bluuebunny/crossref_metadata_2025_split huggingface dataset:
Cyclic Queues with Feedback
Authors: Finch P. D. 
Published: December 2018

SUMMARY
Simple queues, with customers arriving at random for service at a number of service stations in series, are considered. Feedback is permitted either by feedback from the terminal server, or by feedback from each server of the series to the queue waiting for service at that stage. A constraint is introduced by imposing an upper limit on the number of customers in the system at any time. The service time of each server is supposed to be negative exponential.
Maximizing a Function in a Convex Region
Authors: Zoutendijk G. 
Published: December 2018

Summary
The problem is considered of maximizing a function in a convex region. to solve this problem a new method is developed, to be called “method of feasible directions”. It is a method of steep ascent. Starting with a feasible solution a sequence of feasible trial solutions with ever-increasing values for the objective function is obtained. This sequence will converge to a (local) maximum solution in all cases of importance. to obtain a new trial solution from an old one we have to determine (a) a direction in which the objective function increases and the solution remains feasible and (b) the length of the step to be taken in this direction. The method of feasible directions is first developed for problems with linear constraints and applied to the special cases of a linear and a quadratic objective function. In the latter two cases the number of steps is finite. An extension of the method to problems involving non-linear constraints is also considered.
On the Distribution of the Weighted Difference of Two Independent Student Variables
Authors: Ruben Harold 
Published: December 2018

Summary
The distribution of the d-statistic, the weighted difference of two independent t-variables, is first obtained in integral form. This allows d to be interpreted as the ratio of two independent random variables, the numerator of which is a Student variable and the denominator a function of a Beta variable. It is suggested that the simplicity of the above integral form should enable extensive computation and tabulation of the d-statistic to be effected. Explicit forms for the distribution of d as finite or infinite series involving Incomplete Beta Function Ratios and Incomplete Gamma Function Ratios are derived for the special cases when (i) the degrees of freedom and weights of the component variables are equal and (ii) one of the components is normal.
A Problem of Delayed Service—I
Authors: Ben-Israel A. , Naor P. 
Published: December 2018

SUMMARY
A system is considered possessing the following characteristics: A repairman tends a number of machines—liable to break down from time to time—and some of his time is possibly taken up by ancillary duties, inspection, walking, etc. It is assumed throughout this study that the time consumed by attendance to a particular machine is independent of the state of the machine—working or idle. On the basis of this assumption a variety of models is discussed differing among themselves by the following considerations: (a)successional as against simultaneous attendance to machines;(b)constant Poisson breakdown intensity of the whole system as against constant Poisson breakdown intensity of individual machines in working order;(c)different assumptions regarding attendance time distributions. Expressions are developed for the mean, variance and, in some cases, the functional form of the distribution of (i)the number of idle machines as observed by a random controller;(ii)the number of idle machines as observed by the repairman during one round; and(iii)the waiting time of an idle machine.
A Problem of Delayed Service—Ii
Authors: Ben-Israel A. , Naor P. 
Published: December 2018

SUMMARY
The system analysed in the preceding paper under the two alternative extreme assumptions of successional as against simultaneous attendance to machines is reconsidered under a “mixed” assumption: Machines are attended to in groups; repair of machines belonging to the same group is simultaneous, but different groups are dealt with in succession. Expressions are developed for the mean and variance of the number of idle machines as observed by a random controller and as observed by the repairman during one round.
A Method of Estimation of Missing Values in Multivariate Data Suitable for Use with an Electronic Computer
Authors: Buck S. F. 
Published: December 2018

