bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Test of Homogeneity of Means Under Restricted Alternatives
Authors: Bartholomew D. J. 
Published: December 2018

SUMMARY
Suppose that observations x1, x2, …, xk have been obtained from normal populations with unknown means μ1, μ2, …, μk and known standard deviations σ1, σ2, …, σk. The paper discusses tests of the hypothesis μ 1, μ 2, … = μk when prior information is available about the μ‘s under the alternative hypothesis. A generalized form of the χ 2-test, denoted by x2¯, has been developed for use when this information takes the form of order restrictions between some or all of the μ‘s. The distribution is shown to depend on that of χ 2 and certain probabilities which have been determined for many sets of order restrictions. The power function has been obtained in certain cases and used to compare the x2¯-test with χ 2, which assumes no prior information. This shows that the utilization of order information often leads to a considerable gain in power. Power comparisons with other versions of x2¯ and with tests based on scores suggest that no worthwhile improvement over x2¯ is possible. The paper is an extension and generalization of work contained in two earlier papers (Bartholomew, 1959a, b).
Closed Queueing Systems: A Generalization of the Machine Interference Model
Authors: Benson F. , Gregory G. 
Published: December 2018

SUMMARY
A closed loop of queues in series is considered in which the time taken by any customer to travel between consecutive service gates is a random variable. The case of a single server at each gate is analysed, where in addition to the customers from the closed loop, each server may also have customers arriving from sources outside the system and, after completion of service, departing to destinations again outside the system. Limiting cases are examined, firstly where the number of customers in the closed loop becomes large, and secondly where, in addition to this condition, the average transit time between one pair of consecutive service gates also tends to infinity.
The Randomization Bases of the Problem of the Amalgamation of Weighted Means
Authors: Barton D. E. , Mallows C. L. 
Published: December 2018

SUMMARY
A generalization is given of a theorem of Miles on the probability distribution of the number of resultant means arising from a process of amalgamation of a set of weighted values, under an hypothesis of randomization. Two proofs are given, one inductive and one combinatorial. These are based on a geometrical representation. The theorem is used to provide a non-parametric test for trend. The connection of this probability distribution with that of the number of records (in the sense of Foster and Stuart) is explored and an explicit formula for the variance of their round trip test is obtained. Two tests, based on the number of records and on the number of resultant means, are applied to two sets of data. Three standard tests are also applied for comparison.
A Method of Maximum-Likelihood Estimation
Authors: Richards F. S. G. 
Published: December 2018

SUMMARY
Knowledge of one or more of the parameters in a maximum-likelihood problem sometimes results in a very considerable simplification, the analysis becoming almost trivial. A method of obtaining maximum-likelihood estimates and their asymptotic covariance matrix is given which makes it possible to capitalize on simplifications of this sort when they arise. Application is mainly in the field of regression, but other examples are mentioned. A numerical example of exponential regression is given.
A Waiting Line with Interrupted Service, Including Priorities
Authors: Gaver D. P. 
Published: December 2018

SUMMARY
A single-server system with stationary compound Poisson input and general independent service times, the latter being subject to random interruptions of independently but otherwise arbitrarily distributed durations, is studied. For a variety of service-interruption interactions (including the preemptive-repeat) the distributions of busy period duration, of queue length, and of waiting time are characterized by transforms and by moments. Applications are made to priority scheduling problems.
On the Distribution of Certain Quadratic Forms in Normal Variates
Authors: Bhat B. R. 
Published: December 2018

SUMMARY
This paper is concerned with the characterization of the variance covariance matrix for a normal family in which certain quadratic forms are independent and follow cχ 2 distributions. It is also proved that the necessary and sufficient condition for any quadratic or linear form to be distributed independently of a sum of a finite number of non-negative definite quadratic forms is that it is distributed independently of each one of them.
Confidence Sets for the Mean of a Multivariate Normal Distribution
Authors: Stein C. M. 
Published: December 2018

