bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Queueing Model for Road Traffic Flow
Authors: Miller Alan J. 
Published: December 2018

SUMMARY
It is proposed that on roads which are uninterrupted by traffic signals, intersections, etc., vehicles should be considered as travelling in random queues. Criteria for determining the queues in actual traffic are found. A crude model is then used to study the formation of these queues in an attempt to derive the Borel–Tanner distribution of queue lengths. The random queues model is then used to study waiting times for pedestrians (or vehicles) wishing to cross one lane of traffic.
First Emptiness in a Finite Dam
Authors: Weesakul B. 
Published: December 2018

SUMMARY
This paper discusses problems of first emptiness in a finite discrete dam (i) before overflow occurs, and (ii) where there is overflowing. Equations for probabilities of first emptiness in both cases are derived, and their generating functions found. The latter are shown to be the ratio of two polynomials. For geometric inputs, explicit expressions for these polynomials may be found similar to Feller’s results for classical random walk.
The Construction of Optimal Designs for the One-Way Classification Analysis of Variance
Authors: Aitchison John 
Published: December 2018

SUMMARY
A consideration of the purpose of some one-way classification experiments leads us to introduce a criterion of F-optimality of design, a compromise measure which concentrates on the detection of certain specified effects while allowing at least the inspection of a wider class of effects. to give added validity to this notion we first establish its equivalence to a min–max weighted variance design criterion. The actual construction of F-optimal designs is our main purpose. The direct min–max approach is difficult, and so our next main result directs attention to the equivalent problem of finding optimal strategies for a certain two-person zero-sum non-matrix game. Finally, we provide a computational scheme for the solution of this game and illustrate the technique by examples.
On Some Properties of the Asymptotic Variance of the Sample Quantiles and Mid-Ranges
Authors: Sen P. K. 
Published: December 2018

SUMMARY
In this paper, some properties of the asymptotic variance of the sample quantiles and the derived mid-ranges are studied and the role of the sample median is critically discussed. It is shown that among the class of sample quantiles, the sample median will have asymptotically the smallest variance only under somewhat restrictive regularity conditions; while among the class of sample mid-ranges, the sample median (being the central mid-range) has asymptotically the smallest variance only for a class of non-regular parent density functions.
Some Results on Inventory Problems
Authors: Thatcher A. R. 
Published: December 2018

SUMMARY
Approximations are given for the expected numbers of orders and shortages per unit time, in the steady state, under a variety of formulations of the inventory problem. These take specific account of the distribution of the quantity demanded, when this varies from one occasion of demand to another. Special reference is made to a model which has been found to give a realistic representation of many actual demand distributions. An approximation is given for the frequency of shortages at an individual store, when a policy of the (s, S) type is applied to the total stock in a system of N stores. A proof is given of an optimal property of the (s, S) policy when applied to a single store, with a corresponding approximate result for a system of N stores. The paper concludes with formulae for finding the policy which minimizes costs when these are of linear form, together with some suggestions for practical application in cases where the shortage cost is indeterminate.
Congestion Systems with Incomplete Service
Authors: Downton F. 
Published: December 2018

SUMMARY
In a queueing system with m servers, customers arrive at random, each customer being given a desired service time. If all the servers are busy, the newly arrived customer displaces that customer with smallest unexpired service time. The efficiency of the system is measured by the ratio, I, of mean achieved service time to mean desired service time under conditions of statistical equilibrium. Cox (1961) determined I when the desired service time had an exponential distribution for the case m = 2, and for general m when the service time was of fixed length. The solution for a general service time distribution and for general m is given in this paper. A conditional replacement system is also considered and a numerical comparison is given.
On the Effect of Non-Normality on the Estimation of Components of Variance
Authors: Atiqullah M. 
Published: December 2018

SUMMARY
The effect of non-normality in estimating variance components in a random effects or mixed effects linear model is studied. It is shown that for a wide variety of balanced situations the interval estimation of the upper variance component is likely to be relatively little affected by non-normality in the error component. A method is suggested for constructing a confidence interval for a ratio of variance components in a balanced model, without assuming normality.
The Analysis of Stationary Processes with Mixed Spectra—I
Authors: Priestley M. B. 
Published: December 2018

