bluuebunny/crossref_metadata_2025 huggingface dataset:
Comparisons of pedometer‐determined weekday physical activity among Swedish school children and adolescents in 2000 and 2017 showed the highest reductions in adolescents
Authors: Raustorp Anders , Fröberg Andreas
Published: December 2018

Aim

This study compared differences in weekday physical activity among school children and adolescents in middle‐class communities in south‐eastern Sweden in 2000 and 2017.

Methods

Data were drawn from two independent cross‐sectional cohorts of children and adolescents aged 8, 11 and 14. The same six schools, protocols, procedures and instruments were used in both years, with 332 subjects in 2000 and 562 in 2017. Mean steps per day (SPD) were measured with a Yamax SW‐200 pedometer.

Results

The mean weekday SPD was similar among eight‐year‐old girls in both years, but 8% (p = 0.040) higher among eight‐year‐old boys in 2017. However, among 11‐year‐old children, the mean SPD were 12% lower among both girls (p = 0.033) and boys (p = 0.001). The SPD among 14‐year‐old adolescents were 24% (p = 0.012) and 30% (p < 0.001) lower among girls and boys, respectively.

Conclusion

This school‐based study from south‐eastern Sweden showed that weekday physical activity differed between age groups in 2000 and 2017. The highest reductions were seen among older children and adolescents, particularly 14‐year‐old girls and boys. The only group that increased was eight‐year‐old boys, with no significant change in eight‐year‐old girls. A possible explanation might be the dramatically increased use of the Internet on phones and tablets.
System justification theory at 25: Evaluating a paradigm shift in psychology and looking towards the future
Authors: Osborne Danny , Sengupta Nikhil K. , Sibley Chris G.
Published: December 2018

Since first being proposed 25 years ago, system justification theory has become a paradigm‐shifting framework for understanding intergroup relations and political psychology. Based on the thesis that people are motivated to defend and bolster the societal status quo, system justification theory helps to explain varied phenomena, including resistance to change, outgroup favouritism, and other instances of false consciousness. This paper summarizes four tenets of the theory including the following: (1) antecedents to system justification, (2) palliative effects of system justification, (3) status‐based asymmetries in conflict between justification motives, and (4) societal consequences of system justification. Throughout our review, we highlight how system justification theory helps to explain why disadvantaged groups might sometimes support the status quo, emphasizing research conducted outside the United States when possible. We conclude by calling on future research to (1) further utilize nationally representative and multi‐level data, (2) investigate the relational motives behind system justification, (3) address social change from a system justification perspective, and (4) extend system justification theory's focus beyond WEIRD societies.
Gastroduodenal intussusception of a gastric carcinoma
Authors: Suda Tsuyoshi , Hodo Yuji , Shirota Yukihiro
Published: December 2018

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Getting cosy in freshwater: Assumed to be brackish pike are not so brackish after all
Authors: Birnie‐Gauvin Kim , Birch Højrup Lasse , Kragh Theis , Jacobsen Lene , Aarestrup Kim
Published: December 2018

Pike (Esox lucius) occupy coastal streams and rivers of the Baltic Sea, where they attain large sizes (>5 kg). These large sizes are perhaps due to the fact that they can tolerate relatively high salinities and can thus forage in the nearby more productive brackish environments. In an attempt to quantify the extent to which pike utilise brackish environments, and to provide some insight into the underlying causes for brackish water migrations, we tagged 30 pike from a western Baltic river with acoustic transmitters and were able to track 21 individuals for 1 year. Based on experienced from local anglers, this population was assumed to be brackish in nature, where individuals underwent freshwater migrations to spawn. Our findings however suggest that the smallest and most active individuals make short exits into brackish waters and do so on rare occasions. Our results further indicate that neither sex nor size is related to activity level. We suggest that these patterns reflect two distinct behaviours—active and passive—and that large pike can be supported by the food availability in the river, without the need to venture into coastal zones, thus defying the conventional view that Baltic pike are all brackish in nature.
The selfie trap: A novel camera trap design for accurate small mammal identification
Authors: Gracanin Ana , Gracanin Vanja , Mikac Katarina M.
Published: December 2018

