bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Correlation Structure of the Departure Process of the M/Eλ/1 Queue
Authors: Jenkins J. H. 
Published: December 2018

Summary
The joint distribution in the stationary case of four random variables is studied in this paper. Two of these are discrete and arise as the numbers of customers left behind in the queue by two successive departing customers in the imbedded Markov chain analysis. The other two are continuous, being the time intervals between three successive departures. The marginal joint distribution of the latter two random variables is found; in particular, the autocorrelation of lag 1 for intervals in the departure process in a stationary system is evaluated. By extending the analysis to the study of three successive departure intervals the autocorrelation of lag 2 for the process is evaluated. Burke (1956) and Finch (1959) proved that with Poisson arrivals, and service times independent for a single-server queue in equilibrium, the departure intervals are independent if and only if service time is exponentially distributed. This paper gives a measure of the dependence in the important case when the service times are special Erlangian.
On a Generalized Queueing System with Poisson Arrivals
Authors: Shanbhag D. N. 
Published: December 2018

Summary
This note shows that an inductive method used by Prabhu (1960) to obtain the distribution of the busy period of the queueing system M/G/1 may be used to obtain the busy period distributions for the queueing system M1M2, …, M1/G 1, G2, …, Gr/1 first derived using a somewhat longer method by Welch (1965).
Hypothesis Testing When the Sample Size is Treated as a Random Variable
Authors: Bartholomew D. J. 
Published: December 2018

Summary
In the Neyman-Pearson theory of hypothesis testing it is customary to calculate significance levels and power functions on the assumption that the sample size is fixed. The main purpose of this paper is to propagate the view that the restriction of the theory to reference sets in which the sample size is constant is neither necessary nor desirable. The paper falls into two parts. In the first we consider the test of a simple null hypothesis versus a simple alternative. In this case it is pointed out that the optimum test requires the rejection of the null hypothesis if the likelihood ratio is less than a constant, K, which is independent of n, the sample size. In this respect it is identical with Bayesian and likelihood methods of dealing with the same problem. Two methods for determining a suitable value for K in the absence of knowledge about the distribution of sample size are proposed. These ideas are extended, in the second part of the paper, to the case of a simple null hypothesis and a composite alternative. Since no uniformly most powerful test exists, a variety of tests suggested by Bayesian and likelihood considerations are compared from a frequentist point of view. This work is exploratory, being based on numerical calculations, but provides a partial justification for treating sample size as if it were fixed.
Asymptotic Properties of Bayesian Single Sampling Plans
Authors: Hald A. 
Published: December 2018

Summary
The model to be considered is based on a differentiable prior distribution, a general loss function, an operating characteristic written as an Edgeworth expansion, and sampling costs expressible as a polynomial in the sample size. Asymptotic expressions for the Bayesian single-sampling plan are derived and it is shown how previously known results may be found as special cases of the present one. The efficiency of non-optimum plans is discussed.
Models of the Second Kind in Regression Analysis
Authors: Fisk P. R. 
Published: December 2018

Summary
Regression models of the first and second kind are distinguished by the absence or presence, respectively, of variable regression coefficients. A characteristic of a model of the second kind is its heteroscedasticity. The problems of estimation in a general regression model of the second kind are discussed briefly. A more detailed examination is given of the properties of various estimators of the coefficients in the overall regression and scedastic curves for the linear model of the second kind. Models appropriate to replicated and unreplicated data are treated separately.
On the Prediction of Non-Stationary Processes
Authors: Abdrabbo N. A. , Priestley M. B. 
Published: December 2018

Summary
We consider the problem of linear least-squares prediction for a class of non-stationary processes which possess “evolutionary spectral representations”. It is shown that, under certain conditions, such processes admit moving-average representations in terms of time-dependent coefficients. This feature enables us to develop a close analogue of the Wiener–Kolmogorov approach to the corresponding problem for stationary processes.
Distribution-Free Sufficiency in Sampling Finite Populations
Authors: Joshi V. M. 
Published: December 2018

Summary
The concept of distribution-free sufficiency, (DF-sufficiency for short) for estimation in survey sampling, which has been introduced by Godambe (1966), is investigated. Uncorrelatedness in Godambe's definition is shown to be equivalent to statistical independence, as is claimed on the author's behalf in the appendix to Godambe's paper. But the second result claimed there, that every DF-sufficient estimate must necessarily be of the form a(s).∑i∈sxi+b(s) is false, as the complete class of DF-sufficient estimates consists of estimates which involve all the variates represented in the sample. This second result, however, remains valid with an alternative definition of DF-sufficiency. A second alternative definition is also discussed.
On Some Tests for Several Linear Relations
Authors: Basu A. P. 
Published: December 2018