SUMMARY
We consider a normal stationary process whose spectrum may contain harmonic components superimposed on a non-uniform continuous spectral density function. The problem of separating the discrete and continuous spectral components is discussed, and it is shown that the bandwidth of the spectral density function must be restricted, in relation to the number of observations, in order to make the problem tractable. Assuming only that this bandwidth is known, the presence of harmonic components is then detected by performing a “spectral” analysis on the tail of the autocovariance function, and a test is constructed based on the theory of random walks with absorbing barriers. A brief discussion of the case of non-normal processes is included.
Sequential Estimation of Quantal Response Curves
Authors: Wetherill G. B. 
Published: December 2018

SUMMARY
We suppose that it is required to estimate percentage points of a quantal response curve, and efficient use of observations is important. Strategies currently available are critically examined, including the Robbins-Monro process and Dixon and Mood’s Up and Down method. Some new alternative strategies are suggested and studied using empirical sampling on an electronic computer. The procedure recommended for estimation of 50 per cent. points has advantages of ease of operation and estimation, besides high efficiency; studies on the estimation of other percentage points were less successful. A sketch is given of problems demanding further study.
The Epochs of Emptiness of a Semi-Infinite Discrete Reservoir
Authors: Lloyd E. H. 
Published: December 2018

SUMMARY
This note discusses, on a discrete time scale, the waiting times to first emptiness and to nth emptiness of a semi-infinite Moran reservoir subject to mutually independent stationary integral-valued inputs, and unit output. Discrete analogues are obtained of Kendall’s (1957) integral equation for the first-empty time, and intuitive arguments are given to exemplify the non-uniqueness of the solutions of integral and difference equations of this type. Kendall’s solution to his integral equation is shown to give the distribution of first-empty time for the semi-infinite discrete reservoir with positive initial contents. Simple expressions are obtained for the distributions of the duration of an empty period and of the duration of a non-empty period.
A Multi-Stage Renewal Process
Authors: Bartholomew D. J. 
Published: December 2018

SUMMARY
This paper derives the theory of a multi-stage renewal process and discusses two applications. The process consists of several self-renewing aggregates arranged in series. When a failure occurs in the ith stage it is replaced by an item already operating in the (i − 1)th stage; the vacancy thus created is filled by a member of stage (i − 2) and so on. The main object of the analysis is to determine the failure rates in each stage and the transfer rates between stages. Two rules for selecting the item to be transferred are considered; in one case the selection is made at random, in the other the oldest member is selected. General methods for obtaining transient and equilibrium solutions are given for both rules. Simple explicit solutions are obtained when the life distribution is negative exponential and for certain other distributions. The application of the theory to the study of wastage and promotion in hierarchical organizations and to the determination of optimum industrial replacement schemes is briefly discussed.
On Plackett’s Test for Contingency Table Interactions
Authors: Goodman Leo A. 
Published: December 2018

SUMMARY
Based on a transformation matrix the rows of which are orthogonal to each other, a matrix that comes naturally to analysis of variance users, Plackett (1962) has proposed a test for zero second-order interaction in an r × s × t contingency table which requires that the user invert t +1 matrices, each having (r − 1) (s − 1) rows and (r −1) (s −1) columns. Based on a transformation matrix the rows of which are not orthogonal to each other, we present herein a modification of Plackett’s method of analysis which will require that the user invert only one matrix of side (r − 1) (s − 1) and t matrices each of side (u − 1), where u = min [r, s]. Thus, when u = 2, the user applying the method given here will compute the inverse of only one matrix of side (r — 1) (s − 1), while the user applying Plackett’s method will have to compute the inverse of t+ 1 such matrices (when max [r, s] &gt; 2). The test of zero second-order interaction presented herein will usually be easier to apply than the other valid tests of this null hypothesis appearing in the literature; its outcome is actually equivalent to Plackett’s test, which we note in turn is asymptotically equivalent (under the null hypothesis) to tests proposed by Bartlett (1935), Roy and Kastenbaum (1956), Darroch (1962), and Goodman (1963a).
On Combining Estimates of a Ratio of Means
Authors: Bennett B. M. 
Published: December 2018