Camera traps are a popular tool for monitoring wildlife though they can fail to capture enough morphological detail for accurate small mammal species identification. Camera trapping small mammals is often limited by the inability of camera models to: (i) record at close distances; and (ii) provide standardised photos. This study aims to provide a camera trapping method that captures standardised images of the faces of small mammals for accurate species identification, with further potential for individual identification. A novel camera trap design coined the ‘selfie trap’ was developed. The selfie trap is a camera contained within an enclosed PVC pipe with a modified lens that produces standardised close images of small mammal species encountered in this study, including: Brown Antechinus (Antechinus stuartii), Bush Rat (Rattus fuscipes) and Sugar Glider (Petaurus breviceps). Individual identification was tested on the common arboreal Sugar Glider. Five individual Sugar Gliders were identified based on unique head stripe pelage. The selfie trap is an accurate camera trapping method for capturing detailed and standardised images of small mammal species. The design described may be useful for wildlife management as a reliable method for surveying small mammal species. However, intraspecies individual identification using the selfie trap requires further testing.
Previously uncharacterized amino acid residues in histone H3 and H4 mutants with roles in DNA damage repair response and cellular aging
Authors: Thakre Pilendra K. , SV Athira , Golla Upendarrao , Chauhan Sakshi , Tomar Raghuvir S.
Published: December 2018

Chromatin regulates gene expression and genome maintenance, and consists of histones and other components. The post‐translational modification of histones plays a key role in maintaining the structure and function of chromatin under different pathophysiological stress conditions. Here, we investigate the functions of previously unexplored amino acid residues in histones H3 and H4. To do so, we screened a library of yeast histone mutants following DNA damage and identified that substitution mutations of histone H3 (H3Q5A/E and H3Q120A) and H4 (H4Y88A/E and H4R78K) render yeast cells sensitive to DNA‐damaging agents. These histone mutants show an activated DNA damage response, Rad53 phosphorylation and Sml1 degradation in the presence of methyl methanesulfonate (MMS). In histone H3Q5A/E mutants, RNR2 and RNR3 genes were induced at low level, as was RNR3 in H4 histone mutants following DNA damage. In H3 mutant cells, the cell cycle was deregulated, leading to inefficient cell cycle arrest in the presence of MMS, and genes involved in aging and DNA damage repair pathways were constitutively upregulated. In H3 mutants (H3Q5A, H3Q5E and H3Q120A), we observed reduced chronological lifespan (CLS), compared with extended CLS in the H4R78K mutant. Histone mutants also showed altered H3K4me and H3K56ac modifications and improper activation of the stress responsive Slt2 and Hog1 kinases. Thus, we have determined the significance of previously uncharacterized residues of H3 and H4 in DNA damage response, cell cycle progression and cellular aging.
Coordination of a two‐echelon supply chain in presence of market segmentation, credit payment, and quantity discount policies
Authors: Taleizadeh Ata Allah , Rabiei Naghmeh , Noori‐Daryan Mahsa
Published: December 2018

In today's competitive business markets, a revenue optimization method is always one of the most crucial issues ahead of commercial supply chains so that it is utilized by the managers to improve their profitability. On the other hand, enhancing coordination and collaboration between the chains’ members has taken a vital role in increasing their efficiency and profitability. Thus, managers tend to employ/design marketing and coordinating incentive mechanisms using the revenue optimization method, as the most influential tools, to motivate the purchasers to order more and subsequently increase their market share. Here, this issue is studied in a two‐echelon supply chain by designing incentive contracts in order to evaluate the profit of organizations and enterprises and assess the best contract, which causes the highest profit, as the main goal of the businesses. In this study, a pricing‐inventory model is developed for a single‐item two‐echelon supply chain consisting of a manufacturer and a retailer in the presence of three different scenarios. In the first scenario, a credit payment (delay‐in‐payment) contract is considered between the chain members. In the second scenario, we studied a market segmentation policy in which the market demand is divided into price and quality oriented customers’ demand while a quantity discount contract is assumed as the third one. The profit of supply chain under these new conditions is computed by some numerical examples and then the effects of cost parameters on the decision variables and the profit are analyzed.
Part II: An Evaluation of Factor Analysis from the Point of View of a Psychologist
Authors: Smith B. Babington
Published: December 2018

Summary of Contents

The need for such a method—Some historical points—What goes in and what does not—Some aspects of method—Q and R techniques—Burt’s reconciliation of Q and R and their relationship to analysis of variance—Stephenson’s treatment of trait universes—The importance of factors—Conclusions.
The Productivity of Machines Requiring Attention at Random Intervals
Authors: Benson F. , Cox D. R.
Published: December 2018