Summary
In this paper we consider several tests for the parameters of k linear relations among the p variables ξ1, ξ2 ‥, ξp where the ξ's are not observable and p &gt; k. This extends the work of Villegas (1964) who considered the above problem for the special case k = 1. The applicability of the above model in an econometric problem is also considered.
Least-Squares Fitting of a Polynomial Constrained to be Either Non-Negative, Non-Decreasing or Convex
Authors: Hudson Derek J. 
Published: December 2018

Summary
An algorithm is provided to fit the (unique) least-squares polynomial Y(x) to n data points (x, y) subject to a constraint that it be either non-negative, non-positive, non-decreasing, non-increasing, convex or concave at all points x in a closed interval I. Some generalization to a general linear model can be handled, and certain alternative constraints can also be dealt with.
The problem is close to the classical problem of Quadratic Programming (Q.P.), and some of the known results in Q.P. may be used in fitting the curve.
The algorithm terminates in at most three steps. The number of steps depends on the degree of the polynomial Y(x) and the data. When no more than two steps are required, the algorithm is very easy to carry out but when three steps are necessary, it becomes more difficult.
A useful statistical application is the fitting of a polynomial to growth data. In that case, we might like the fitted curve to be non-decreasing over the range of interest.
Filtering Non-Stationary Signals
Authors: Abdrabbo N. A. , Priestley M. B. 
Published: December 2018

Summary
We observe a record consisting of a “signal” plus “noise” up to the time instant t, and wish to extract the value of the signal at the time instant (t + m) by means of a linear filter. Here, m may be positive (corresponding to “prediction”) or negative (corresponding to “smoothing”). In this paper we consider the case where both the signal and noise processes are non-stationary and possess evolutionary spectral representations. Using this approach we obtain a close analogue of the Wiener–Kolmogorov treatment of the stationary case, and show that the optimum filter is uniquely determined by the form of the evolutionary spectra.
Multivariate Stochastic Differential and Difference Equations with Periodic Coefficients
Authors: Siskind V. 
Published: December 2018

Summary
The theory of multivariate stochastic processes specified by linear matrix differential or difference equations is extended to the situation in which the coefficient matrices contain periodic terms. Questions of stationarity and ergodicity are discussed and algorithms for computing the autocovariance and spectral matrices given in outline. The paper concludes with a few remarks on applications and estimation problems.
An Integral Equation Approach to Equipment Failure
Authors: Downton F. 
Published: December 2018

Summary
An integro-difference equation relating the distributions of the times between successive failures of a piece of complex equipment is obtained. It is shown that in the limit this equation yields the exponential distribution (or its discrete analogue, the geometric distribution). The way in which this limit is approached is discussed and some data on the successive times to failure of bus engines are examined in the light of the results obtained.
Linear Compounds of Normal Linear Regression Coefficients
Authors: Kabe D. G. 
Published: December 2018

Summary
In the literature the double linear compounds of the multivariate linear normal regression coefficients are tested by using Roy's maximum root test, see, for example, Khatri (1962) and Morrison (1967, p. 109, equation (13)). The test statistic is Student's t. The t statistic gives narrower confidence bounds than those given by Roy's maximum root statistic. Morrison uses Hotelling's T2 statistic for testing linear compounds of the mean vector. However, the exact test statistic is Student's t.
On Asymptotic Relative Efficiencies of a Class of Rank Tests
Authors: Gastwirth Joseph L. 
Published: December 2018

Summary
A partial ordering is introduced in a class of rank tests according to the weight or emphasis they place on the middle ranks versus the extreme ones. This notion of order is shown to be related to van Zwet's partial ordering of symmetric densities according to the probability in their tails. Bounds on Pitman's asymptotic relative efficiency (a.r.e.) of several tests to the Wilcoxon test are established. Finally, a sharp lower bound for the asymptotic power of the Ψ-test is obtained.
Distribution of Residual Autocorrelations in the Regression Model with Autoregressive–Moving Average Errors
Authors: Pierce David A. 
Published: December 2018

Summary
In examining the adequacy of a statistical model an analysis of the residuals is often carried out; and for models involving a time series structure the serial correlations of the residuals are natural statistics to consider. In this paper it is shown that asymptotically the first s sample autocorrelations of the residuals, calculated from a least-squares fit of a regression model in which the errors follow a stationary autoregressive–moving average time series, possess a multivariate normal distribution. For moderately sized s this is nearly a singular distribution, with the “singularity” concentrated heavily on the autocorrelation coefficients of lowest order or lag. This distribution was first obtained by Box and Pierce (1970) for time series with no deterministic component; that it is independent of the regression structure of the model is shown to follow from general specification results of Durbin (1970), utilizing the large sample distribution of the parameter estimates recently obtained by the author (1971). Application of these results to testing model adequacy is also considered.
Some Families of Selection Probabilities for Sampling with Probability Proportional to Size
Authors: Dodds D. J. , Fryer J. G. 
Published: December 2018