SUMMARY
Estimation of statistical parameters from multivariate data results in wasted information, if units with incomplete data are rejected entirely, and perhaps in inconsistencies in the variance–covariance matrix if the variances and correlation coefficients are estimated from all available data on individual variates and pairs of variates respectively. An alternative is to estimate the missing values by regression techniques and to calculate a revised variance–covariance matrix. This method is suitable for use with an electronic computer. It is shown that with this method the resultant covariances are unbiased, but that the variances require correction for bias. A numerical example is given.
Evaluation of Determinants, Characteristic Equations and Their Roots for a Class of Patterned Matrices
Authors: Roy S. N. , Greenberg B. G. , Sarhan A. E. 
Published: December 2018

SUMMARY
The variance–covariance matrices arising in the analysis of variance, response-surface fitting and order statistics have special patterns expediting and facilitating their algebraic manipulation. By appropriate triangulation and partitioning devices, the determinants of these matrices can be evaluated from general formulae. The characteristic equations, and sometimes their roots, can also be obtained in a direct single step.
The Interaction Algorithm and Practical Fourier Analysis: An Addendum
Authors: Good I. J. 
Published: December 2018

SUMMARY
In the original paper it was misleadingly stated that the Yates algorithm is effectively self-inverse. This statement is here elucidated, and a numerical example is given. Attention is drawn to a discrete analogue of Poisson’s summation formula, which provides many additional relationships between yields and interactions.
Prediction by Exponentially Weighted Moving Averages and Related Methods
Authors: Cox D. R. 
Published: December 2018

SUMMARY
The mean square error of prediction is calculated for an exponentially weighted moving average (e.w.m.a.), when the series predicted is a Markov series, or a Markov series with superimposed error. The best choice of damping constant is given; the choice is not critical. There is a value of the Markov correlation ρ 0 below which it is impossible to predict, with an e.w.m.a., the local variations of the series. The mean square error of an e.w.m.a. is compared with the minimum possible value, namely that for the best linear predictor (Wiener). A modified e.w.m.a. is constructed having a mean square error approaching that of the Wiener predictor. This modification will be of value if the Markov correlation parameter is negative, and possibly also when the Markov parameter is near ρ 0.
The Intervals between Regular Events Displaced in Time by Independent Random Deviations of Large Dispersion
Authors: Lewis T. 
Published: December 2018

SUMMARY
Suppose events, planned as regular, in fact occur at instants displaced from the planned arithmetic progression by independent random deviations. Assume these deviations have a common continuous distribution, with variance so large that the realized order of the events differs from the planned order. The paper discusses statistical properties of the time intervals between such events, and compares some of the theoretical formulae with some known empirical results.
Exact Fiducial Limits in Non-Linear Estimation
Authors: Williams E. J. 
Published: December 2018

SUMMARY
In the problem of estimating an unknown parameter of a distribution (in normal regression or in more general situations), the determination of a point estimate and its distribution is contrasted with the setting of fiducial limits for the parameter value. The use of a point estimate is effective for setting fiducial limits only when the estimate is a sufficient statistic for the parameter. Exact fiducial limits can be determined for the non-linear parameters in a normal regression function. Let the regression of y on x be linear in f(x, γ), which is a non-linear function of γ. If f′(x, γ) is the derivative of f(x, γ) with respect to γ, the partial regression of y on f vanishes when γ takes the least-squares value. Exact fiducial limits are defined as those values making this partial regression coefficient significant at the required level of probability. A pathological example of fiducial limits is discussed. The extension of the principle to general estimation problems is indicated.
Queues in Series
Authors: Ghosal A. 
Published: December 2018

SUMMARY
It has been demonstrated in this paper how Lindley’s analytical method of solving the integral equation for the waiting-time distribution in a queue with a single server can be extended to obtain the waiting-time distribution in different queues, when queues are in series and each queue has a single server. The input has been taken as Poisson, but the service time has been assumed to follow a gamma distribution in the first queue and an exponential distribution in the second queue.
Some Optimal Sequential Schemes for Estimating the Mean of a Cumulative Normal Quantal Response Curve
Authors: Marks B. L. 
Published: December 2018

