the Unbalanced One‐Way Random Model
Authors: Ahrens H. , Kleffe J. , Tenzler R.
Published: May 2007

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.
Accuracy Analysis with Special Reference to the Prediction of Grassland Yield
Authors: Allen O. Brian , Raktoe B. L.
Published: May 2007

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.
On the robustness of Hotelling'sT2
Authors: Bauer P.
Published: May 2007

The influence of outliers in one of the samples on Hotelling's generalizedT10is 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.
A More Powerful Simultaneous Test Procedure in Configural Frequency Analysis
Authors: Lehmacher W.
Published: May 2007

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.
A Multivariate Permutation Test for the Analysis of Arbitrarily Censored Survival Data
Authors: Marcuson R. , Nordbrock E.
Published: May 2007

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.
The MARKOV Process Approach to Survival Analysis
Authors: Tan W. Y.
Published: May 2007

Consider a two organs system for which one of the two organs must function for the individual to survive. This paper derives the survival probability distributions under more general situations by adopting Markov process approach, thus providing extensions of results given in GROSS, CLARK and LIU (1971) and KODLIN (1967). The results obtained are then extended to a k‐organs system.
Effect of Non‐normality on Response to Selection in small Populations
Authors: Rao M. Gopinath , Jain J. P.
Published: May 2007

The expressions for the r‐th largest standardised deviate have been derived for beta, gamma, exponential and log‐normal distributions. Using these expressions the intensities of selection have been computed for different parametric values of the distributions and of p, the proportion saved for samples of size upto 10 and compared with the corresponding values for normal distribution. The normal approximation to beta and gamma distributions is seen to be quite robust in predicting response to selection under moderately heavy and low cullings.
Random Networks of Catalytie Biochemical Reactions
Authors: Sonntag I. , Feistel R. , Ebeling W.
Published: May 2007

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.
On the Second‐Order and Orientation Analysis of Planar Stationary Point Processes
Authors: Ohser J. , Stoyan D.
Published: May 2007

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.
GOMPERTZ Model with Heredity in Random Environment
Authors: Prajneshu
Published: May 2007

In this paper we investigate the GOMPERTZ model in a randomly varying environment after incorporating the aspect of heredity. Exact expressions for the first two moments of the logarithm of population size are obtained. Special case of the dichotomic MARKOV process being a white noise process is considered. The stability of the system is also discussed.
An Alternative Approach to Modelling the Assortative Mating Process
Authors: Wilson Susan R.
Published: May 2007

In this article we demonstrate how the difficulties encountered from consideration of two‐sided assortation for a characteristic (or set of characteristics) in human populations can be overcome. This is achieved, essentially, by postulating a socio‐environmental variable (based on an individual's lifetime experiences) over which individuals are mating assortatively. The value an individual has on this scale determines his mean value for the characteristic under consideration. In other words, there is a relationship between the characteristic and the socioenvironmental scale. As well, individuals may be mating assortatively for the characteristic under consideration (although not necessarily). Thus we achieve assortative mating for a single characteristic as a result of mixing, simultaneously, over more than just one variable. Expansions to more ‘mixing’ scales than a single socio‐environmental variable are quite straightforward.
On Asymptotically Distribution‐Free Confidence Bounds for P (X1≥X2) Based on Samples not Necessarily Independent
Authors: Hilgers R.
Published: May 2007

If X1, X2, denote the random variables of measurement under two treatments then the probability P (X1 ≥ X2) is a quantity of great practical interest, especially if we consider both to be measured for the same unity. In this case the random variables cannot be assumed to be independent any longer. The following paper describes a procedure to compute approximate confidence bounds for P (X1 ≥ X2) where correlations between X1, X2 are admitted as well as between replications of the Xj. There is some relation to the FRIEDMAN‐statistic with or without repeated measurements and as a special case to the sign‐test. Application may be extended to ordinal data.
On the Modified and Inflated Discrete Distributions
Authors: Lingappaiah G. S.
Published: May 2007

Firstly, a modified bivariate discrete distribution is considered where a set of counts are misreported as another set of counts with different modification rates. Variances and covariances are put in the closed form and for the case when all modification rates are the same, these variances and covariances are expressed as parabolic functions and they are actually evaluated for the bivariate negative binomial. Regarding the asymptotic distributions of the estimates, elements of variance‐covariance matrix are obtained. Next, a multivariate inflated discrete distribution is taken up. For the case of inflated multivariate negative binomial, Bayesian estimates of inflation as well as those of parameters are given.
Nonparametric, GINI‐like Measures of Location and Dispersion
Authors: Lienert G. A.
Published: May 2007