In many industrial processes an operative attends a number of machines which stop from time to time. Each time a machine stops the operative has to do a certain amount of work before it can be restarted. If at any time two or more machines are stopped simultaneously, there will be a loss of production due to the period the machines have to wait for attention. In this paper we derive methods of estimating this loss of production when the operative has no duties away from the machines and discuss modifications to the theory when the operative has other duties.
Computation and Interpretation of Multiple Regressions
Authors: Woolf Barnet
Published: December 2018

Full practical directions are given for the expeditious calculation of regression equations, which are built up by successive insertion of additional variates. The computer can readily measure the contribution made by each new variate to the goodness of fit, omit variates which do not make a significant contribution, and select that group of independent variates which together give the lowest residual mean square in the dependent variate. The statistical properties of the regression equation, and of the successive reciprocal matrices from which it is derived, are discussed in detail, with special reference to the proper interpretation of the equation and its associated tests of significance. In dealing with experimental or observational data it is rarely necessary to work to more than four or at most five significant figures.
On Certain Probability Distributions Arising from Points on a Line
Authors: Sukhatme B. V.
Published: December 2018

The paper discusses for m points of k different colours on a line, the distributions for the number of (i) joins between points of different colours, (ii) triplets, quadruplets and s-plets, and (iii) runs of length r and total number of runs of lengths r1 and r2 of a specified colour. The expressions for the first four cumulants for all these distributions are given and found to be linear in m. It is shown that the distributions tend to the normal form when m tends to infinity, except when the probability of the points taking a specified colour is very small. In the latter case the distributions tend to the Poisson form.
Some New Designs of Latin Square Type
Authors: Pearce S. C.
Published: December 2018

A study is made of certain designs of Latin square type, namely, Latin squares with (a) a column added, (b) a row and a column added, and (c) a column added and a row omitted.

Recommendations are given for the analysis of data by a method leading to an unbiased test. It is shown that sufficient randomization is obtained by writing down a possible configuration of plots and permuting rows and columns at random.
Some Recent Work on Systematic Experimental Designs
Authors: Cox D. R.
Published: December 2018

An experimental design in which there is no randomization by the experimenter, except possibly in naming the treatments, is called systematic. Recent work is reviewed on systematic designs for use when the residual variation is (i) autocor-related and (ii) formed from a trend plus a random error. An example is given of the application of the second type of design in wool textile research.
Second Order Autoregressive Schemes with Time-Trending Coefficients
Authors: Hartley H. O.
Published: December 2018

It has been suggested that the departure of certain time series from a fitted second order autoregressive scheme is due to time-trending coefficients in the generating differential equation. If coefficients with linear time-trends are introduced into the scheme the correlogram of the resulting non-stationary series can, in special cases, be evaluated exactly in terms of Airy integrals and is found to be approximately of the form sin s/s where s is proportional to the lag.
The Analysis of Multiple Stationary Time Series
Authors: Whittle P.
Published: December 2018

After some preparatory work, the least square estimation equations are derived for a purely nondeterministic stationary multiple process (Th. 6). The asymptotic covariances of the parameter estimates are calculated for a normal process (Th. 9) and a test of fit derived (Th. 10). The testing of a sunspot model provides an illustration of the methods developed.
Control Charts for the Mean of a Normal Population
Authors: Page E. S.
Published: December 2018

The paper discusses the choice of sample size and of control limits for controlling the mean of a normal population in the most economical manner by the control chart method. Some tables are given to enable the best choice to be made easily.
The Errors of Lattice Sampling
Authors: Patterson H. D.
Published: December 2018

Lattice samples are samples selected from a multiple classification of units with one unit in each subclass in such a way that they include equal numbers of units from each main class or from each combination of two, three or more main classes in different classifications. The present paper provides a discussion of the errors of such samples.

Methods for determining the sampling variances from the complete data, when these are available, for purposes such as a comparison of different sampling methods, are described for several methods of selection. The estimation of the sampling variances from the sample data is also considered. In general estimates of error can be obtained (a) from samples consisting of special patterns of units or (b) from random samples of several mutually exclusive sets each of which itself constitutes a lattice sample. If suitable elements of randomization are introduced method (a) is satisfactory for selecting samples of 2p units from a p × p lattice, samples of 2p2 units from a p × p × p lattice and, in general, 2pn–1 units from a pn lattice. In other cases, however, the estimated means and errors may be inaccurate. Method (b) is most useful when several lattices have to be sampled.