SUMMARY
If a relation between stimulus and response is quantal and the response curve is the cumulative of a normal distribution, then the mean of the underlying distribution can be estimated by performing trials with various stimuli. An estimation scheme is studied in which the stimuli are chosen in the light of the results of the previous trials and of the prior probability distribution for the mean. For some special cases optimal policies for choosing the stimuli are found analytically, or computed by dynamic programming, and compared with the optimal non-sequential layouts.
Further Results on Tests of Separate Families of Hypotheses
Authors: Cox D. R. 
Published: December 2018

SUMMARY
It is required to test a composite null hypothesis. High power is desired against a composite alternative hypothesis that is not in the same parametric family as the null hypothesis. In an earlier paper a modification of the Neyman-Pearson maximum-likelihood ratio test was suggested for this problem. The present paper gives some general comments on the formulation of the problem, a general large-sample form for the test, and, finally, a number of examples.
On the Consistency of the Fiducial Method
Authors: Fraser D. A. S. 
Published: December 2018

SUMMARY
Lindley (1958) and Sprott (1960) have proposed several criteria for the satisfactory application of the fiducial method of inference to statistical problems. The criteria are concerned with consistency when there are various ways of applying the method. In sections 1 and 2 these criteria are discussed briefly, and the range of problems that yield fulfilment of the criteria is shown to be considerably larger than that indicated by Lindley and Sprott. A frequency interpretation for a fiducial distribution has been proposed and discussed in two recent papers (Fraser, 1961a, b); this interpretation is available for problems that are invariant in a natural sense under translation and transformation groups. If the purpose of the fiducial method of inference is to produce posterior probability statements about the parameter that have a frequency interpretation and are consistent according to criteria such as Lindley’s and Sprott’s, then the range of validity can be substantially extended by making a small modification to the method; this is discussed in sections 3 to 6.
Estimation of Means and Standard Errors in the Analysis of Non-Orthogonal Experiments by Electronic Computer
Authors: Freeman G. H. , Jeffers J. N. R. 
Published: December 2018

SUMMARY
Various methods of estimating means and standard errors for non-orthogonal designs are considered from the point of view of their generality and suitability for programming on an electronic computer. The use of the variance-covariance matrix is shown to have a number of advantages, and this method is described for designs with two or three classifications; the method of analysis for three classifications, no two of which are orthogonal, is new. Programmes have been written for the Ferranti Pegasus computer for two and three classifications; these are outlined and an example of their use is given.
On the Comparison of the Sensitivities of Experiments
Authors: Dar S. N. 
Published: December 2018

SUMMARY
A large sample test for the comparison of the ratio of components of variance in two identical independent experiments is obtained by using a normalizing transformation. This test agrees closely with the exact test of Schumann and Bradley. Then large sample tests are developed for such comparisons in k identical experiments and for comparisons in dissimilar experiments.
On Direct Probabilities
Authors: Dempster A. P. 
Published: December 2018

SUMMARY
The concept of a direct probability argument is introduced. This is a means of assigning distributions a posteriori which satisfies the requirement that such distributions shall be valid conditional on the observations, but which differs from the inverse probability argument in that distributions a priori are not needed. Direct probabilities are closely related to fiducial probabilities. This theory requires a generalized concept of sampling a family Fθ of distributions which is discussed in Section 3. Direct inference from a sample of n is discussed in Section 4 for a single continuous parameter and in Section 5 for the non-parametric case.
Models for a Bacterial Growth Process with Removals
Authors: Gani J. 
Published: December 2018

SUMMARY
The paper considers the extinction of a bacterial colony subject to phage infection. A description of the biological process leads to the construction of a simplified model from which it is possible to derive the probability generating function (p.g.f.) for surviving bacteria in terms of repeated contour integrals. The distributions of phage offspring released by a single bacterium, and of bacterial infections due to these phages, are discussed. For bacterial birth and birth-death processes, it is possible to express the p.g.f. for surviving bacteria explicitly; this is done by first obtaining the p.g.f. conditional on numbers of bacterial infections, and then summing over all such possible infections.
Some Remarks on a Method of Maximum-Likelihood Estimation Proposed by Richards
Authors: Kale B. K. 
Published: December 2018

