bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Reliability of Multiplex Systems with Repair
Authors: Downton F. 
Published: December 2018

Summary
This paper derives expressions for the life-time distributions of systems consisting of a number of components in parallel, where repairs to these components are possible. These distributions reduce to those of first-passage times in a birth-death process or in a semi-Markov (or Markov renewal) process, and have application outside reliability theory. In the reliability context, the effects of altering the number of components and of increasing the repair facilities are briefly compared, and a comparison of different repair distributions is made.
Some Aspects of the Estimation of Quantiles
Authors: Loynes R. M. 
Published: December 2018

Summary
The problem of estimating quantiles in the context where restriction to particular parametric families is inappropriate is considered, for simple random sampling and stratified sampling. For the former type of sampling the distribution-free procedures are obtained and the admissible estimators identified, and certain other questions are dealt with. In the stratified sampling situation similar problems are considered, less successfully.
Balanced Factorial Designs
Authors: Kshirsagar A. M. 
Published: December 2018

Summary
Kurkjian and Zelen (1963) have proved that factorial designs possessing a particular structure for their C matrix (they call this property A) are factorially balanced. This paper proves the converse of this result, viz. factorially balanced designs are (a) EGD/(2n - 1)-PBIB designs as defined by Hinkelmann (1964), and (b) possess property A. The latent roots and vectors of the C matrix of such designs are obtained in a much simpler form than that given by Hinkelmann.
Optimization of a Hot Rolling Mill
Authors: Dowson D. C. 
Published: December 2018

Summary
This paper is concerned with constructing rules for determining the times at which slabs have to be fed into successive stages of a hot rolling mill so as to optimize the working of the mill. The errors entering the system are assumed to form stationary stochastic sequences and the method adopted for determining the appropriate feedback is that of linear least squares. The analysis is carried through and results tabulated for the case of uncorrelated errors and also for one, fairly general, case of correlated errors.
Optimum Utilization of Auxiliary Information: πPs Sampling of Two Units from a Stratum
Authors: Hanurav T. V. 
Published: December 2018

Summary
For the estimation of the population total of a character y, defined over a finite population of known size, “optimum” sampling strategies for the case when auxiliary information X of a type commonly met with in practice are recalled. A method of sampling two units from a stratum such that the probability of inclusion of one unit is exactly proportional to the value of X on the unit is given. This method incidentally furnishes not only an optimum estimator of the population total but also a stable non-negative unbiased estimator of the variance of the main estimator. The method is compared with two other methods in varying probability sampling. Illustrative examples are given.
Four-Letter Words: The Distribution of Pattern Frequencies in Ring Permutations
Authors: Barton D. E. , David F. N. 
Published: December 2018

Summary
An alphabet of c letters is considered. There are, then, ck possible ordered sequences of k of these. Such k-sequences are grouped into λ mutually exclusive and exhaustive sets; members of each set (called k-patterns) are counted the same. A general expression for the joint generating function of the frequencies of occurrence of the different k-patterns is obtained when r letters, with fixed numbers of each sort, are randomly arranged in a ring. In particular, k-sequences which comprise the same set of letters, in whatever order, are called k-words. Explicit expressions are obtained for the cases k = 3, 4, c = 2 both from the generating function and by direct combinatorial arguments. The asymptotic (multinormal) limiting distribution is obtained for the general case and more explicitly for k-letter words.
The Choice of Variables in Multiple Regression
Authors: Lindley D. V. 
Published: December 2018

Summary
This paper is concerned with the analysis of data from a multiple regression of a single variable, y, on a set of independent variables, x 1,x 2,...,xr. It is argued that the form of the analysis should depend on the use that is to be made of the regression, and that therefore an approach employing ideas from decision theory may be worth while. Two situations are analysed in this way: in the first it is desired to predict a future value of y; in the second we wish to control y at a preassigned value. The two analyses are found to be different: in particular, the standard errors of the regression coefficients are found to be irrelevant in the prediction problem, but not in the control problem. In the former it is shown that, under rather special assumptions on the multiple regression experiment, the analysis is similar to that recommended by other writers. If the costs of control do not depend on the values at which the control takes place, a similar analysis holds for the second problem. The approach throughout is Bayesian: there is no discussion of this point, I merely ask the non-Bayesian reader to examine the results and consider whether they provide sensible and practical answers.
Small Sample Power of a Non-Parametric Test for the Bivariate Two-Sample Location Problem in the Normal Case
Authors: Mardia K. V. 
Published: December 2018

Summary
The exact power of a test U (Mardia, 1967) is obtained for normal location alternatives, but even for small samples the expression cannot be simplified. The empirical power function of the U-test is obtained and compared with the power of Hotelling's T2 by extending some efficiency measures and developing a new non-central T2 routine. It is found that the efficiency of the U-test relative to Hotelling's T2 test decreases with N and lies between 79 and 93 per cent.
Multiparameter Bayesian Indifference Procedures
Authors: Novick Melvin R. 
Published: December 2018