The case of the square lattice is considered in detail and rigorous proofs of the various formulae are given. In the section on cubic lattices a method is given whereby the required expressions can be written down immediately in terms of components of variance. This method is extended to the general case of sampling a pn lattice. Examples of rectangular lattices and multistage sampling are also briefly considered.
Limits for the Ratio of Means
Authors: Creasy Monica A.
Published: December 2018

Limits for the ratio of the means of two normal distributions are obtained by a method which appears to be analogous to that used in finding fiducial limits for the difference of two means with possibly unequal variances (the Fisher-Behrens problem). The properties of these limits are compared with those obtained using Fieller’s solution of this problem, for the case of known variances and zero correlation. The extension to more general cases is also discussed.
Problems of Sample Allocation and Estimation in an Agricultural Survey
Authors: Church B. M.
Published: December 2018

A sampling method which has been used in fertilizer surveys in England and Wales is described. The relative efficiencies and biases of several methods of estimating average fertilizer dressings are determined from the results of eight surveys carried out in 1950. The unbiased method of estimation is found to be 65 per cent efficient relative to the unweighted mean of the field observations; this latter method is only slightly biased. An alternative method of estimation, eliminating any gross bias which might occur in the unweighted mean, has a relative efficiency of 90 per cent.

The size and most appropriate form of sample for given accuracy are discussed and compared with those adopted in recent surveys. The advantage of revisiting the same farms when estimating trends in fertilizer practice is examined.
Least Squares Regression Analysis for Trend-Reduced Time Series
Authors: Jowett G. H.
Published: December 2018

The difficulties of obtaining a valid estimate of the standard error of a regression coefficient between two time series are discussed. It is shown how a preliminary trend-reducing operation on the series, using a moving average, makes it possible to obtain such a valid estimate. A method of analysis is described, along with considerations which affect the best choice of moving average for the purpose, which is applicable when the local variational properties of the series resemble those of Markoff series.
A Rectifying Inspection Plan
Authors: Wurtele Zivia S.
Published: December 2018

In an article in the Supplement to the Journal of the Royal Statistical Society (1946), Anscombe discusses rectifying inspection plans which control the probability of using a substandard lot. A method is given for calculating the stopping points of one of these.
Some Applications of Zero-One Processes
Authors: Lomnicki Z. A. , Zaremba S. K.
Published: December 2018

Zero-one processes are defined as discrete-parameter stochastic processes in which the random variables take the values 0 and 1 only. Various processes of this kind can be derived from any discrete-parameter stochastic process; they include, in particular, the upcross and peak processes. Apart from the intrinsic interest of some of them, the study of these processes yields reasonably accurate methods of estimating the parameters of a Gaussian primary process by means of mere counting. The consistency proofs are based on an elementary lemma concerning the normal probability integral over the positive orthant of the four-dimensional Euclidean space. Applications to autoregressive schemes are discussed.
A Significance Test for the Difference in Efficiency between Two Predictors
Authors: Healy M. J. R.
Published: December 2018

Hotelling has derived a method of testing whether one predictor is significantly more efficient than another, in the sense of giving rise to a smaller residual standard deviation about a linear regression. His results are derived by an alternative method and put into a form suitable for practical use.
On a Test of Significance in Pearson’s Biometrika Tables (No. 11)
Authors: Fisher Ronald
Published: December 2018

The publication by Pearson and Hartley of numerical values for the proposed solution of Behrens' problem developed by Welch, affords an opportunity of clarifying in concrete terms, ideas which have in the past been disputed in perhaps a too abstract an atmosphere. Behrens' problem was to find a test of significance suitable for testing the hypothesis that two normal populations with unknown variances had a common mean. The fact that an unknown variance-ratio entered into the test was a comparatively novel feature, and has led to the problem being described as a test-case for examining different views of the process of testing hypotheses.
A Sequential Test for Randomness of Intervals
Authors: Bartholomew D. J.
Published: December 2018

This paper gives a sequential version of the test discussed by Moran (1951) for the random division of an interval.
An Elementary Method of Solution of the Queueing Problem with a Single Server and Constant Parameters
Authors: Champernowne D. G.
Published: December 2018