SUMMARY
Richards (1961) suggested a method of maximum-likelihood estimation for the case of several parameters. Some gaps in the general theory given by him in support of the method are pointed out. Though the method is justifiable, the justification is shown to depend on the correct use of the implicit function theorem and is not connected with the joint asymptotic normality and the asymptotic efficiency of the maximum-likelihood estimates.
Hotelling’s Generalized T2 in the Multivariate Analysis of Variance
Authors: Ghosh M. N. 
Published: December 2018

SUMMARY
Hotelling’s generalized T2 is the sum of the roots of the determinantal equation |Z - θY/n| = 0, where Y and Z have central and non-central p-dimensional Wishart distributions with d.f. Q and n. Y and Z are obtained as the sum of products matrices for p-variate normal distributions N(0, σ1) and N(b(q), σ1). The distribution of this statistic is shown to be a monotonic increasing function of each of the population roots. An unbiased estimate of a linear function of the sum of population roots, which may be considered as a convenient measure of non-centrality, is also obtained from this statistic, and simultaneous confidence intervals for all linear functions of b(q) are obtained from it. The mean of the statistic is calculated for all p and the variance for p = 3 and p = 4.
On the Independence of Quadratic Expressions
Authors: Good I. J. , Welch L. R. 
Published: December 2018

SUMMARY
Let y1, y2, · · ·*** be pairwise independent quadratic expressions in x, not necessarily homogeneous, where x has a multinormal distribution. Then y1, y2, …*** are also mutually independent. Various conditions for independence are given. In the Appendix, it is shown that x is a linear transformation of a vector z, where z has a spherically symmetric distribution, and where the y’s depend on disjoint subsets of the components of z.
Periodogram Analysis and Variance Fluctuations
Authors: Herbst Laurence J. 
Published: December 2018

SUMMARY
Two problems in the subject of time-series analysis are considered: (A) the effect of fluctuating variances on the periodogram of a set of independent Gaussian data with zero means; (B) the possibility of using the periodogram of squares of independent Gaussian data with zero means as a tool in the Fourier analysis of the variances of the data. The basic effect of fluctuating variances on the periodogram is to introduce correlations (expressible in terms of the Fourier coefficients of the variance) which do not decrease as the sample size increases. The periodogram of squares of independent Gaussian data with zero means is shown to be an appropriate tool in the Fourier analysis of the variances.
Some Applications of Exponential Ordered Scores
Authors: Cox D. R. 
Published: December 2018

Summary
There are simple standard tests for the comparison of samples assumed to arise from exponential distributions, but the properties of these tests are known to depend severely on the assumption of exponential form. However, the observations can sometimes usefully be ranked, and then replaced by the corresponding expected values of order statistics in sampling the unit exponential distribution, before calculating the appropriate test statistic. Some special tests of this type are examined. The procedure is analogous to the use of Fisher and Yates's scores in normal theory. Savage (1956) gave the test of this type for comparing two samples, in the course of a general study of rank tests for the two-sample problem.
A Deformation Method for Quadratic Programming
Authors: Zahl Samuel 
Published: December 2018

Summary
This paper presents a new method for minimizing a positive definite quadratic function subject to linear inequality constraints. It is based on a continuous deformation of the quadratic, starting from one giving rise to an almost trivial problem and ending with the desired quadratic. The method is particularly suitable for problems (one such is outlined) involving large numbers of inequality constraints, since the size of the variable space is independent of the number of inequalities. The method is readily extended to linear programming by embedding the linear objective function in a second degree polynomial with positive definite quadratic component, solving the resulting problem by the above method, then driving the quadratic component to zero, i.e. deforming the second-degree programming problem back to the original linear one.
The Linear Hypothesis and Idempotent Matrices
Authors: Seber G. A. F. 
Published: December 2018

