bluuebunny/crossref_metadata_2025_split huggingface dataset:
Distribution-Free Tests in Time-Series Based on the Breaking of Records
Authors: Foster F. G. , Stuart A. 
Published: December 2018

Summary
Two simple statistics are proposed as distribution-free tests of the randomness of a series of observations. They are linear functions of the numbers of upper and lower records which occur in the series. They are uncorrelated and asymptotically normally distributed. One provides a consistent test against trend in the mean and the other a consistent test against trend in the variance. Power functions for the former test have been computed, and it is pointed out that this test is considerably more powerful than three well-known tests. It is not as powerful as the rank-correlation tests, but is on the other hand very much simpler to compute. Illustrative applications are made to data from meteorology and athletics.
The Comparison of Means of Sets of Observations from Sections of Independent Stochastic Series
Authors: Jowett G. H. 
Published: December 2018

Summary
A method of applying the formula for the sampling variance of the mean of a section of stationary time series, using an analysis of half the squared differences between sample values, is developed. The formula and method are generalized for application to the comparison of means of several independent stretches of series, with and without superimposed systematic patterns of variation, and to more general series such as spatial configurations of data. The methods are applied to some observed series.
Generalized Hypergeometric Distributions
Authors: Kemp C. D. , Kemp A. W. 
Published: December 2018

Summary
An examination is made of the conditions under which the hypergeometric series provides discrete frequency distributions; eight sets of conditions exist. Urn model representations, other derivations and special forms are discussed. The limiting forms are positive and negative binomials and the Poisson distribution. Other special forms, besides the familiar case of sampling without replacement from a finite population, are the distributions described by Skellam and Irwin. Illustrative examples are given.
The existence and nature of the factorial moments is considered for each of the eight sets of conditions—under some circumstances distributions exist for which there are no finite moments. Formulae are given for the finite moments and for the indices of dispersion and skewness; these indices can take a very wide range of values.
Moment and maximum likelihood estimation of the parameters is also mentioned; for some forms this involves the problem of estimating restricted parameters.
Some Equilibrium Results for the Queueing Process EK/M/1
Authors: Jackson R. R. P. , Nickols D. G. 
Published: December 2018

Summary
A queueing process is studied in which the inter-arrival time of customers is proportional to a variate distributed as χ2, the service time distribution is negative exponential and a single server serves customers in order of arrival. Using Erlang’s method, the steady state equations are obtained and the generating function for state probabilities evaluated. Limiting distributions are found and the case of a “regular” input is derived. The solutions are made to depend upon the real positive root of a certain equation. This root is easily obtained by the usual numerical methods and the solutions are easily computed functions of this root.
Some Further Results in the Non-Equilibrium Theory of a Simple Queue
Authors: Bailey Norman T. J. 
Published: December 2018

Summary
A number of new results are obtained in the non-equilibrium theory of a simple single-server queue with random arrival and departure, involving both the frequency distribution and distribution function of queue length, the derivation of exact and asymptotic expressions for means and variances, and the distribution of the time taken to reach a pre-assigned state.
Fiducial Distributions and Bayes' Theorem
Authors: Lindley D. V. 
Published: December 2018

SUMMARY
x is a one-dimensional random variable whose distribution depends on a single parameter θ. It is the purpose of this note to establish two results: (i)The necessary and sufficient condition for the fiducial distribution of θ, given x, to be a Bayes' distribution is that there exist transformations of x to u, and of θ to τ, such that τ is a location parameter for u. The condition will be referred to as (A). This extends some results of Grundy’s (1956).(ii)If, for a random sample of any size from the distribution for x, there exists a single sufficient statistic for θ then the fiducial argument is inconsistent unless condition (A) obtains: And when it does, the fiducial argument is equivalent to a Bayesian argument with uniform prior distribution for τ.
The note concludes with an investigation of (A) in the case of the exponential family.
The Comparison of Correlations in Time-Series
Authors: Quenouille M. H. 
Published: December 2018