Summary
The method of minimum necessary samples formulated by Novick and Hall from a suggestion by Lindley is refined and extended to cover multiparameter models. A number of such models are studied and Bayesian indifference specifications are obtained for each within extended natural conjugate families. In all cases the one-parameter conditional specifications derived from the multiparameter specifications are consistent with specifications derivable from corresponding one-parameter models.
Models studied include the multinomial models, one- and two-parameter uniform models, an exponential model with a range parameter, and the two-parameter normal model. For these models the specifications seem entirely straightforward.
Indifference specifications are also obtained for the simple regression model and the bivariate normal model. It is noted that these specifications do not agree but the relationship between these two specifications is described and in part justified. It is pointed out that these differences could, in fact, mirror important differences in the structural assumptions of these models. A random effects model of value in mental test theory is studied briefly. This model provides a framework for a discussion of the multiple comparisons problem. Finally, some summary comments on the methods of this paper are offered.
Some Non-Orthogonal Fractions of 2N Designs
Authors: John Peter W. M. 
Published: December 2018

Summary
This paper is concerned with the class of fractions obtained when a 2n-k fraction is omitted from a complete 2n factorial. The three-quarter replicate is a special case. It is shown that the maximum-likelihood estimates of effects are the averages of estimates from over-lapping half replicates. Examples are given, including a seven-eighth fraction of a 25 design of resolution VII, a design of resolution VI for eight factors in 112 points and a design of resolution V for eleven factors in 96 points.
A Note on the Posterior Mean of a Population Mean
Authors: Ericson W. A. 
Published: December 2018

Summary
It is a well-known result, see for example Lindley (1965) and Raiffa and Schlaifer (1961), that if x̄ is the mean of a sample of independent observations distributed N(μ, σ2) where σ2 is known, and if μ has been assigned a normal prior distribution, N(m, v), then the posterior expectation of μ, given the sufficient statistic x̄, has the form {x̄(n/σ2) + m/v}/{(n/σ2)+1/v}, that is, has the intuitively appealing form of a weighted average of the prior mean and sample mean with weights inversely proportional to the prior variance and the conditional sampling variance of X̄ respectively. In this note we present an extremely simple generalization of this result which seems not to have been noted explicitly before and which holds for a variety of distributions other than the normal.
Testing for Linear Contagion—Inverse Sampling
Authors: Peritz E. , Shlom E. 
Published: December 2018

Summary
Let Tr (r = 0, 1, …) be independent, positive, exponentially distributed random variables with parameters λ + rΨ. It is shown that the uniformly most powerful unbiased test of the null hypothesis Ψ = 0 against alternatives Ψ &gt; 0 rejects the former for small values of Z=(∑r=1nrTr)(∑r=0nTr)−1. The power function of the test is given and the test is shown to be consistent. Unbiasedness is shown for a wider class of alternatives. A sequential version of the test is presented. A generalization of the results for a model relevant to accident research is given in the last section of the paper. Selected values of the power function are tabulated in the Appendix.
Asymptotic Properties of Bayesian Decision Rules for Two Terminal Decisions and Multiple Sampling. I
Authors: Hald A. , Keiding N. 
Published: December 2018

Summary
The model is based on a differentiable prior distribution, a linear loss function, an asymptotically normal sampling distribution and sampling costs proportional to the sample size. Asymptotic expressions are derived for sample sizes, acceptance and rejection criteria and the minimum regret by minimizing the average regret for a k-stage sampling and decision procedure. The results generalize previously known results for k = 1 and 2 and bridge the gap to sequential sampling.
Correlation between Two Vector Variables
Authors: Kshirsagar A. M. 
Published: December 2018

Summary
Ruben (1966) has suggested a simple approximate normalization for the correlation coefficient in normal samples, by representing it as the ratio of a linear combination of a standard normal variable and a χ variable to an independent χ variable and then using Fisher's approximation to a χ variable. This result is extended in this paper to a matrix, which in a sense is the correlation coefficient between two vector variables x and y. The result is then used to obtain large sample null and non-null (but in the linear case) distributions of the Hotelling–Lawley criterion and the Pillai criterion in multivariate analysis. Williams (1955) and Bartlett (1951) have derived some exact tests for the goodness of fit of a single hypothetical function to bring out adequately the entire relationship between two vectors x and y, by factorizing Wilks's A suitably. These factors are known as “direction” and “collinearity” factors, as they refer to the direction and collinearity aspects of the null hypothesis. In this paper, the other two criteria viz. the Hotelling-Lawley and Pillai criteria are partitioned into direction and collinearity parts and large sample tests corresponding to them are derived for testing the goodness of fit of an assigned function.
A Method for Discriminating between Models
Authors: Atkinson A. C. 
Published: December 2018