The queueing problem, in which the input and service time have independent negative exponential distributions with constant parameters, is studied for the single server case. The “simple” problem with constant parameters, dealt with first by W. Ledermann and G. E. H. Reuter (1954), and by A. B. Clarke (1953) was considered by these writers in relation to far more general problems, and their solutions are accordingly less simple than is possible in the special case: This special case has recently been investigated by Bailey (1954) by means of a generating function technique. In view of its importance I propose to obtain the result directly: it will be found in terms of Bessel Functions in the form obtained by Dr. A. B. Clarke. He has pointed out there that this solution is easily adapted to the case where the ratio of the exponential parameters for the two waiting times is constant but where each parameter is not necessarily constant.
Note on Some Criticisms Made by Sir Ronald Fisher
Authors: Welch B. L.
Published: December 2018

In a recent note Sir Ronald Fisher (1956) has commented upon some tables which were calculated under my direction and first published in Biometrika about seven years ago (Aspin, 1949). Fisher is concerned with what he supposes to be errors in the values given. The object of the present reply is to explain once more what the tables aim to do, and to maintain that there is no justification in Fisher’s criticism.
The Spectral Analysis of Time-Series
Authors: Jenkins G. M. , Priestley M. B.
Published: December 2018

(i) A review has been made of spectral analysis and its relation with other branches of time-series analysis. A detailed account has been given of the methods available for estimating the spectral density, the band spectrum and the integrated spectrum; suggestions have also been made for confidence intervals for the latter two estimators. (ii) Emphasis has been laid throughout upon the difficulties which are met in practice and gaps in the theoretical structure have been indicated. In applications to physical problems, it is suggested that an empirical statistical approach is not enough by itself and that more realistic descriptions of each particular phenomenon should be attempted. (iii) Reference has already been made in Section 9 to a sampling investigation in which it is proposed to apply the techniques mentioned in this paper to a large number of artificially constructed series of the type given by (1).
On Estimating the Spectral Density Function of a Stochastic Process
Authors: Lomnicki Z. A. , Zaremba S. K.
Published: December 2018

On the basis of an expected-mean-square-error criterion, the authors discuss the various hitherto proposed estimators of the spectral density function of a discrete-parameter process; they also introduce a new estimator. Any of these estimators depends on some parameter, and indications are given as to how this parameter should match those of the process in order to optimize the estimator. The alleged conflict between resolvability and statistical reliability is discussed. By way of illustration, the case of a first-order Markov process is treated in detail. Numerical applications are also given.
Joint Asymptotic Distribution of the Median and a U Statistic
Authors: Sukhatme Balkrishna V.
Published: December 2018

It is shown that under mild restrictions on the density function, the joint distribution of the median and a U statistic is asymptotically normal. This result is extended to random vectors as also to generalised U statistics occurring in the two-sample problem.
On the Use of the Normal Approximation in the Treatment of Stochastic Processes
Authors: Whittle P.
Published: December 2018

A method of treating nonlinear Markov processes is discussed, based on the assumption that the variates are normally distributed. The method is applied to models of logistic population growth, plant competition, and animal predation. In the preparatory section (§2) an alternative form (9) of the Bartlett relation is deduced, which is relatively convenient if one wishes to derive equations for the cumulants of a Markov process; the relation is particularly useful in the case of normal processes. In order that one may treat the joint distribution of the variate values at several instants of time, the Bartlett relation is generalized to provide equations (40) and (41) for the characteristic functional of the process. The validity of the “normalization technique” is discussed in the final section, and a comparison made with other methods.
Normal Approximation to Machine Interference with Many Repairmen
Authors: Naor P.
Published: December 2018

An approximate solution of the machine interference problem with many repairmen is derived in terms of the normal distribution.
The Fitting of Markoff Serial Variation Curves
Authors: Davies Hilda M. , Jowett G. H.
Published: December 2018

The generalized least squares method is used to establish a practical method of fitting the function θ(1 — ρ  |τ|) to the first few serial variation statistics of a time series for use as an approximation to the beginning of a serial variation function of more general type. A large-sample goodness of fit test is given, and also a method of testing the goodness of fit of a common or specified function, or functions with a common or specified value of ρ, to several series.
Bandwidth and Variance in Estimation of the Spectrum
Authors: Grenander Ulf
Published: December 2018