GINI's nonparametric measure of dispersion, defined as the mean of (n/2) pairs of a sample of n measurements, is modified for triplets. That way a GINI‐like measure of location G* is defined as the mean of the (n/3) triplet medians, and a GINI‐like measure of dispersion is defined as the mean of the (n/3) triplet ranges. G* and g* are less sensitive to outlier measurements than are the corresponding parametric measures, arithmetic mean and standard deviation, in small samples. Applications and application‐related problems are discussed.
Methods of Discrimination Among Stochastic Models of the Negative Binomial Distribution with an Application to Medical Statistics
Authors: Rockhold F. W. , Kilpatrick S. J.
Published: May 2007

The Negative Binomial Distribution (NBD) can be derived from several underlying stochastic processes. For the NBD to be useful in practice as a descriptive model, it would be of interest to know which underlying process it is characterizing. In this paper, methods for discriminating among three different NBD underlying processes, proneness, linear contagion, and spells, are developed and studied. The methods are based on the characteristics of the processes and employ the theory of the bivariate NBD and waiting times. The NBD has been shown to consistently fit data on the incidence of disease. Knowledge of the underlying process generating the data is important for meaningful interpretation of such findings.
The Correlated Bivariate Inverted Beta Distribution
Authors: Lee P. A.
Published: May 2007

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.
Sample Sizes in Sequential Survival Clinical Trials
Authors: Nagelkerke N. J. D. , Hart A. A. M. , Strackee J.
Published: May 2007

In survival clinical trials the response, i.e. (time to) death is delayed. As a result there are at any time patients that have not responded, yet. Given a stopping rule based on the number of deaths, the distribution of the total number of patients that will enter the trial is examined. Besides, a simple approximation to the expected number of patients is presented.
On a Characterization of the Exponential Distribution by Weak Homoscedasticity of Record Values
Authors: Ahsanullah M.
Published: May 2007

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<XL(n−1)), with L(0) = 1.

Let Zn=XL(n)− XL(n−1), n ≤ 1. We will show that the conditional variance of Zn given XL(n−1)=x does not depend on × if and only if F(x) is exponential.
A Product‐Type Estimator in Double Sampling
Authors: Ray S. K. , Singh R. Karan
Published: May 2007

The use of ratio and product estimators, using auxiliary information, for estimating the mean of a finite population is well known. The efficiency of ratio estimator or product estimator is high depending on whether the auxiliary character is highly positively or negatively coorelated with the main character of interest. This paper proposes a product‐type estimator which is more efficient than the usual ratio and product estimators in practical situations. We consider the case of double sampling from which the single sampling results may easily be derived.
On the Bayeaian Estimation with Changing Failure Rate
Authors: Gupta R. P. , Shah S. M.
Published: May 2007

In certain‐life experiments it may happen that the failure rate may change after some initial period of time. Thie meane that the failure rate during certain interval of time and that of thereafter will differ significantly. Thie suggests a failure model in which one failure rate is assumed to be operative during period of time, say[0, T]. and another failure rate ie operative thereafter, that is after time T. In thie paper, Bayesian point estimates of these fnilure rates are obtained when underlying probability law law is exponential and T is known.
Mathematical Modelling of a Class of Paleontological Evolution Processes
Authors: Stoyan D. , Stoyan G.
Published: May 2007

The time‐dependent behaviour of number of genera in taxa replacing one another phylogenetically is studied with the help of a simple differential equation model with time‐dependent or state‐dependent coefficients.
On the WILCOXON‐MANN‐WHITNEY‐Test as Nonparametric Analogue and Extension oft‐Test
Authors: Hilgers R.
Published: May 2007

In the present paper some basic aspects of the WILCOXON‐MANN‐WHITNEY‐test under various assumptions concerning the underlying distributions are studied. Starting with a formal analogy to Student'st‐test its specific sensibility is worked out and the connexion to the problem of testing differences in location is discussed in detail as well as to the model with ordered alternatives. Further a counter example is given showing that the common verbal formulation the WILCOXON‐MANN‐WHITNEY‐test being a test on ‘differences in distribution’ in general is misleading. As an example of an extended application of the WILCOXON‐MANN‐WHITNEY‐statistic the test of POTT‐HOFF(1963) on differences in medians of symmetric distributions is treated together with a discussion on suitable variance estimators to guarantee appropriate asymptotic distribution.
On Generalized Indices of Diagnostic Efficiency
Authors: Bennett B. M.
Published: May 2007