Summary
Three families of simple exact selection probabilities for sampling two units from N with probability proportional to size (p.p.s.) are described. All three schemes include the well-known Brewer solution as a special case. Using the Horvitz–Thompson statistic, the efficiencies of the schemes are calculated for some well-known populations, and it is shown that considerable variations in efficiency may exist within any family. Finally, some criteria for choosing a particular member of a family in practice are examined.
Weakly Stationary Point Processes and Random Measures
Authors: Daley D. J. 
Published: December 2018

Summary
A weakly stationary point process on the real line is a point process with counting measure N(A) defined on Borel subsets A of the real line such that the first two moments of N(A) are finite for bounded Borel sets and invariant under translation. The expected number of points falling in an interval of length u equals μu and serves to define the intensity parameter μ of the process. The variance of the number of points falling in an interval of length u defines the variance function V(u) which, with μ, characterizes weakly stationary point processes. V(.) is absolutely continuous with its left- and right-hand derivatives differing on at most a countable dense set, with V′(0 +)= α=lim⁡θ→∞πG([O,θ])/θ and G(.) a uniquely determined σ-finite spectral measure on [0, ∞) in terms of which V(u)=∫[0,∞)(sin 12θu/12θ)2 G(dθ). These general results are also true of any weakly stationary signed random measure.
To any operation on a point process there corresponds an operation on the spectral measure, and the analogues of superposition, independent random motion of the points, deletion and multiplication of points and of forming cluster processes are exhibited.
The paper attempts to expound a rigorous basis for the general theory preceding Bartlett's (1963) development of spectral analysis for point processes.
Asymptotic Properties of Bayesian Decision Rules for Two Terminal Decisions and Multiple Sampling. Ii
Authors: Hald A. , Keiding N. 
Published: December 2018

Summary
The paper is a continuation of a paper by the same authors.
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 for some k-stage sampling and decision procedures.
In the present paper three cases not considered in the previous paper are treated. Some comments on the relation to sequential sampling, the relation to models for clinical trials and efficiency problems are also given.
Regression Models and Life-Tables
Authors: Cox D. R. 
Published: December 2018

Summary
The analysis of censored failure times is considered. It is assumed that on each individual are available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.
A Test for Time-Dependence of Linear Open-Loop Systems
Authors: Rao T. Subba , Tong H. 
Published: December 2018

Summary
We consider the problem of testing a given open-loop system for time-dependence. The test is based on just a single realization of the input and a single realization of the output. It makes use of the concept of the “evolutionary cross-spectra” of a non-stationary vector process and rests essentially on testing the “uniformity” of a set of vectors, whose components consist of the “evolutionary gain-spectra” and “evolutionary phase-spectra”.
Using a logarithmic transformation on the evolutionary gain-spectra, we show that the mechanics of the test are formally equivalent to a two-factor multivariate analysis of variance (MANOVA) procedure.
Numerical illustrations of the proposed test procedure are included.
Linear Ordered Rank Tests Which are Asymptotically Efficient for the Two-Sample Problem
Authors: Deshpandé Jayant V. 
Published: December 2018

Summary
In this paper the nonparametric two-sample problem is considered and tests are proposed for the hypothesis of identity of the two distribution functions. These tests are based on statistics which are linear combinations of ranks of the order statistics of one of the samples, in the two-sample rank order. It is seen that many existing statistics, proposed mainly on heuristic grounds, are members of this class. The asymptotic distribution of such statistics is discussed and those statistics which lead to tests with maximum ARE in this class are derived. It is seen that their ARE with respect to the “optimal” parametric tests is 1. In the appendix, we give the coefficients to be used for forming linear combinations which lead to the maximum ARE in certain specific cases.
The work reported here was carried out when the author was a Visiting Fellow at the University of Sheffield.
Minimum Risk Estimators with Applications
Authors: Swartz G. B. , Murthy V. K. 
Published: December 2018

Summary
Methods for obtaining minimum risk estimators with various loss functions and restrictions on the class of estimators are presented. The results are applied to estimators using order statistics and to estimation by graphical procedures. Minimum risk estimators of the Weibull reciprocal-shape parameter that use two order statistics are given.
Non-Orthogonal Main-Effect Designs for Asymmetrical Factorial Experiments
Authors: Margolin Barry H. 
Published: December 2018

Summary
Two techniques are presented for constructing efficient non-orthogonal main-effect designs. The first technique is an extended method of collapsing that permits non-orthogonality in the derived design. The second technique is a modification of the fold-over method of design construction to produce new main-effect plans. The designs in this paper supplement the major work on orthogonal asymmetrical main-effect plans by Addelman and Kempthorne. The new designs require fewer observations than the corresponding Addelman–Kempthorne plans; this advantage is gained at a sacrifice of orthogonality. The new plans are potentially useful in exploratory studies involving a few multi-level factors plus many two-level factors. Being more nearly saturated than the Addelman–Kempthorne plans, the new designs usually require graphical analysis or testing via a valid external measure of variability. The relationship of some of the new designs to Latin squares and Graeco-Latin squares is also discussed briefly.
The Number of Variables When Searching for an Optimum
Authors: Curnow R. N. 
Published: December 2018