This paper deals with the uncertainty principle that governs the behaviour of bandwidth and variance in the estimation of the spectrum of a stationary stochastic process. Lomnicki and Zaremba (1957) have tried to show that this principle is not valid. It will be shown below that their reasoning is not correct. Further it will be shown, that not only is the uncertainty principle correct as it was originally stated, but that it can be extended in various directions. Guided by the uncertainty principle we discuss the basic questions in construction of estimates of the spectral density.
The Analysis of Latin Square Designs with Individual Curvatures in One Direction
Authors: Cox C. P.
Published: December 2018

It has been shown that in some circumstances individual regressions may advantageously replace one of the non-treatment classifications in the analysis of a Latin square arrangement. A simple explicit solution has been obtained. The concept of the relevance of a mathematical model to an experimental situation has been discussed.
The Estimation of the Spectral Density after Trend Removal
Authors: Hannan E. J.
Published: December 2018

A correction for bias, in the estimate of the spectral density, is derived for the case where a general form of trend has been removed, and a general expression for the bias (to the order n  –1) in the serial correlations, due to trend removal, is obtained from this.
On a Multivariate Version of Fieller’s Theorem
Authors: Bennett B. M.
Published: December 2018

The use of Fieller’s theorem for determining confidence limits for a ratio α of bivariate normal means is a standard procedure in biological assay problems (Fieller, 1940, 1944; Finney, 1952, Chapter 2). Occasionally situations arise wherein several successive samples of correlated measurements are involved, and then particular interest attaches to the corresponding problem of confidence limits for the common ratio of multivariate means based on successive samples. For example, in clinical trials on experimental subjects concerning the effectiveness of a certain therapeutic substance as compared with a control or placebo, correlated clinical measurements may be obtained at a number of participating research laboratories. An approximate method is also discussed by Clarke (1956) for an example in microbiological assay.
Contagious Occupancy
Authors: Barton D. E. , David F. N.
Published: December 2018

In the Occupancy theory of distribution of elements into a set of “boxes” (alias intervals, cells, groups, categories, subsets, compartments, etc.) the random distribution (a) is contrasted with distributions reflecting (b) heterogeneity, (c) limitation on the number of elements which may be contained in a box, or (d) a mixture of these. The following models are proposed, n balls being assumed dropped into N boxes. The distribution of the number of boxes containing no balls is obtained assuming the individual distribution in a single box is (a) Poisson, (b) Negative Binomial, (c) Positive Binomial, (d) Positive Binomial with varying probability. The large sample powers of the Index of Dispersion and the Zeros Test are compared in regard of these alternatives and the question of optimum cell size is dealt with.
The Limiting Frequencies of Integers with a Given Partitional Characteristic
Authors: Bodmer W. F.
Published: December 2018

The integers can be classified according to partitions characterizing their prime decompositions. Formulae are obtained for the limiting frequencies of integers of a given type, and a table of the frequencies greater than 0·001 per cent. is given. The calculation is made possible by developing certain symmetric function product sums, which reveal a proof of the validity of the rule given by Sukhatme for evaluating the bipartitional function Gs(P, Q). It is possible, using the results given, to investigate the association between integers with different partitional characteristics, and also to give values for the quantity dk considered by Renyi. The classification of 330 integers according to their partitional characteristics is discussed.
A Renewal Problem with Bulk Ordering of Components
Authors: Cox D. R.
Published: December 2018

Suppose that k components are in use simultaneously, that batches of n items are ordered, and that all items in use at one time must be from the same batch. After n — k + 1 failures have occurred the remaining k — 1 items are wasted. Properties of the system are investigated and different strategies of use compared.
A Different Loss Function for the Choice between Two Populations
Authors: Maurice Rita
Published: December 2018

In previous discussions of the problem of balancing sampling costs against the cost of choosing the wrong population it has been assumed that the cost of sampling is equal to the sample size multiplied by a constant known unit cost. In the present paper the cost of sampling is assumed to be the cost of an incorrect choice for half of the sample programme (which is divided evenly between the two populations). The resulting loss function is considered when the choice is between two normal populations of known equal variance, the standard of performance being determined by the mean. Wald's (1950) minimax principle is used to determine fixed size and sequential sampling procedures, and the performance of these procedures is examined.
Optimum Experimental Designs
Authors: Kiefer J.
Published: December 2018

After some introductory remarks, we discuss certain basic considerations such as the nonoptimality of the classical symmetric (balanced) designs for hypothesis testing, the optimality of designs invariant under an appropriate group of transformations, etc. In section 3 we discuss complete classes of designs, while in section 4 we consider methods for verifying that designs satisfy certain specific optimality criteria, or for computing designs which satisfy such criteria. Some of the results are new, while part of the paper reviews pertinent results of the author and others.
A Table of the Integral of the Bivariate Normal Distribution Over an Offset Circle
Authors: Lowe J. R.
Published: December 2018