SUMMARY
For a bivariate normal distribution with variances and covariance given multiples of an unknown σ2, methods are presented for the combination of several separate estimates of the ratio of means, and for assessing confidence limits when an estimate of σ2 is available. A numerical example is presented of the application of this method in combining estimates of relative potency based on several parallel line assays of insulin.
Power of Tukey's Test for Non-Additivity
Authors: Ghosh M. N. , Sharma Divakar 
Published: December 2018

SUMMARY
The problem of testing for non-additivity in a two-way classification has been considered in this paper where the mean μii can be expressed as μ+αi+βi where αi and βi are the effects of the two ways of classification (i = 1, …,p;j = 1, …,q). Tukey (1949) has suggested a test for non-additivity. The power function of this test has been found in this paper for alternatives of the form μii = μ+αi+βi+cαi βi and numerical calculations made for the case of p = q = 6. For the sake of comparison the special case of α2i–1 = α2i, β2j–1 = β2j has also been considered, when an F-test is available with d.f. (4, 27). It is seen that the power of Tukey's statistic is slightly less than that of the F-test for smaller values of C 2 σ2 and ∑αi2σ2=∑βj2σ2, but for a wide range of values of these parameters, the performance of Tukey's statistic is better.
Higher Moments of a Maximum-Likelihood Estimate
Authors: Shenton L. R. , Bowman K. 
Published: December 2018

SUMMARY
For a distribution depending on a single parameter the first four sampling moments of the maximum-likelihood estimate to orders N−2, N−3, N−3 and N−4 respectively are given. Expressions for the measures of skewness γ1 and γ2 are also given. Several illustrative examples are included as a check on the heavy algebra. The paper extends earlier work by Haldane and Smith.
Higher-Order Properties of a Stationary Point Process
Authors: McFadden J. A. , Weissblum Walter 
Published: December 2018

SUMMARY
This paper is concerned with joint distributions, joint moments, and joint renewal functions in a stationary point process. The random variables considered are (a) the numbers of events in adjacent intervals of given lengths, located either arbitrarily in time or by an arbitrary event, and (b) the lengths of intervals measured to the various events, beginning either at an arbitrary point or at an arbitrary event. The different bivariate probability functions are related to each other by means of transforms. Moments are considered. In particular, the marginal moments of the number of events, counted by either method, are related to transforms of the multivariate renewal functions. Each product moment of the interval lengths is expressed as a multiple integral of the joint probability of certain numbers of events. A new theorem is proved, more general than in a previous paper, concerning the superposition of two independent stationary point processes. This theorem gives conditions under which the successive intervals between events can be independent in each of the constituent processes and also in the merged process.
An Approximate Solution of the Integral Equation of Renewal Theory
Authors: Bartholomew D. J. 
Published: December 2018

SUMMARY
An approximation is given to the solution of the integral equation for the renewal density. The approximation is of particular value when the renewal distribution has a high degree of positive skewness. For an important class of such distributions it also provides an upper bound to the renewal density. Some numerical comparisons are given for renewal processes in discrete time. Other methods of obtaining an approximate solution to the equation are briefly reviewed and compared with the new method.
A Test for Variance Heterogeneity in the Residuals of a Gaussian Moving Average
Authors: Herbst Laurence N. 
Published: December 2018

SUMMARY
A large sample test for variance heterogeneity in the residuals of a Gaussian moving average is presented, based upon periodogram-ratios of the data. For long series, it is shown that neither the null-hypothesis nor alternative-hypothesis behaviour of the test statistic is dependent upon the coefficients of the moving average (and these need not be estimated in advance). The alternative-hypothesis behaviour of the test statistic is discussed in terms of the coefficients in a Fourier expansion of the non-constant variance function.
On the Asymptotic Behaviour of Queues
Authors: Keilson J. 
Published: December 2018