SUMMARY
The problem considered is that of comparing two lengths of time-series to test whether their correlation structures are similar. It is pointed out that this may be usefully done only if assumptions are made concerning the type of correlation structure of each series. A test is given depending upon assumed values for a common correlation structure. This test is shown to be insensitive to errors in these assumed values.
On a Property of Incomplete Blocks
Authors: Jones R. Morley 
Published: December 2018

SUMMARY
In a balanced incomplete block design, two orthogonal treatment contrasts may each be split up into inter- and intra-block components, all four components being mutually orthogonal. This property is shown to be closely related to the condition that the two components of a treatment contrast estimate the same thing. A proof is given of a theorem of Yates, that the sum of the relative losses of information on a set of orthogonal contrasts in a balanced arrangement is equal to the number of degrees of freedom confounded in each replicate. It is also shown that designs can be found similar to the balanced incomplete blocks, but with blocks of varying size.
The Two-Pack Matching Problem
Authors: Joseph A. W. , Bizley M. T. L. 
Published: December 2018

Summary
The Two-pack Matching Problem is described. The number of derangements is obtained by applying an adaptation of the Laguerre polynomial considered as an operator and this leads to explicit formulae and generating functions for the number of r-hits. Some useful properties of the adapted Laguerre polynomials are given from which recurrence formulae are developed for the number of derangements both generally and also when the pack consists of n different sets of p like cards. It is shown how to build up a hit generating function stage by stage by a simple numerical process. Tables of numbers of derangements and r-hits are given in an Appendix.
Some Notes on Pistimetric Inference
Authors: Roy A. D. 
Published: December 2018

SUMMARY
The Pistimetric method, in which the probability distribution of parameters is determined by means of a pivotal quantity as soon as the number of observations permit, and posterior probability distributions are subsequently deduced by Bayes’s theorem, is here applied in outline to a variety of situations. These include cases where the variate is discrete, where it is continuous, and when events occur in continuous time.
The Moment Generating Function of the Truncated Multi-Normal Distribution
Authors: Tallis G. M. 
Published: December 2018

SUMMARY
In this paper the moment generating function (m.g.f.) of the truncated n-dimensional normal distribution is obtained. From the m.g.f., formulae for E(Xi) and E(Xi Xj) are derived, and are used to investigate certain special cases. Some applications of these results to statistical genetics are also discussed.
Testing for a Jump in the Spectral Function
Authors: Hannan E. J. 
Published: December 2018

SUMMARY
The problem of testing for a jump in the spectral function of a stationary time series is considered. The test based on the greatest periodogram ordinate divided by an estimate of the spectral density is discussed and a modification is suggested which consists essentially of taking out regression on the harmonic with frequency 2πj/n, before computing the estimate of the spectral density at that frequency. The regression can be approximately effected by using the corresponding periodogram ordinate.
A Note on Maximum-Likelihood in the Case of Dependent Random Variables
Authors: Silvey S. D. 
Published: December 2018

SUMMARY
The validity of certain statistical procedures depends on the “classical” properties of the method of maximum-likelihood, viz., its consistency and the fact that it leads to an estimator whose asymptotic variance can be derived easily from the likelihood function. These properties are well established for the case where successive observations are independent. Here it is shown that their extension to the dependent case involves suitable behaviour of two semi-martingales and a martingale, and general conditions are given which ensure this behaviour. While interest is centred on the theoretical rather than on the practical side of the problem, these conditions may have some practical value.
Similarities between Likelihoods and Associated Distributions a Posteriori
Authors: Sprott D. A. 
Published: December 2018

