bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Numerical Investigation of Least Squares Regression Involving Trend-Reduced Markoff Series
Authors: Scott J. F. , Small V. J. 
Published: December 2018

Summary
The variation in the standard error of the regression coefficient between two trend-reduced time series, constructed from Markoff series, is examined for various choices of the trend-reducing operator. Tables are given to facilitate computation, for the regression between trend-reduced time series which approximate to Markoff series in their local variational properties.
A Contribution to the “Travelling-Salesman” Problem
Authors: Morton G. , Land A. H. 
Published: December 2018

Summary
This paper is concerned with finding the shortest closed path joining n points where the distances between all pairs of points are given.
For a set of points in a metric space we establish that the shortest path will consist of a single loop circuit that will never cross itself. The problem is formally stated in Linear Programming terms. The difficulty in the Linear Programming formulation is to avoid the appearance of sub-cycles. This has been effected by making the programme dynamic. The computational cost of a complete enumeration of all possible circuits or the cost of solving the Linear Programme being prohibitive for a large number of points, we attempt a practicable computing routine. The method proceeds by writing down the set of distances as a square matrix and selecting from the matrix a set of n links which will form an initial single loop circuit: the circuit is changed by simultaneously removing three links and introducing three new links without destroying the single loop form of the circuit.
Related methods and problems are discussed.
Algebraic Theory of the Computing Routine for Tests of Significance on the Dimensionality of Normal Multivatiate Systems
Authors: Binet F. E. , Watson G. S. 
Published: December 2018

Summary
Before attempting to allot individuals to one of a set of normal multivariate populations, it is usual to make preliminary tests of significance to discover the structural relationships of the populations. In order to secure this reduction there are two separate methods, due to Fisher and (essentially) to Wilks.
A simple algebraic proof is given for the identity of the statistics obtained from the two methods, and the condition under which Fisher’s method leads to less computation is pointed out.
To facilitate the contrast of the two methods, some well known principles and procedures have been restated in a more convenient form.
Partitions in More than One Dimension
Authors: Bennett J. H. 
Published: December 2018

Summary
Several important properties are derived for the new partitional functions introduced by Fisher (1950) in his enumeration of the number of partitions of an integer in an arbitrary number of dimensions. These functions readily lead to the enumeration of the number of partitions of an integer in more than one dimension and with given marginal partitions. This enumeration is given for bipartitions of the integers 1 to 8 inclusive.
On the Estimation of Small Frequencies in Contingency Tables
Authors: Good I. J. 
Published: December 2018

Summary
Suppose that we require estimates of the population frequencies corresponding to small entries in a large pure contingency table containing heterogeneity. It would be natural to lump rows or columns together with weights depending on the correlation coefficients. But if the rows, say, are nearly orthogonal, no lumping method will be reasonable. Moreover, if many of the entries in the table are missing, a lumping method may fail. A method is given here (which it may be possible to combine with a lumping method when appropriate) that depends on an assumption for the initial distribution of the “association factor” in each cell, i.e. the ratio of the population frequency in the cell to the product of the population frequencies of its row and column. If the logarithm of the association factor is assumed to have, initially, a normal distribution, then the final expectations and variances of the population frequencies and of their logarithms can be expressed in terms of the “after-effect” function which was originally tabulated by K. W. Wagner for an electrodynamical application. Instead of a log-normal distribution, a Pearson Type III distribution may be assumed for the association factor. This assumption may be less accurate but is easier to handle.
The paper concludes with a list of properties of the after-effect function (and of some of its generalizations) that may be useful for further tabulation.
The Within-Animal Bioassay with Quantal Responses
Authors: Claringbold P. J. 
Published: December 2018

Summary
The four-point cross-over design is four times as economical in animals as the standard Allen-Doisy quantal bioassay.
This finding is applicable to other bioassays provided the total variation of response includes components due to animal differences and due to secular trends in response.
Analysis of quantal data with one animal per treatment group may, if the expected proportion responding is in the interval 5–95 per cent., be simplified by scoring the responses as 0 or 1, and performing an analysis of variance.
On Limiting Distributions Arising in Bulk Service Queues
Authors: Downton F. 
Published: December 2018

Summary
The limiting behaviour is discussed of a simple queueing process, in which customers. arrive at random, form a single queue in order of arrival, and are served in batches, the size of each batch having a fixed maximum, as this maximum tends to infinity. Limiting distributions are obtained for the situations where the service interval has a χ2 distribution with an even number of degrees of freedom, and the queue is assumed to be in equilibrium. These situations include as special cases random service and regular service. A similarity is noted between these limiting results and the solution to other queueing situations.
Some Experimental Designs of Use in Changing from One Set of Treatments to Another, Part I
Authors: Freeman G. H. 
Published: December 2018