Summary
It is desired to determine which of several alternative models adequately describe the data. The properties of a combined distribution containing the component models as special cases are investigated. Using this distribution, statistics are developed for testing for departures from one model in the direction of another and for testing the hypothesis that all models fit the data equally well. The relationship with other procedures is investigated. Examples are given of the use of the method, especially when there are two component models belonging to separate parametric families.
The Measurement of Association in a Contingency Table: Three Extensions of the Cross-Ratios and Metrics Methods
Authors: Altham Patricia M. E. 
Published: December 2018

Summary
The methods of cross-ratios, equivalence classes and metrics that were introduced in a previous paper (Altham 1970) are extended to three further problems. First the interdependence of the rows, columns and layers of a three-way contingency table is discussed. There are essentially four different types of association to be considered: the complete dependence of rows, columns and layers, the dependence of rows and columns conditional on a given layer, the dependence of the two classifications “rows-and-columns” and layers, and the second-order interaction of rows, columns and layers. The relations between these four types of association are discussed in terms of the appropriate equivalence classes. In order to obtain measures of dependence of rows, columns and layers, metrics are defined on the equivalence classes. Some examples of metrics are given. The consideration of three-way tables is concluded by a discussion of the asymptotic posterior distributions of certain special metrics, which are suggested by the work of Lindley (1964), and Plackett (1962).
Cross-ratios methods are also extended to the problem of measuring association in a two-way table with some cells deleted. The paper is concluded by consideration of the problem of comparing associations in two distinct contingency tables, some of whose cells may be deleted.
The Efficient Use of Supplementary Information in Standard Sampling Procedures
Authors: Foreman E. K. , Brewer K. R. W. 
Published: December 2018

Summary
Use is made of a well-known heteroscedastic super-population model to obtain comparisons of the efficiencies of six methods of sampling in common use. These are simple random sampling with unbiased estimators, simple random sampling with ratio estimators, and sampling with probability proportional to size with unbiased estimators; each with and without replacement. The resulting comparisons are readily interpretable, thus affording simple criteria for comparing the efficiencies of these widely used sample plans. They also provide heuristic explanations of their properties.
The Covariance Structure of the Departure Process from M/G/1 Queues with Finite Waiting Lines
Authors: King Ralph A. 
Published: December 2018

Summary
This paper contains a study of the departure process from M/G/1 queues with a waiting space of size N&gt;0. The property of the departure process which receives the most attention is the covariance of pairs of departure intervals, although a more thorough investigation of the probabilistic structure is undertaken for the case N = 1. A main result of the paper is that in the M/G/1 queue with N = 1, departure intervals separated by one or more intervals are independent. When G is the deterministic server, the departure stream is a renewal process. The paper concludes with an expression for the covariance of any pair of intervals in the departure process for any value of N, and numerical values for correlations in the case of a deterministic server with N = 2.
Properties of Some Two-Sided Sequential Tests for the Normal Distribution
Authors: Billard L. 
Published: December 2018

Summary
A general procedure for sequentially comparing a null hypothesis with a two-sided alternative hypothesis concerning a normal mean is described and its properties are derived. The procedure is defined in terms of geometrical parameters which can be evaluated so as to give an optimum procedure. A particular set of specified values for these parameters permit close approximations to the O.C. function and the A.S.N. function for the Wald procedure and the Armitage procedure to be obtained.
A Note on the Admissibility of a Response Surface Design
Authors: Kupper Lawrence L. 
Published: December 2018

Summary
A generalization of a result by Box and Draper (1959) on the minimization of integrated squared bias is used in conjunction with some ideas from decision theory to develop the notions of variance (V-), bias (B-) and mean square (MS-) admissibility, which have particular appeal to response surface workers. A theorem is given characterizing an important situation in which an experimental design can be said to possess one of these types of admissibility.
Survey Design, Symmetry and Posterior Distributions
Authors: Scott Alastair , Smith T. M. F. 
Published: December 2018

Summary
It is now well known that the sample design is irrelevant in a Bayesian analysis of survey data provided the units are labelled and the sampling is non-informative. However, information about the labels is often not available for the analysis, and in this situation the design will contain information about the labelling and hence affect the inferences. There is one important exception: if the prior distribution is exchangeable and we are interested only in symmetric functions of the unit values then the design is still irrelevant even without the labels.
Scientific Reporting and Personal Probabilities: Student's Hypothesis
Authors: Dickey James 
Published: December 2018