SUMMARY
The homogeneous process N(t) on the lattice of integers in continuous time is discussed. When the increment probability generating function ϵ(u) is analytic at u = 1, the transition functions γn(t) = p{N(t) = n | N(0) = 0} are Bessel-like functions with simple asymptotic properties. The asymptotic behaviour of a variety of M/G/1, G/M/1 and related queueing systems may be deduced from these properties. An appendix is devoted to a review of saddle point methods and central limit behaviour for processes in continuous time.
Further Models for Estimating Correlation in Discrete Data
Authors: Tallis G. M. 
Published: December 2018

Summary
This note considers the distribution of the sum of n identically distributed multinomial variates Xi, the correlation coefficient for Xi and Xj being ρ for all i, j, i ≠ j. The initial model, with n and p' = (p1, p2,…,pk) fixed, is generalized by allowing first n, then p and finally both n and p to be random variables.
Relationships between Bayesian and Confidence Limits for Predictions
Authors: Thatcher A. R. 
Published: December 2018

Summary
Given the number of successes in a random sample, prediction limits can be determined for the number which will be observed in a second sample, in a way which does not depend on any assumption or inference about the unknown proportion in the population. Such “confidence limits” for the prediction are found to correspond to Bayesian solutions based on two particular prior distributions, and are related to Laplace's rule of succession. The results suggest a possible type of “prediction strategy”.
Note on Interval Estimation in Non-Linear Regression When Responses are Correlated
Authors: Halperin Max 
Published: December 2018

Summary
Recent papers by Williams and Halperin discuss procedures for obtaining confidence regions† for parameters in non-linear regression. These results assume, among other things, independence and homoscedasticity of variance of the dependent variables. This note points out that by using some results of Rao it is possible to drop these latter assumptions.
A Proposed Two-Sample Rank Test: The Psi Test and its Properties
Authors: Gibbons Jean D. 
Published: December 2018

Summary
Since the power of the Psi test proposed by Gibbons (1964) compares favourably with that of other one-sided, two-sample rank tests on the equality of two distribution functions, its properties merit further investigation. This paper is devoted to such a study. A table of exact critical values for the test statistic is given for selected small sample sizes, and compared with critical values for the approximate distribution which is a function of Student's t. The agreement is good even for small samples. Using the results of Chernoff and Savage (1958), the asymptotic distribution is found to be normal in both the null and alternative cases. The null mean and variance are 0 and rπ 2l(3mN) respectively. Expressions are given for the alternative moments. The relation of the Psi test to other test statistics, specifically Terry's c 1 test, the Wilcoxon or Mann-Whitney test, and Savage's DN statistic, is investigated in terms of correlation coefficients in the null case. The test is most similar to Terry's c 1 statistic.
Some Statistical Problems Connected with Crystal Lattices
Authors: Domb C. 
Published: December 2018

Summary
Three statistical problems are discussed which are of importance in physics. The first arises from the statistical mechanics of interacting systems on crystal lattices, and the statistical problem concerns the distribution of nearest neighbour contacts when two different species randomly occupy the sites of a crystal lattice. The relation between the partition function in statistical mechanics and the characteristic function in statistics is investigated. The second problem concerns the mean cluster size in such a random mixture, and a feature of particular interest is the critical concentration at which there is a non-zero probability of clusters stretching right across the crystal. The third problem deals with the properties of self-avoiding walks on lattices, such as their total number, mean square length, and resultant space distribution.
Confidence-Region Tests
Authors: Aitchison J. 
Published: December 2018

Summary
To test a hypothesis that a parameter has value θ* we usually ask whether an observation falls in a critical region of the outcome space. It is well known that, by a suitable choice of confidence region, an equivalent test is to ask whether θ* lies outside the confidence region. In this paper the concept of such a confidence-region test is extended in directions which are relevant to the study of data-snooping and multiple-hypothesis testing. These problems are investigated for linear models and, in the asymptotic case, for more general parametric models.
Polynomial Projecting Properties of Multi-Term Predictors/Controllers in Non-Stationary Time Series
Authors: Ray W. D. , Wyld C. 
Published: December 2018