The usual definitions of sensitivity, specificity and predictive value of a diagnostic testTrefer only to the situation of the presence or absence of disease. There is then question of the appropriate extensions of these definitions in cases where there are more than two diagnostic categories, especially with ordered or graded responses. This paper deals with some aspects of this problem. An example with the data of BERGESONand STEINFELD(1974) on gradings of fever in children by palpation is analyzed, using the methods discussed in this paper.
Comparing two independent binomial proportions by a modified chi square test – Required sample sizes
Authors: Schouten H. J. A.
Published: May 2007

An approximate formula is derived for determination of the sample sizes needed to detect a difference between two binomial probabilities.
Stochastically Independent Components in the Analysis of Variance
Authors: Drwięga T.
Published: May 2007

In this paper an analysis of a sum of squares for linear hypothesis in a fixed linear model is presented. The analysis is based on a partition of sum of squares into independent components. These components are treated as sums of squares for hypotheses implied by an overall one. In the special case components of a sum of squares are distributed with one degree of freedom each and hypotheses concern single parametric functions. In the model not of full rank the form of a sum of squares is transformed before partitioning. The case of the model for cross classification is considered in details. Next the cases of the model of full rank and the one with restrictions on parameters are discussed. The model for balanced design with unweighted restrictions on parameters is considered in details. In this case sume of squares for orthogonal contrasts are obtained from analysis of the sum of squares for hypothesis concerning main or interaction effects.
Canonical Analysis
Authors: Krzyśko M.
Published: May 2007

Several fundamental properties of canonical variates are developed. In addition, the equivalence of the redundancy coefficient and the composite coefficient of determination is demonstrated; the latter is used in evaluating the prediction of input variables by canonical variates.
Tables of the critical values for simultaneous and sequential Bonferroni‐z‐tests
Authors: Lienert G. A. , Ludwig O. , Rockenfeller K.
Published: May 2007

Simultaneous and sequential BONFERRONI‐tests (HOLM, 1979) are going to replace the traditional global tests (ANOVA, PEARSON‐χ2). To facilitate (sequential) BONFERRONI‐evaluation, BONFERRONI‐test limits for the normal distribution are tabulated for r = 1(1)100, 100(2)300, 300(5)800, 800(10)1600, 1600(20)3200, 3200(50)10000 tests and for some conventional alphas in one‐ and two‐sided alternatives.
Some Third‐Order Rotatable Designs
Authors: Huda S.
Published: May 2007

Some new third‐order rotatable designs are obtained in 5, 6, 7 and 8 dimensions. Many of these designs are of a sequential type and some require fewer experiments than the known designs with minimal number of experiments.
Using Ranks in Parallel Line Assays
Authors: Pettitt A. N.
Published: May 2007

An approximation to the likelihood of a sample, based on the ranks of the observations only, is used to analyze data from a biological assay. Inferences, depending only on the ranks of the observations, are made about the potency and about the validity of assumptions made in the analysis. Inferences are made in both Bayesian and sampling theory frameworks. An example of parallel line assay is given.
On the COLTON Model for Clinical Trials with Delayed Observations‐Dichotomous Responses
Authors: Langenberg P. , Srinivasan R.
Published: May 2007

In the COLTON model for clinical trials a choice is to be made between two medical treatments where there is a known patient horizon N. In an earlier paper we studied the COLTON model under the additional assumption that there is a time lag between the administration of the treatments and the availability of the responses where the responses are normally distributed. Here we extend the results of the earlier paper to the case where responses are dichotomous. The relative performance of two simple procedures for dealing with the patients who arrive during the waiting period between the end of the administration of treatment in the trial phase and observation of the final trial response is discussed within a BAYESIAN framework.
Estimation of the P(CS) with a Computer Program
Authors: Dudewicz Edward J.
Published: May 2007

In the area of ranking and selection, recent papers have presented procedures which attempt to allow experimenters to take at least partial advantage of more‐favorable configurations of the population parameters (compared to the least‐favorable configuration). The current paper presents a computer program which allows experimenters to dispense with all of inequalities, an indifference‐zone, and known equal variabilities in their assessment of the probability of correct selection. It has additional uses in implementation of recently‐proposed sequential adaptive selection procedures.
How Large is the Probability for the Estimate of a Variance Component to be Negative?
Authors: Verdooren L. R.
Published: May 2007