SUMMARY
Some methods of constructing distributions a posteriori are based on rules of mathematical manipulation that ignore the logical role played by the likelihood. The effect of such methods has been to alter the relationship between variates as they occurred in the likelihood, and so change what may be called their relative weight. Thus, although in a sense no information has been lost, there certainly has occurred a distortion. The concept of relative weight is examined in the case of one parameter, and is used to investigate, in a particular example, what happens logically to samples that are combined by Bayes's theorem. The multiparameter case is also examined in an effort to set up methods of constructing such distributions a posteriori that will preserve the essential form of the likelihood, and so perhaps qualify as genuine fiducial distributions. Examples are given from the literature in which this is not the case.
Efficient Estimates and Optimum Inference Procedures in Large Samples
Authors: Rao C. Radhakrishna 
Published: December 2018

SUMMARY
The concept of efficiency in estimation is linked with closeness of approximation to the derivative of log likelihood, which plays an important role in statistical inference in large samples. Various orders of efficiency are defined depending on degrees of closeness, and properties of estimates satisfying these criteria are studied. Such measures of efficiency appear to be more appropriate than the one related to asymptotic variance of an estimate for judging the performance of an estimate, when used as a substitute for the whole sample in drawing inference about unknown parameters. It is found that, under some conditions, the maximum likelihood estimate has some optimum properties which distinguish it from all other large sample estimates.
Time-Dependent Solution of the Head-Of-The-Line Priority Queue
Authors: Jaiswal N. K. 
Published: December 2018

SUMMARY
The method of supplementary variables has been used to obtain the Laplace transform of the time-dependent probabilities in a head-of-the-line priority queue characterized by Poisson arrivals and general service-time distributions. An explicit solution has, however, been obtained under exponential service-time distributions with equal mean rates. The queue length probabilities, under steady-state conditions, have been evaluated and are found to be different from those obtained by Miller, thus showing that for complex queues, the asymptotic probability distribution obtained by considering the evolution of the queueing process in continuous time need not be the same as the one obtained by the imbedded Markov chain technique.
The Simplex-Centroid Design for Experiments with Mixtures
Authors: Scheffé Henry 
Published: December 2018

SUMMARY
A new design for experiments with mixtures of q components comprises the 2q − 1 points representing the mixtures consisting of all possible subsets of the q components, present in equal proportions. A suitable regression equation is proposed and fitted. Designs and regression equations permitting the introduction of n “process variables” in addition to the q “mixture variables” are considered, and fractional replication of the designs in the case where the process variables are all at two levels.
On Formulae for Confidence Points Based on Integrals of Weighted Likelihoods
Authors: Welch B. L. , Peers H. W. 
Published: December 2018

SUMMARY
Lindley’s problem, relating to the conditions under which there is formal mathematical equivalence between Bayesian solutions and confidence theory solutions, is discussed. A result concerning location parameters is extended. The corresponding asymptotic theory is developed and a modification of the problem is also discussed.
On the Monotonicity Property of the Three Main Tests for Multivariate Analysis of Variance
Authors: Srivastava J. N. 
Published: December 2018

Summary
This paper presents a unified and relatively simple proof of the monotonicity property of the three well-known tests for the multivariate analysis of variance (MANOVA), viz., (i) Hotelling-Lawley trace criterion, (ii) Wilks's likelihood-ratio criterion, and (iii) Roy's largest root criterion. The last one has already been considered by Roy and Mikhail (1961). Their proof, however, has a gap at one place, which has been bridged in this paper.
Characterization Theorems for Some Univariate Probability Distributions
Authors: Patil G. P. , Seshadri V. 
Published: December 2018

Summary
Suppose that one is dealing with a bivariate distribution of random variables X and Y where only the conditional distribution of X given X + Y is known. What can be said of the marginal distributions of X and Y? This paper attempts to answer this question for situations involving certain univariate distributions known in the statistical literature.
On Certain Properties of the Exponential-Type Families
Authors: Patil G. P. , Shorrock Richard 
Published: December 2018

Summary
Certain structural properties of the exponential-type families are studied under three headings: (1) mean value function and the exponential-type families, (2) a characterization of the Gamma family and (3) the quality of the first two Bhattacharya bounds and the exponential-type families.
On a Property of the Random Walks Describing Simple Queues and Dams
Authors: Loynes R. M. 
Published: December 2018