SUMMARY
An attempt is made to determine confidence sets for the mean of a multivariate normal distribution with known covariance matrix that take advantage of the fact that the sample mean is not the best estimate when the loss is a non-singular quadratic function of the error vector. Only the case of high dimension is considered. The geometrical size and shape of the confidence sets, the probability of covering false values, and the relation to posterior probabilities are studied, unfortunately somewhat incompletely.
Some Statistical Aspects of Adaptive Optimization and Control
Authors: Box G. E. P. , Jenkins G. M. 
Published: December 2018

SUMMARY
It is often necessary to adjust some variable X, such as the concentration of consecutive batches of a product, to keep X close to a specified target value. A second more complicated problem occurs when the independent variables X in a response function η(X) are to be adjusted so that the derivatives ∂η/∂X are kept close to a target value zero, thus maximizing or minimizing and the paper is devoted mainly to the estimation from past data of the “best” adjustments to be applied in the first problem.
On the Lengths of Intervals in a Stationary Point Process
Authors: McFadden J. A. 
Published: December 2018

SUMMARY
The paper is concerned with the lengths of intervals in a stationary point process. Relations are given between the various probability functions, and moments are considered. Two different random variables are introduced for the lengths of intervals, according to whether the measurement is made from an arbitrary event or beginning at an arbitrary time, and their properties are compared. In particular, new properties are derived for the correlation coefficients between the lengths of successive intervals. Examples are given. A theorem is proved, giving conditions under which two independent stationary point processes with independent intervals may be superposed, giving a new point process which also has independent intervals. Mention is made of the application to the theory of binary random processes and to the zeros of a Gaussian process.
Problems of Selection with Restrictions
Authors: Rao C. Radhakrishna 
Published: December 2018

SUMMARY
The paper considers a practically important generalization of the theory of regression. A linear function of a set of variables x l, …, xp, called predictor variables, is constructed so as to maximize its correlation with a criterion variable y 1 subject to the condition that its correlations with other criterion variables y 2,…,yq are non-negative. It is suggested that a linear function so determined is useful when selection of individuals is done on the basis of x 1,…,xp to achieve the maximum possible progress in the mean of y 1, while ensuring that no deterioration takes place in the mean values of y 2,…,yq in the selected group, compared with the original group of individuals from which selection is made.
Approximate Confidence Limits for the Relative Risk
Authors: Gart John J. 
Published: December 2018

SUMMARY
The relative risk or odds ratio has been proposed as one alternative to the difference in proportions in measuring the degree of association in two by two tables. This paper proposes two new methods for finding confidence limits on the relative risk, one appropriate for large numbers, and a second for small numbers. The first is related to the usual chi-square test and the second to an approximation to the Fisher-Irwin test. The methods are compared to those previously proposed by Cornfield (1956), Cox (1958), and Woolf (1954).
The Use of Control Observations as an Alternative to Incomplete Block Designs
Authors: Atiqullah M. , Cox D. R. 
Published: December 2018

SUMMARY
The use of a control treatment as an alternative to incomplete block designs is considered, two possible methods of analysis being proposed. Theoretical efficiency factors are evaluated. These confirm conclusions of Yates (1936) that the efficiency is lower with a control than with an appropriate incomplete block design. The difference is not great for the larger values of k, the number of units per block, and the greater flexibility and simplicity of analysis of the methods with a control may lead to their being preferred, especially when a control treatment is necessary for other reasons, or when no simple incomplete block design is available. Extensions to the two-way elimination of error are considered.
Confidence Interval Estimation in Non-Linear Regression
Authors: Halperin Max 
Published: December 2018

SUMMARY
In a recent paper, E. J. Williams presents a procedure for obtaining what are described as fiducial intervals and regions for the non-linear parameters in non-linear regression. The linear parameters are not included in the regions which are developed and the class of non-linear regression functions for which his results hold is not clearly delineated. In this paper, it is shown how some results from standard regression theory can be used to discuss these points; the discussion also implies that the intervals and regions described by Williams are confidence intervals and regions.
Treatment of the Non-Equilibrium Theory of Simple Queues by Means of Cumulative Probabilities
Authors: Sack R. A. 
Published: December 2018