Summary
It is suggested here that a scientific researcher can report his statistical data by summarizing the application of Bayes's theorem to whole ranges of prior distributions, devised to include the opinions of his readers. The Jeffreys-Savage view is taken that interesting actual prior opinions can be usefully approximated by assuming positive probability on a sharp null hypothesis (point hypothesis). Graphical tools and bounds are given for reporting the weighted likelihood ratio, or Bayes factor, the ratio of the posterior odds to the prior odds, for a vague alternative to a null value for the mean of a Normal distribution.
Dependency of Intervals between Events in Superposition Processes
Authors: Lawrance A. J. 
Published: December 2018

Summary
Arbitrary event initial conditions for the superposition of a finite number of stationary point processes are derived; these are used to obtain the general joint distribution for the intervals between events following an arbitrary event. Specific consideration is given to the univariate, bivariate and trivariate distributions of successive intervals between events. Various numerical results are given for the first two serial correlations.
Multisample Tests for Multimodal and Axial Circular Populations
Authors: Mardia K. V. , Spurr B. D. 
Published: December 2018

Summary
We propose an l-modal c-sample non-parametric test U on a circle based on uniform scores. The test is derived with the help of an l-modal von Mises type distribution. Critical values of the distribution are given and the asymptotic distribution of U and its parametric competitor V are obtained. For the shift-type alternatives we derive Bahadur's efficiency of the U-test relative to the V-test and consider some particular cases. We also examine the small sample powers of U and V for the von Mises type distributions. For von Mises populations, the power of the U-test is studied in relation to the power of another reasonable non-parametric test U'. We then indicate how these tests can be used for the axial case. Numerical examples are given to illustrate the use of the tests.
Bayesian and Classical Analysis of Poisson Regression
Authors: El-Sayyad G. M. 
Published: December 2018

Summary
This paper is concerned with the problem of testing the existence of a trend in the means θi of Poisson distributions. It is assumed that these means are changing exponentially, that is, log θi = α + βxi. A classical method is reviewed which is used for testing the hypothesis β = 0. The exact Bayesian distribution for β is derived and a Bayesian approximation suggested which proved to be very useful. Finally, a comparison of these three methods by means of numerical examples is made.
The Measurement of Belief
Authors: Suppes Patrick 
Published: December 2018

Summary
This paper criticizes some of the claims of the standard theories of subjective probability. The criticisms are especially oriented toward the structural axioms that cannot be regarded as axioms of pure rationality and the general results that yield exact measurement of subjective probabilities. Qualitative axioms for upper and lower probability are introduced to provide a theory of inexact measurement of subjective probability. Only minor modifications of de Finetti's qualitative axioms yield the desired theory. The paper concludes with a comparison of the measurement of belief to the measurement results characteristic of Euclidean geometry, and also examines briefly some possibilities for using learning models as simplified abstract processes for constructing belief.
Bayesian Single Sampling Acceptance Plans for Finite Lot Sizes
Authors: Thyregod P. 
Published: December 2018

Summary
We discuss a general model for acceptance/rejection decisions regarding finite populations.
The model is based on an exchangeable prior distribution of the population characteristics and additive costs. A fundamental property of the model is that the original two-decision problem regarding the characteristics of the finite population is equivalent to a classical decision problem regarding a parameter in the prior distribution of population characteristics. In the general discussion of the model we verify some simple results for the optimal sampling scheme, viz. that the expected decision cost per individual is decreasing and the optimal sample size is increasing with the population size.
A substantial part of the paper is devoted to the study of monotonely regular problems, i.e. problems admitting a sufficient statistic with a monotone likelihood-ratio. A main result of the discussion is that the optimal decision criterion is a monotone function of the sample size.
It is shown that the theory describes the standard situations in quality control with lot-by-lot sampling, where the distribution of the item characteristics belongs to an exponential family, and in an example we suggest a simple algorithm for determination of the Bayesian sampling scheme.
Confounding in Factorial Experiments
Authors: Raja J. Sundara 
Published: December 2018

Summary
Various methods of construction of confounded designs and determination of the confounded effects of a confounded design are available in the literature. An alternative method based on the theory of groups is given in this paper. The problems of construction of the Principal Block (P.B.) and determination of the effects confounded from the elements of P.B. are made simple for any number of factors in 2n factorial experiments.
Bayesian Estimation Methods for Two-Way Contingency Tables
Authors: Leonard Tom 
Published: December 2018

Summary
Estimation methods are proposed for the row, column and interaction effects in two-way contingency tables, the one-way table being treated as a special case. The methods are appropriate when the parameters are thought a priori to be related to each other. The posterior estimates have the practical effects of smoothing the contingency table, and are valid even if some of the cell frequencies are zero. The main case treated is where particular assumptions of exchangeability are reasonable a priori for the unknown parameters. Some possible relaxations of the exchangeability assumptions are discussed. The methods are used to provide a numerical analysis of a mobility table originally due to Karl Pearson, and to measure the association between the occupations of fathers and sons in this table.