Summary
A so-called duality principle, which has been given by previous authors for simple queues and dams, is here shown to be valid in more general circumstances. The conditions under which the result, relating the stationary distribution of one random walk with absorption probabilities in another, is applicable are investigated.
On the Estimation of the Intensity Function of a Stationary Point Process
Authors: Cox D. R. 
Published: December 2018

Summary
The intensity function of a stationary point process gives as a function of x the conditional probability, given an event at time t, of an event in the interval (t + x, t + x + Δx). A very nearly unbiased estimate of the grouped intensity function is constructed. its sampling properties are investigated when the data are generated by a Poisson process.
A General Class of Coefficients of Divergence of One Distribution from Another
Authors: Ali S. M. , Silvey S. D. 
Published: December 2018

Summary
Let p1 and p2 be two probability measures on the same space and let φ be the generalized Radon-Nikodym derivative of p2 with respect to p1. If C is a continuous convex function of a real variable such that the p1-expectation (generalized as in Section 3) of C(φ) provides a reasonable coefficient of the p1-dispersion of φ, then this expectation has basic properties which it is natural to demand of a coefficient of divergence of p2 from p1. A general class of coefficients of divergence is generated in this way and it is shown that various available measures of divergence, distance, discriminatory information, etc., are members of this class.
Design Relations for Non-Stationary Processes
Authors: Priestley M. B. 
Published: December 2018

Summary
Further developments in the theory of evolutionary spectra are discussed, and some asymptotic results are derived in the sampling theory of spectral estimates. Various forms of “design” criteria for spectral estimation are constructed in terms of resolvability conditions, and it is shown that by introducing the concepts of “frequency-domain” and “time-domain” bandwidths, estimates may be obtained which satisfy the required conditions.
Exponential Smoothing for Multivariate Time Series
Authors: Jones Richard H. 
Published: December 2018

Summary
A method is presented for estimating the optimum weight matrix for the exponential smoothing and prediction of multivariate time series. A recursive version of the estimation equations is given. A variation allows the estimation to forget the remote past in order to follow a process in which the structure varies slowly with time. It is pointed out that the method generalizes to non-linear processes when the non-linear structure is known. The practicality of the method is demonstrated by a numerical simulation study.
Some Applications of Probability Generating Functionals to the Study of Input-Output Streams
Authors: Vere-Jones D. 
Published: December 2018

Summary
Probability generating functionals are used to obtain simple proofs of Mirasol's theorem on the output to an M/G/∞ queue, the limit theorem for the superposition of point processes, and a limit theorem for the output from a sequence of G/G/∞ queues.
A Test for Non-Stationarity of Time-Series
Authors: Priestley M. B. , Rao T. Subba 
Published: December 2018

Summary
We consider the problem of testing a given time-series for stationarity. The approach is based on evolutionary spectral analysis, and the proposed method consists essentially in testing the “homogeneity” of a set of evolutionary spectra evaluated at different instants of time.
Using a logarithmic transformation, we show that the mechanics of the test are formally equivalent to a two-factor analysis of variance procedure when the residual variance is known, a priori.
In addition to testing stationarity, the analysis provides also a method for testing whether the observed series fits a “uniformly modulated” model, and a test for “randomness” (constancy of spectra).
Exact Bayesian Analysis of a 2 × 2 Contingency Table, and Fisher's “Exact” Significance Test
Authors: Altham Patricia M. E. 
Published: December 2018

Summary
A relationship is derived between the posterior probability of negative association of rows and columns of a 2 × 2 contingency table and Fisher's “exact” probability, as given in existing tables for testing the hypothesis of no association of rows and columns. The result for the 2 × 2 table is generalized to provide the posterior probability that one discrete-valued random variable is stochastically larger than another.
Application of Likelihood Methods to Models Involving Large Numbers of Parameters
Authors: Kalbfleisch John D. , Sprott D. A. 
Published: December 2018