Summary
A description is given of various designs of use in changing from one set of treatments to another. Most of the designs are well known, but one, which involves new treatments partially balanced with respect to both blocks and original treatments, has not previously been described in general. The analysis of variance is given for this design, together with the variance of treatment differences, a lemma of use for the derivation of the latter also being proved. The analysis of covariance is given, this presenting no difficulties, and the design is also shown to be valid. An example is given, showing the derivation of all the parameters in an actual design.
Routine Analysis of Replicated Experiments on an Electronic Computer
Authors: Yates F. , Healy M. J. R. , Lipton S. 
Published: December 2018

Summary
The paper describes the methods that have been developed for the analysis of replicated experiments on the electronic computer at Rothamsted. The general principle followed is to make the machine carry out the whole of the analysis, including the calculation of standard errors and residuals, the results being given in a form suitable for immediate transmission to the experimenter. Missing plots and covariance can also be handled. Preliminary computations on the raw data are carried out by the machine, using a routine which is common to all types of design. The data are punched on tape, a variate at a time, in the order they are received from the experimenter, i.e. without de-randomization.
Programmes have now been written for the commoner types of design such as randomized blocks, Latin squares, 33 (single replicate), and 2n designs. As an example, one of the more complex programmes, that for 2n designs, is described in some detail. This programme handles all types of 2n design containing up to 128 plots, including confounding, estimation of error from high order interactions, fractional replication, factors at 4 and 8 levels, and 8 × 8 quasi-Latin squares.
A brief outline of the mode of operation of electronic computers is given.
The Modified Latin Square
Authors: Rojas B. , White R. F. 
Published: December 2018

Summary
The modified latin square design (semi-latin square) is described and discussed. The expectations of the mean squares are derived and, from these, the nature of the bias is developed. Empirical values of the bias are obtained from some corn uniformity data and found to be small. An unbiased estimator of the error of a comparison among treatments is obtained. A formula for obtaining the efficiency of the modified latin square relative to randomized blocks, using modified latin square data, is given and this formula is applied to the uniformity data. The efficiency of the modified latin square with this type of data is found to be of the order of lattice designs. The analysis of variance of a group of modified latin square designs performed at different “places” is discussed.
Statistical Approach to Problems of Cosmology
Authors: Neyman Jerzy , Scott Elizabeth L. 
Published: December 2018

SUMMARY
The basic hypothesis underlying current deterministic cosmologies, namely the so-called cosmological principle, can be stated precisely only in terms of probabilistic concepts. Consequently, considerable progress and aesthetic gain may be expected if determinism is abandoned and replaced by a frank probabilistic treatment of cosmology. This requires the adoption of the view that the Universe is a realization of a stochastic process which is stationary in the three (spatial) co-ordinates (cosmological principle) and possibly also stationary in the fourth (time) co-ordinate (“perfect” cosmological principle). Two examples are given of problems relevant to deterministic cosmological theories that elude deterministic treatment, but lend themselves to an indeterministic statistical study.
The Effect of the Size of the Waiting Room on a Simple Queue
Authors: Finch P. D. 
Published: December 2018

SUMMARY
The effect of the size of the waiting room on a queue with a random input process is considered, a particular case studied is that for which the service time is also random. The study originated in an investigation of storage problems along a production line and in an analysis of the provision of the internal buffer storage in electronic digital computers. For this reason the study is formulated in terms applicable to storage problems.
The Behrens-Fisher Distribution and Weighted Means
Authors: James G. S. 
Published: December 2018

SUMMARY
(1) The Behrens-Fisher and Welch solutions of the two-means problem are compared, and the former shown to be lacking in sensitivity. (2) Yates’s and the author’s tests for a weighted mean are compared, and the former shown to reject the true value of the mean, in error, more often than is indicated by the nominal significance level (in extreme cases nearly twice as often). (3) A new test for weighted means is put forward which does not neglect the information on the variances supplied by the difference between the means, and which is “exact”. (4) An incidental by-product is the Cornish-Fisher expansion for a symmetrical distribution, taken to some further terms.
Some Simple Duration-Dependent Stochastic Processes
Authors: Mercer A. 
Published: December 2018

SUMMARY
The problem considered is that of two discrete states in continuous time; the transition probabilities depend on the total time, t, spent in, say, state 1. The probability that at a given time τ the process is in state i and the total time spent in state 1 lies in (t, t + δt) is derived. Some limiting cases for which the transition probabilities are powers of t are considered. The probability that the total time spent in state 1 reaches t in the interval (τ τ+ δτ) is also considered and some limiting distributions are obtained.
A Statistical Theory of Remnants
Authors: Aitchison J. 
Published: December 2018