SUMMARY
The treatment of simple single-server queues with random arrivals and exponentially distributed serving times is facilitated by the use of cumulative sums of which the lowest order represents the probability that there are at least a given number of customers in the queue. For constant arrival and departure rates λ and μ the deviations from the steady-state conditions are essentially symmetric in λ and μ; they can be expressed as integrals over modified Bessel functions which are slightly simpler than equivalent expressions given by Bailey. Asymptotically these terms decay approximately exponentially with an effective rate κ=(λ−μ)2.
Theory of Cyclic Rotation Experiments
Authors: Patterson H. D. 
Published: December 2018

Summary
The paper reviews some of the statistical problems arising in the design and analysis of long-term cyclic experiments comparing different crop rotations. Three types of design are distinguished and their properties considered. These are basic designs with all phases of the rotations in each block, reduced designs with mutually exclusive groups of phases kept in separate blocks and phase-confounded designs in which some contrasts between test crops are partially confounded with block differences.
Methods of analysing the yields of test crops by estimating the mean effects of the rotations over the years and regressions on seasonal and time variates are discussed theoretically for replicated experiments of basic or reduced design. The analysis is complicated by correlations between yield values recurring on the same plots and by lack of homogeneity in residual year-to-year variations in rotation effects. The main topics considered are (1) the estimation of errors, (2) the losses of information due to using unweighted means and regressions ignoring the correlations, (3) methods for recovering this information.
Prediction by Progressive Correction
Authors: Dobben de Bruyn C. S. 
Published: December 2018

Summary
A new kind of non-linear predictor is introduced, called a progressive corrector. The predictor is closely related to the exponentially weighted moving average, which can be regarded as a degenerate case of a progressive corrector. An attempt is made to approximate the mean square error of prediction. Mean square error is criticized as a criterion for the optimality of a predictor which is being used as part of an inventory control system.
Two Papers on the Comparison of Bayesian and Frequentist Approaches to Statistical Problems of Prediction: Bayesian Tolerance Regions
Authors: Aitchison J. 
Published: December 2018

Summary
In the theory of statistical tolerance regions, as usually presented in frequentist terms, there are inherent difficulties of formulation, development and interpretation. The present paper re-examines the basic problem from a Bayesian point of view and suggests that such an approach provides a set of widely applicable, mathematically tractable tools, often more tailored to the requirements of users than the corresponding frequentist tools. For the one-dimensional case, Bayesian intervals are quoted for a number of standard distributions and prior densities, and the customary feature of a Bayesian analysis—that special prior densities give rise to standard frequentist results—is briefly demonstrated. A problem which seems to be of greater practical significance, namely the selection of an optimum tolerance region from a set of possible tolerance regions, is also investigated and the overwhelming advantages of the Bayesian approach are indicated.
On the Bayesian Estimation of Multivariate Regression
Authors: Tiao George C. , Zellner Arnold 
Published: December 2018

Summary
In this paper, we use a Bayesian approach to analyse sets of regression equations with correlated error terms. In the case that the matrix of “independent variables” is the same for all equations, our model reduces to the traditional multivariate regression model. For this case, the marginal posterior distribution of the regression coefficient vector for any equation is shown to be of the multivariate-t form. Further, the variances and covariances of the error terms have an “inverted” Wishart distribution a posteriori. Some properties of this distribution are given. Finally, the joint posterior distribution of the regression coefficients in the general model is derived and discussed.
A Note on the Solution of Dam Equations
Authors: Lloyd E. H. , Odoom S. 
Published: December 2018