Summary
Box and Jenkins (1962, 1963) introduce a practical predictor for handling non-stationary types of time series and they show it to be optimal for a particular class of stochastic processes. As a consequence the predictor can be shown to follow stochastic as well as deterministic polynomial trends in the series. The present paper sets out to evaluate the bias term in the expression for the error when applying this predictor, and shows how the bias can be reduced sometimes to zero for particular values of the parameters. This determination of bias is done in the context of deterministic polynomial trends but it can be shown to apply to the stochastic case also.
The Statistical Fourier Analysis of Variances
Authors: Herbst L. J. 
Published: December 2018

Summary
Let Xt (t = 1, 2, …, N) denote a series of independent normal random variables, with zero means and non-zero finite variances ft (t = 1, 2, …, N). Then ft and ft−1 admit finite Fourier expansions. The present paper is a study of the statistics N−1∑t=1NXt2cos (2πts/N) and N−1∑t=1NXt2sin (2πts/N) as estimators of the sth Fourier coefficients of ft, and of the distributional properties of suitable ratios of these statistics as (sufficient) test statistics for non-constancy of ft, directed at alternatives where the Fourier expansion of ft−1 has a simple form.
Recursive Relations for Predictors of Non-Stationary Processes
Authors: Whittle P. 
Published: December 2018

Summary
It is shown that if a process {xt} is generated recursively by a relation of type ∑j=0pajtxt−j=∑k=0qbktϵt−k+λt, where ajt, bkt and λt, are time-dependent sequences and {ϵt} is a process of unautocorrelated variables, then in general the linear least-square predictor of xt+m based upon {xs; s≤t}, denoted vt, obeys a recursion of the type ∑k=0qβktξt−k=∑j=0τcjtxt−j+vt, where r = max(p – 1, q – m). A method is given for obtaining the coefficients βkt, cjt and vt, and this solution is made explicit for various special cases.
Bayesian Estimation of Parameters of a Multivariate Normal Distribution
Authors: Evans I. G. 
Published: December 2018

Summary
A significant omission from the work of Raiffa and Schlaifer (1961) relating to a multivariate normal distribution is consideration of the case when the dispersion matrix is completely unknown. This paper partially fills the gap by applying the methods of Raiffa and Schlaifer to the particular problems of estimating the mean μ, the dispersion matrix ∑, and the generalized variance | ∑ |, when either or both of μ and ∑ are unknown.
The Basic Birth-Death Model for Microbial Infections
Authors: Williams T. 
Published: December 2018

Summary
On the assumption that parasite populations in vivo are governed by a linear, homogeneous birth-death process with undistributed parameters and that they generate only marginally faster than the host can destroy them, the distribution of their number at any time is obtained in terms of a Bessel function of imaginary argument. From this is derived the distribution of incubation period, defined as the first-passage time to a high response threshold. Various properties of the model are noted and compared with known characteristics of the infectious process.
Quasi-Stationary Distributions and Time-Reversion in Genetics
Authors: Seneta E. 
Published: December 2018

Summary
Finite absorbing Markov chains appear frequently as models for genetic processes. Although in such chains absorption in a finite time is certain, this time may be long, and it is then of interest to consider quasi-stationary distributions as describing the process in such situations; this is also true of certain infinite chains. Two such distributions are discussed, and derived for three particular genetic models as diffusion approximations. The distribution regarded as more satisfactory has interesting properties as regards “time-reversion” of the genetic process. A general discussion of this concept leads to the quasi-stationary generalization of Wright's formula for stationary distributions.
An Approach to the Study of Markov Processes
Authors: Kingman J. F. C. 
Published: December 2018

Summary
Whenever random processes are studied or applied, Markov processes almost inevitably appear. This paper looks at such processes from the point of view of an observer who takes note of the process only when it is in one particular state. This apparently perverse standpoint has yielded a powerful tool for the study of Markov processes on a discrete state space.