SUMMARY
In certain manufacturing processes where varying lengths of material are produced and subsequently cut up into unit lengths the problem of loss from wasted material arises. In this paper we postulate a statistical model of such a process and study how and in what sense we may minimize this loss. Two simple tests of whether a process is under optimum control are proposed. Finally we consider briefly two extensions of the theory to corresponding problems in k dimensions.
Estimation of Location and Scale Parameters for the Rectangular Population from Censored Samples
Authors: Sarhan Ahmed E. , Greenberg B. G. 
Published: December 2018

Summary
Best linear estimates of location and scale parameters under conditions of Type II censoring are obtained for the rectangular distribution. In addition, functions of the location and scale parameters such as the start and end of the distribution, as well as percentile points, are also estimable. A special case occurs where the rectangular distribution starts at the origin. Tables are available from the authors to furnish coefficients to facilitate all computations for samples of size up to 10. Graphs are included to show the effect on the relative efficiency caused by censoring.
The Output Process of the Queueing System M/G/1
Authors: Finch P. D. 
Published: December 2018

Summary
It has been proved by Burke (1956) and Reich (1957) that the output process of a single server queue with a Poisson input process and negative exponential distribution for service time is again a Poisson process with the same parameter as the input process. In this paper single server queues with a Poisson input process and a general class of service time distribution are considered. It is shown that successive interdeparture intervals are independent in the limit only in the case the service time is negative exponential. It is shown also that if the size of the waiting room is taken into account as in Finch (1958) then successive departure intervals are not independent in the limit even when the service time is negative exponential.
The Busy Period in Relation to the Single-Server Queueing System with General Independent Arrivals and Erlangian Service-Time
Authors: Conolly B. W. 
Published: December 2018

Summary
The Busy Period relating to GI/Ek/1 is investigated by the method used by Conolly (1959) for GI/M/1. The system is simulated by a model in which arrivals take place in groups of fixed size k, service on each customer being random. This is an alternative to the more familiar “phase-service” concept used, for instance, by Wishart (1956).
Estimation of Parameters in Time-Series Regression Models
Authors: Durbin J. 
Published: December 2018

Summary
We consider the estimation of the coefficients in a general linear regression model in which some of the explanatory variables are lagged values of the dependent variable. For discussing optimum properties the concept of best unbiased linear estimating equations is developed. It is shown that when the errors are normally distributed the method of least squares leads to optimum estimates. The properties of the least-squares estimates are shown to be the same asymptotically as those of the least-squares coefficients of ordinary regression models containing no lagged variables, whether or not the errors are normally distributed. Finally, a method of estimation is proposed for a different model which has no lagged dependent variables but in which the errors have an autoregressive structure. The method is shown to be efficient in large samples.
Maximum-Likelihood Estimation Procedures and Associated Tests of Significance
Authors: Aitchison J. , Silvey S. D. 
Published: December 2018

Summary
The essence of many statistical problems, including most standard techniques, is to test whether or not the unknown parameters of an appropriate statistical model satisfy certain restrictions; and the outcome of such a test dictates whether it is necessary to provide estimates of these parameters which also satisfy the restrictions. In this paper we discuss and illustrate the relative merits, as practical tools for the consulting statistician, of two large-sample techniques of wide applicability to such situations: (i) unrestricted maximum-likelihood estimation with its associated Wald test, (ii) restricted maximum-likelihood estimation with its associated Lagrange-multiplier test. The discussion falls into two main sections corresponding to two methods of specifying restrictions, as constraint equations in the parameters, or as freedom equations expressing the parameters in terms of a second smaller set of parameters. The methods are modified by a simple device to apply to the case where constraints on the parameters are necessary to allow their identification.
Confidence Limits for Multivariate Ratios
Authors: Bennett B. M. 
Published: December 2018

SUMMARY
As a generalization of Fieller’s theorem for the case of two or more multivariate populations, confidence limits are derived for several ratio problems. These confidence limits are the shortest interval provided by the real roots of a certain high-order polynomial, the coefficients of which are subject to sampling variation. An example from anthropometry is given for the practical determination of these confidence limits.
The Time-Dependent Solution for an Infinite Dam with Discrete Additive Inputs
Authors: Yeo G. F. 
Published: December 2018

SUMMARY
This paper considers an infinite dam in discrete time fed by independent additive inputs and having a unit release at the end of each unit time interval, unless the dam is empty. The time-dependent solution for the dam content distribution is obtained. This depends on the probability of emptiness, which is itself determined as a function of the known probability of first emptiness. The general result is used to find solutions for the dam with negative binomial and Poisson inputs.
A Test of Homogeneity for Ordered Variances
Authors: Vincent Shirley E. 
Published: December 2018