Summary
The application of idempotent matrices to the testing of linear hypotheses is discussed and several properties of idempotent matrices are given to simplify the calculation of the F-test statistic. It is also shown that the F-test is based on the so-called Wald principle of large sample theory and this approach is put forward as an alternative to the usual likelihood ratio method of deriving the F-statistic.
Some Properties of Counts of Events for Certain Types of Point Process
Authors: Lewis T. , Govier L. J. 
Published: December 2018

Summary
A stationary point process being supposed characterized by the counts Xl of events in time intervals of equal length l, a discussion is given of relationships, valid for a wide class of processes, between the variance-time function var Xl, the autocorrelation function of the Xl-series, and the autocovariance density. “Controlled variability” processes are then defined and discussed. A study is made of particular controlled variability processes, “(a, b) processes”, in which events occur at times a 0 + ia + bi, the bi being independent identically distributed random variables. In particular, it is shown that the autocovariance density for an (a, b) process is proportional to the convolution probability density of the difference of two independent bi's, with a closely related result for the autocorrelation function of counts.
A Branching Poisson Process Model for the Analysis of Computer Failure Patterns
Authors: Lewis Peter A. W. 
Published: December 2018

Summary
Current reliability models predict that the failure pattern of a computer should form a Poisson process. Experience has shown, however, that the times-between-failures of a computer are not exponentially distributed, and that successive times-between-failures are not independent. These deviations from a Poisson process are due to imperfect repair of failed components; the resulting failure pattern is described by a branching Poisson process model. The probabilistic properties of this model are derived and used to analyse three series of computer failures.
Estimation in the Uniform Covariance Case
Authors: Geisser Seymour 
Published: December 2018

Summary
There are three basic methods (confidence, fiducial, Bayesian) of obtaining interval estimates or estimating regions for the parameters of the multivariate normal distribution, none of which need necessarily yield a unique solution, although this has been claimed as a property of the fiducial argument. It has been previously demonstrated that they are not consistent with one another, i.e. they yield different regions for the same parameters. In this paper we show that if the structure of the covariance matrix is uniform the three methods yield the same regions for the vector mean and the same intervals for the common correlation coefficient.
Supplement to “A Deformation Method for Quadratic Programming”
Authors: Zahl Samuel 
Published: December 2018

Summary
This note has two purposes. The first is to show how additional linear inequality restrictions can be added to a quadratic programming problem, given the solution for the original set of inequalities, using the author's (1964) deformation algorithm. The second purpose is to replace the sufficient conditions of Proposition 2 of the earlier paper by a set of necessary and sufficient conditions which are easier to implement. These new conditions are based on the Kuhn and Tucker (1951, Section 3) necessary and sufficient conditions for an inequality constrained maximum. Because the new conditions are both necessary and sufficient, degeneracy three of the earlier paper cannot, in fact, occur.
Mixture Designs for Three Factors
Authors: Draper Norman R. , Lawrence Willard 
Published: December 2018

Summary
Scheffé, in two recent papers (1958, 1963), has given designs for experimenting with mixtures. The basis of these designs is the choice of symmetrical arrangements of points in the factor space and the fitting of carefully chosen models which have exactly as many coefficients as there are data points. The designs are such that some of the experiments do not contain any of one or more ingredients of the mixture. This may or may not be a disadvantage depending on the problem involved. Here an alternative form of design selection is made for the case of mixtures of three factors. (The method has also been extended to four factors.) This involves the premise that, in the absence of specialist knowledge about the form of the true response function, it is desired to fit a response surface equation of first or second order over the factor space of possible mixtures, and experimental runs are needed which, in a certain sense, ensure the best surface fit possible. The principles used in the choice of appropriate designs will be those originally introduced by Box and Draper (1959).