A table is given for the integral of a bivariate normal distribution with zero correlation over a circle with arbitrary centre and radius. By linear transformation the integral of an arbitrary bivariate normal distribution over an ellipse can be derived.
Necessary Restrictions for Distributions A Posteriori
Authors: Sprott D. A.
Published: December 2018

The combining by the method of Bayes of two samples each yielding a fiducial distribution, does not often yield a unique result. Necessary restrictions are given which it seems reasonable to impose on a posteriori distributions. If, in combining two samples having sufficient statistics following the same continuous distribution, the a posteriori distributions obtained by Bayes’s method satisfy these conditions, they are identical with the fiducial distribution based on the combined sample. The same result seems to hold for samples having sufficient statistics following two different continuous distributions. The paper is confined to single parameter distributions in which the range is independent of the parameter.
Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments
Authors: Good I. J.
Published: December 2018

The main purpose of this paper is to consider what explicata are possible for corroboration and explanatory power of a hypothesis. The work is intended to sharpen some previous work by Popper. It will be found, for example, that the only possible explicatum for explanatory power, satisfying the desiderata, is a monotonic function of amount of information (without expectations). Corroboration has a wider variety of explicata, one of them being “weight of evidence”. This, too, is essentially unique if probabilities of hypotheses are not to appear explicitly in the formula.

In the choice of an experimental design we may have difficulty in judging the relevant utilities. In such cases it may be reasonable to base the choice on a knowledge of the probability distribution of some measure of corroboration, and especially on the expectation.
A Queueing Model for Road Traffic Flow
Authors: Miller Alan J.
Published: December 2018

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.
Reply to Mr Quenouille’s Comments About My Paper on Mixtures
Authors: Scheffé Henry
Published: December 2018

Comments are made on the differences between two methods proposed for dealing with experiments with mixtures.
The Real Stable Characteristic Functions and Chaotic Acceleration
Authors: Good I. J.
Published: December 2018

The real stable characteristic functions are found to arise naturally in a problem concerning the acceleration of a particle in a chaotic environment.
Inaccuracy and Inference
Authors: Kerridge D. F.
Published: December 2018

The idea of uncertainty, as developed in communication theory, is generalized to “inaccuracy”. The applications of this inaccuracy to the problems of statistical inference are discussed.
A Note on Vacancies on a Line
Authors: Downton F.
Published: December 2018

A number n of vacant sites in a row are occupied by filling adjacent pairs of sites at random until only isolated vacancies remain. From the stretches of occupied sites between vacancies adjacent pairs are selected at random until only isolated filled sites, trapped points, remain. Some properties of these stretches and trapped points are discussed.
Some Sequential Tests Using Range
Authors: Gilchrist W. G.
Published: December 2018

A number of sequential tests analogous to the sequential t-test are discussed, in which the mean range in sub-samples is used as an estimate of the standard deviation. Approximations to the critical limits are found and some values are tabulated.
First Emptiness in a Finite Dam
Authors: Weesakul B.
Published: December 2018

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

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

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

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

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

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

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

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.
Some Logical Aspects of the Fiducial Argument
Authors: Barnard G. A.
Published: December 2018

The papers by Dempster and Williams in this issue are discussed.
The Epochs of Emptiness of a Semi-Infinite Discrete Reservoir
Authors: Lloyd E. H.
Published: December 2018

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

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.
A Contribution to Counter Theory
Authors: Bentley Donald L.
Published: December 2018

A new type counter model is defined and investigated mathematically. The various results are presented and illustrated by examples for Poisson arrivals.
On Plackett’s Test for Contingency Table Interactions
Authors: Goodman Leo A.
Published: December 2018

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] > 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).
A Note on the Asymptotic Efficiency of an Asymptotically Normal Estimator Sequence
Authors: Walker A. M.
Published: December 2018

This paper gives a rigorous yet quite elementary proof that under fairly general conditions, the asymptotic efficiency of an asymptotically normal estimator sequence does not exceed unity. Both estimation of a single parameter and simultaneous estimation of several parameters are considered.
On Combining Estimates of a Ratio of Means
Authors: Bennett B. M.
Published: December 2018

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.