SUMMARY
Suppose that an estimate of variance is available from each of a set of normal populations. The situation in which there is a definite trend in the magnitude of the population variances is considered, and this is represented by assuming the ith variance to be inversely proportional to λ + iμ. A uniformly most powerful unbiased test is developed for the hypothesis μ = 0, and methods for estimating μ and λ are considered.
A Simple Congestion System with Incomplete Service
Authors: Cox D. R. 
Published: December 2018

SUMMARY
Customers arrive at random in a system with m servers, each customer having a desired service-time. If on the arrival of a new customer all servers are busy, one of the m customers being served is displaced, even though his desired service-time is incomplete. The choice of a customer for displacement is specified by a displacement rule. Thus each customer has an achieved service-time, which may be less than the desired service-time. One index of efficiency of the system is the ratio I of the mean achieved service-time to the mean desired service-time. The quantity I is calculated for random arrivals under several different sets of assumptions concerning the displacement rule and the distribution of desired service-time. The problem was suggested by an investigation of systems of production control.
On Quadratic Estimates of the Interclass Variance for Unbalanced Designs
Authors: Read Robert R. 
Published: December 2018

SUMMARY
The optimum properties of the popular estimate of the interclass variance in components of variance models are known if there are an equal number of observations in the subclasses. In contrast to this, it is shown that unbiased quadratic estimates having uniformly minimum variance do not exist if the design is not balanced.
On the Asymptotic Sufficiency of Certain Order Statistics
Authors: Rohatgi Mandakini S. 
Published: December 2018

SUMMARY
The problem of estimating distance to a stellar system, from measurements on the apparent magnitude of the jth brightest object in the system, reduces to estimating the location parameter of a distribution. Astronomical observations provide apparent magnitudes of only a few of the brightest objects in a system. In this connection, two theoretical problems arise. One is to find the best estimate based on available observations, and the other to determine which of the objects should be observed in order to attain the greatest precision for the estimate. It is found that, if the number of objects n in the system is large, then, depending on the luminosity function, either the apparent magnitude of the brightest or the faintest of the available objects is asymptotically sufficient for the location parameter.
The Estimation of Slope When the Errors are Autocorrelated
Authors: Jenkins G. M. , Chanmugam J. 
Published: December 2018

SUMMARY
In this paper an investigation has been made of the problem of constructing systematic and randomized designs for the estimation of slope when the errors are autocorrelated. Some results are obtained for general stationary processes and specific designs given for moving average and autoregressive processes. Comparison is made with randomized block designs. The theory is illustrated on a time-series obtained from a uniformity trial on a batch production process.
Large-Sample Restricted Parametric Tests
Authors: Aitchison John 
Published: December 2018

SUMMARY
Restricted tests are designed to examine a hypothesis not against the natural complete alternative but against some subhypothesis of that alternative. The theory of such tests provides a unification of many aspects of large-sample tests—the analysis of nested hypotheses, the possibility of using tests of increased power and of easing certain computational procedures, the notions of separable hypotheses and of partitioning a test statistic. While many standard results can thus be brought within the framework of this theory the emphasis throughout the paper is on providing the consulting statistician with manageable tools for non-standard situations.
On a Simple Procedure of Unequal Probability Sampling Without Replacement
Authors: Rao J. N. K. , Hartley H. O. , Cochran W. G. 
Published: December 2018

SUMMARY
A simple procedure of unequal probability sampling without replacement is proposed. It leads to an estimator of the population total having a smaller variance than is obtained by sampling with replacement. Other advantages of the present method are simplicity of calculation and the possibility of estimating exactly the variance of the estimator.
Sampling Properties of Tests of Goodness-Of-Fit for Linear Autoregressive Schemes
Authors: Chanda K. C. 
Published: December 2018

SUMMARY
Sampling properties of tests for trend-free linear autoregressive schemes due to Bartlett and Diananda, to Quenouille, and to Whittle have been investigated. The investigation consists of the calculation of the first two moments of the various test-criteria which are χ2‘s with k degrees of freedom, where k is the number of asymptotically independent linear compounds on which the χ2‘s are based. The purpose is to examine the effect of the combination of individual constituents of χ2 on the validity of the test-criteria when the sample is not large. It has been demonstrated that when the sample is not very large, the contributions due to the terms involving k/n are considerable, a fact which confirms the empirical conclusions of Rao and Som (1951). In view of the apparent loss of validity thus entailed a modified test is suggested to be used when the sample size is small.
Analysis of Stationary Processes with Mixed Spectra—Ii
Authors: Priestley M. B. 
Published: December 2018

SUMMARY
We investigate the asymptotic power functions of three types of tests for detecting the presence of harmonic components superimposed on a nonuniform spectral density function. These power functions are tabulated for a range of values of the signal to noise ratio of the process, and each test is applied to several artificial series of the “mixed ”type with known structure.