Summary
The object of this paper is to provide an algorithm for solving the equations giving the equilibrium distribution of reservoir levels, both for Moran's formulation in terms of independent inflows and for Lloyd's formulation involving Markovian inflows. In the case of independent inflows, the equilibrium distribution may be expressed linearly in terms of powers of the roots of a certain polynomial. When the inputs form a Markov chain, the solution may be similarly expressed in terms of the latent roots of a certain matrix, or (more conveniently for computation) directly in terms of powers of that matrix. The method is illustrated by simple examples.
A Model for Rainfall Occurrence
Authors: Green J. R. 
Published: December 2018

Summary
A probability model for the occurrence of wet and dry days at Tel Aviv is proposed as an alternative to an earlier one given by Gabriel and Neumann. The new model, which assumes exponential distributions for the lengths of spells of continuous dryness or continuous rain, is found to fit rainfall data for Tel Aviv well, and to represent certain conditional probabilities more satisfactorily than that of Gabriel and Neumann.
Probability Bounds for a Union of Hyperspherical Cones
Authors: Choi Keewhan 
Published: December 2018

Summary
In this paper are given two methods of obtaining bounds on the probability content of a union of hyperspherical cones in Euclidean N-space when the underlying distribution is normal. The results of a small numerical study are tabulated to indicate the range of applicability of the methods. These methods can be used to obtain bounds on the overall significance level and power-like probabilities in the analysis of variance when many treatment sums of squares are tested against the same error sum of squares.
Association between Random Variables and the Dispersion of a Radon–Nikodym Derivative
Authors: Ali S. M. , Silvey S. D. 
Published: December 2018

Summary
In a previous paper by one of the authors (Silvey, 1964) it was suggested that the Radon–Nikodym derivative of the joint distribution of two, not necessarily real-valued, random variables with respect to the product of their marginal distributions provides the analytic key for discussing association between the random variables. In this paper we shall develop this point and lend some support to the suggestion by proving that in the case of normal random vectors the distribution of this derivative, as determined by the product of the marginal distributions, becomes more widely spread out as association between the vectors increases. More precisely we shall show that the expected value of any continuous convex function of the derivative is a non-decreasing function of each of the canonical correlation coefficients between the two vectors.
The Detection of Partial Association, II: The General Case
Authors: Birch M. W. 
Published: December 2018

Summary
Three criteria are derived for testing null hypotheses of conditional independence of two random variables. The first of these criteria is appropriate when both are qualitative, the second when both are quantitative, and the third when one is qualitative and one quantitative. Each of these criteria may be regarded as a generalization of the criterion for two dichotomous random variables given in Part I.
A Branching Process Allowing Immigration
Authors: Heathcote C. R. 
Published: December 2018

Summary
It is well known that in the absence of immigration, a population of like particles developing under the usual laws for branching processes either increases unboundedly with time or becomes extinct (Feller, 1957, Chapter 12; Harris, 1963, Chapter 1). If migration into the system is permitted, then it is clear that under certain conditions a proper stationary distribution for population size will exist. That this is the case has been shown by Bartlett (1956, Section 3.41) for processes in continuous time, and the present note is concerned with the same problem but considering discrete generations. Our result for the generating function of the stationary distribution of population size reduces to a form analogous to Bartlett's result when the immigration distribution is Poisson.
Transformations and Sufficiency
Authors: Sprott D. A. 
Published: December 2018

Summary
Barnard (1963) gave a definition of the sufficiency of T 2 for θ 2 in the absence of knowledge of θ 1 using groups of transformations. A possible generalization of this is implicit in the method of obtaining fiducial distributions by sets of transformations described by Sprott (1963). The purpose of this paper is to examine sufficiency and transformations in more detail in the special cases relevant for fiducial distributions, and to examine the nature of possible groups of transformations.
Likelihood-Ratio and Confidence-Region Tests
Authors: Aitchison J. 
Published: December 2018