Summary
Likelihood methods of dealing with some multiparameter problems are introduced and exemplified. Specifically, methods of eliminating nuisance parameters from the likelihood function so that inferences can be made about the parameters of interest are considered. In this regard integrated likelihoods, maximum relative likelihoods, conditional likelihoods, marginal likelihoods and second-order likelihoods are introduced and their uses illustrated in examples. Marginal and conditional likelihoods are dependent upon factorings of the likelihood function. They are applied to the linear functional relationship and to related models and are found to give intuitively appealing results.
These methods indicate that in many situations commonly encountered objective methods of eliminating unwanted parameters from the likelihood function can be adopted. This gives an alternative method of interpreting multiparameter likelihoods to that offered by the Bayesian approach.
Further Consideration of the Distribution of the Multiple Correlation Coefficient
Authors: Gurland John , Milton Roy 
Published: December 2018

Summary
A general class of series expansions for the non-null distribution of the multiple correlation coefficient is presented which contains, as special cases, the three expansions obtained by one of the authors (Gurland, 1968). The rate of convergence is investigated, and the closeness of an approximation to the true distribution is indicated.
Bivariate Exponential Distributions in Reliability Theory
Authors: Downton F. 
Published: December 2018

Summary
A simple failure model is used to derive a bivariate exponential distribution. This distribution, although well known in the literature, does not appear to have been considered in a reliability context. its properties are considered and in particular explicit expressions are obtained for the distributions of the larger and of the smaller of a pair of correlated exponential observations. The results are compared with those obtained by Marshall and Olkin (1967a, b) for a different bivariate exponential model motivated by reliability theory.
Some Results on the Sampling Distribution of the Multiple Correlation Coefficient
Authors: Lee Yoong-Sin 
Published: December 2018

Summary
Recurrence formulae for the density function and the probability integral of the multiple correlation coefficient from a normal sample are obtained. When the number of independent variates is odd these formulae are related to the distribution of the simple correlation. Asymptotic expansions in terms of the non-central beta and of the non-central χ2 distributions are derived. Methods of approximation by the central and the non-central F distributions, as well as by the normal distribution, are proposed. Numerical investigations of the accuracies of these approximations are carried out.
Formal Expressions Which Can be Applied to Cusum Charts
Authors: Kemp K. W. 
Published: December 2018

Summary
The paper describes a number of formal expressions which can be used to determine properties of cumulative sum schemes. Formulae given only depend upon very general assumptions with regard to the distribution of the cumulated statistic. Numerical as well as algebraic procedures are described which permit calculation of the average sample run length to a specified degree of accuracy for almost any statistic likely to arise in practice. Methods for generating the sample run length distribution are also given.
Components of Cramér–Von Mises Statistics. I
Authors: Durbin J. , Knott M. 
Published: December 2018

Summary
Let Fn(x) be the sample distribution function derived from a sample of independent uniform (0, 1) variables. The paper is mainly concerned with the orthogonal representation of the Cramér-von Mises statistic Wn2 in the form ∑j=1∞(jπ)−2znj2 where the znj are the principal components of n{Fn(x)−x}. It is shown that the znj are identically distributed for each n and their significance points are tabulated. Their use for testing goodness of fit is discussed and their asymptotic powers are compared with those of Wn2, Anderson and Darling's statistic An2 and Watson's Un2 against shifts of mean and variance in a normal distribution. The asymptotic significance points of the residual statistic Wn2−∑j=1p(jπ)−2znj2 are also given for various p. It is shown that the components analogous to znj for An2 are the Legendre polynomial components introduced by Neyman as the basis for his “smooth” test of goodness of fit. The relationship of the components to a Fourier series analysis of Fn(x) –x is discussed. An alternative set of components derived from Pyke's modification of the sample distribution function is considered. Tests based on the components znj are applied to data on coalmining disasters.