For a balanced one‐way classification, where the normally distributed observations obey a random modelyij=μ+bi+cijwith two variance components var (bi) = δand var (cij) = δ, the probability is given that the analysis of variance estimate of δwill be negative. This probability depends on δ/δand the degrees of freedom in the ANOVA table. Tables for this probability are given. If the normally distributed observations obey an intra‐class correlation model, the probability that the Mean Square between groups is smaller than the Mean Square within groups can also be evaluated from the given tables.
Rank Tests for correlated Random Variables
Authors: Brunner E. , Neumann N.
Published: May 2007

In this paper we consider the asymptotic distribution of linear rank‐statistics allowing certain dependencies between the random variables. General theorems will be given, from which the results contained in SEN(1967a, 1967b, 1968), MEHRA/SEN(1969) and PURI/SEN(1971) can be derived. Applying these theorems we can derive ranktests for the two‐sample problem for tied observations, for the two‐factor mixed model with random interaction and for a hierarchical design. The distribution of the proposed teststatistics for small sample sizes is considered by Monte‐Carlo studies.
Models for irreversible processes, based on cross‐sectional data
Authors: Bauer P. , Binder K. , Husinski I. , Kleinert W. , Künzel W. , Scheiber V. , Überhuber C. W. , Westphal G. , Wohlzogen F. X.
Published: May 2007

The analysis of the time dependent behavior of an irreversible all‐or‐none process on the basis of data from cross sectional surveys requires special methods. Assuming a pure death process three models of different degree of sophistication have been developed, mathematically analyzed and applied to one particular example: the caries attack on the permanent teeth of children.
A Class of Ratio Cum Product‐Type Estimator in Double Sampling
Authors: Sisodia B. V. S. , Dwivedi V. K.
Published: May 2007

A class of ratio cum product‐type estimator is proposed in case of double sampling in the present paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and a good range of α‐values, it is found that the proposed estimator is more efficient than the set of estimator viz., simple mean estimator, usual ratio and product estimators, SRIVASTAVA's estimator (1967), CHAKARBARTY's estimator and product‐type estimator, which are in fact the particular cases of it. The proposed estimator is as efficient as linear regression estimator in double sampling at optimum value of α.
Four Factor Balanced Optimal Designs of Resolution V in Terms of a Modified Trace Criterion
Authors: Nigam A. K. , Gupta V. K. , Bora A. C.
Published: May 2007

Balanced optimal two level fractional factorial designs of resolution V have been reported in series of papers by SRIVASTAVA and CHOPRA (1971a, 1971b, 1974) and CHOPRA and SRIVASTAVA (1973a, 1973b). The optimality criterion considered by them is the trace optimality which implies minimisation of the average variance of the estimated effects which include the general mean μ, main effects, Ai, and first order interactions, Aij. In the present work some new optimal designs have been obtained on the basis of a modified criterion of trace optimality. The criterion requires minimisation of the average variance of each of the main effects, two factor interactions, etc. separately instead of minimising average variance of all the estimated effects.
Measuring Pairwise Agreement Among Many Observers. II. Some Improvements and Additions
Authors: Schouten H. J. A.
Published: May 2007

Weighted kappa was defined as a measure of pairwise interobserver agreement for the case where the observers judging one subject are not necessarily the same as those judging another subject. In this paper improved formulas for the large sample variance of the weighted kappa statistic are derived, a new definition of interclass kappa coefficients is suggested, and the intraclass correlation coefficient is shown to be a special case of weighted kappa.
Orthogonal Components of the Kruskal‐Wallis and Related K‐sample Linear Rank Statistics
Authors: Koziol J. A.
Published: May 2007

It is shown that the KRUSKAL‐WALLIS statistic may be decomposed into components designed to detect trends in the underlying distributions. Extensions to other K sample linear rank statistics and to nonparametric regression statistics are noted.
Minimum Norm Invariant Quadratic Estimation of a Covariance Matrix in Linear Model
Authors: Chaubey Yogendra P.
Published: May 2007

A general linear model with a known covariance structure is considered. The method of Minimum Norm Quadratic estimation extending RAO'S (1972) argument is outlined. This method is illustrated for a particular model where it is noted that MINQE used for estimating intraclass correlation coefficient yields the maximum likelihood estimate.
Detection of Interactive Effects in Carcinogenesis
Authors: Hamilton M. A.
Published: May 2007

The multistage theory for cancer is used to derive models for independent effects and for interactive effects of two carcinogenic agents. The derivation assumes that a tumor is of single cell origin and that a normal cell is transformed to a cancer cell by undergoing a finite number of irreversible, heritable, mutation‐like transitions. The interactions enter the proposed models at the level of single cell transition rates rather than, as is conventional, at the level of animal response proportions. Suggestions are given for the design and analysis of fixed time, binary response, two factor, cancer bioassay experiments.