Summary
A previous paper (Aitchison, 1964) proposed a method of confidence-region testing for multiple-hypothesis situations and developed the theory for linear univariate situations and for the asymptotic parametric case. The present paper shows that the results for these situations are in fact special cases of a basic relation between confidence-region tests and likelihood-ratio tests. This relation allows the easy extension of confidence-region testing to multivariate analysis.
Analytical Surveys with Cluster Sampling
Authors: Sedransk J. 
Published: December 2018

Summary
This paper concerns the designing of certain analytical surveys (utilizing cluster sampling). The general concepts and problems peculiar to this type of study are discussed. The question of the relevant population for inference purposes is treated, and this is reflected in the model considered. Illustrations are given to clarify the situations where this type of model may be applicable. In general, the objective in planning such a survey is to select the sample so that maximum precision for the comparisons to be made is obtained for a specified total cost. Sample size allocations are carried out for several specifications of survey goals—these specifications being related to the type of comparisons to be made.
Moments of a Serial Correlation Coefficient
Authors: Shenton L. R. , Johnson Whitney L. 
Published: December 2018

Summary
For a discrete first-order auto-regressive scheme (with initial value zero) xt = αxt-1 + ϵt, expressions have been found for the first four moments of α̂=∑1nxtxt−1/∑1n−1xt2. The expressions are of two kinds : (i) series in ascending powers of α2, (ii) asymptotic series in descending powers of n. A table of values of μ1‱,σ(α̂),β1(α̂),β2(α̂) is included. For the special case α2 = 1 the dominant terms in the first four moments are stated.
Expected-Cover and Linear-Utility Tolerance Intervals
Authors: Aitchison J. 
Published: December 2018

Summary
Expected-cover tolerance intervals are commonly used as a means of statistical prediction. In their construction the effectiveness of such intervals in relation to a future observation y is assessed only in terms of “success” if y falls in the interval and of “failure” otherwise; no account is taken in the assessment of how far inside or outside the interval y happens to fall. The present paper considers the construction of intervals which do take account of this factor in a linear way. From a Bayesian viewpoint it is found that expected-cover and linear-utility intervals can be regarded as equivalent through a simple relation between the expected cover and the relative cost ratio. For the frequentist approach it is first shown that linear-utility intervals can be simply constructed for the normal and gamma distributions. Comparison of these with expected-cover intervals shows that, while there is not complete identity, there is an equivalence in a “large-sample” sense.
Classifying Youden Rectangles
Authors: Preece D. A. 
Published: December 2018

Summary
Youden rectangles (Youden square designs) of various sizes are classified. The classification procedure is similar to that used by Norton (1939) for 7 × 7 Latin squares. For example, 7 × 4 Youden rectangles are grouped into six “species”, resembling the 147 species of 7 × 7 Latin squares, and the six species into three “families”. The classification led to the discovery of a method for generating balanced 7 × 3 and 11 × 5 row-and-column designs for two non-interacting sets of treatments, one set containing seven or eleven treatments, the other set containing three or five. The derivation of these designs is given. The existence of such designs had been conjectured by Clarke (1963).
The Chi-Square Test for Heterogeneity of Proportions, after Adjustment for Stratification
Authors: Armitage P. 
Published: December 2018

Summary
In testing differences between proportions or rates of occurrence of events in different categories, expected numbers may be calculated separately within certain strata and subsequently summed over strata. For the Poisson case an approximate X2-statistic is derived as a simple modification of the usual test statistic. Other approaches and situations are discussed more briefly.
The Ergodic Queue Length Distribution for Queueing Systems with Finite Capacity
Authors: Keilson J. 
Published: December 2018

Summary
Let M(t) be the queue length process for an M/G/1 queue with finite queue capacity L. A simple expression is given for the ergodic queue length distribution PL(m) = p{M(∞) = m}, in terms of certain Green's function elements for a Markov process Mk imbedded in M(t). The ergodic distribution for the imbedded process and that for the original process are shown to differ in the presence of finite queue capacity. The ergodic queue length distribution for G/M/1 with finite queue capacity is also exhibited.