Summary
Reservations are expressed about the automatic inclusion of a large number of factors in factorial experiments. Assuming a quadratic response surface and using the expected yield at the estimated optimum as a criterion, approximate conditions on the relevant parameters are obtained under which one-variable experimentation is preferred to two-variable experimentation, and no experimentation is preferable to both. The probabilities of mistaking the sign of the curvature of a cross-sectional curve and of the whole surface are also compared. The choice of the best single variable for experimentation is discussed. Practical limitations of the approach are noted.
A General Bayesian Linear Model
Authors: Smith A. F. M. 
Published: December 2018

Summary
Lindley and Smith (1972), using a hierarchical form of prior structure, derived Bayesian alternatives to least squares estimates for the linear model. This paper examines the Bayesian model in more detail and notes some general properties of the resulting estimators. Comparison is made with a least squares approach to models of the second kind, and an example is given.
Some General Points in the Theory of Optimal Experimental Design
Authors: Whittle P. 
Published: December 2018

Summary
This paper is an expansion of comments made by the author in the discussion following the reading of papers by Laycock (1972) and Wynn (1972). Section 2 presents a direct proof and interpretation of the equivalence theorem for the general case of a concave criterion function. This has implications for iterative algorithms of the type suggested by Wynn, as indicated in Section 3. Section 4 is concerned with a characterization of D,-optimality as a criterion which preserves ranking of designs under certain transformations of the problem. Section 5 discusses quasi-linear representations of the criterion for c-optimality.
On Tukey's Confidence Intervals for the Contrasts in the Means of the Intraclass Correlation Model
Authors: Bhargava R. P. , Srivastava M. S. 
Published: December 2018

Summary
In the intraclass correlation model when the variance σ 2 and the intraclass correlation coefficient 'p are both unknown, Tukey's confidence intervals for the contrasts in the means are obtained for the fixed sample and the sequential case. In the latter case confidence intervals of fixed width are obtained and the cost of not knowing σ2 and ‘p has been studied. From these results parallel results for Scheffé's confidence intervals can easily be obtained. A recommendation for the choice between the two is also made.
Evolutionary Spectra in Random Vibrations
Authors: Hammond J. K. 
Published: December 2018

Summary
The evolutionary spectral representation for a class of non-stationary random processes is applied to vibrating systems. Input-response relations are developed for single degree of freedom and multimode systems involving time-varying spectra for both univariate and bivariate processes. Jet noise is modelled as an example of the univariate case and the response of an oscillator to this excitation is considered.
Bayesian Estimation of Box–Jenkins Transfer Function-Noise Models
Authors: Newbold Paul 
Published: December 2018

Summary
The problem of estimating the coefficients of the transfer function-noise models proposed by Box and Jenkins is considered. A Bayesian approach is taken and the exact posterior density function of the coefficients is derived. Because of the complexity of this function, inference about individual parameters is virtually impossible except in the most simple cases.
Accordingly, it is desirable to consider certain approximations. In particular, it is shown that inference based on Student's t distribution provides an approximate solution to the estimation problem.
The Analysis of Covariance under a Randomization Model
Authors: Robinson J. 
Published: December 2018

Summary
The randomization model for the analysis of covariance in a randomized block design is considered. Asymptotic properties of tests and estimates are obtained and it is shown that if the number of replicates is large, then the usual results concerning tests are approximately true. The large sample power of the tests are obtained and it is shown that using the concomitant variate increases the power.
Inference from Complex Samples
Authors: Kish Leslie , Frankel Martin Richard 
Published: December 2018

SummaryThe design of complex samples induces correlations between element values. In stratification negative correlation reduces the variance; but that gain is less for subclass means, and even less for their differences and for complex statistics. Clustering induces larger and positive correlations between element values. The resulting increase in variance is measured by the ratio deff, and is often severe. This is reduced but persists for subclass means, their differences, and for analytical statistics. Three methods for computing variances are compared in a large empirical study. The results are encouraging and useful.
Explicit Form of the Distribution of the Behrens-Fisher D-Statistic
Authors: Rahman M. , Saleh A. K. Md. Ehsanes 
Published: December 2018

Summary
The distribution of the Berhens-Fisher d-statistic is given explicit form for all combinations of (v 1 v 2) the degrees of freedom whether odd or even, or one odd and one even. The density function of the d-statistic is expressed in terms of an Appell function which lends itself to easy computation of tail-probabilities. Values of 97.5 and 95 per cent points of the distribution are tabulated for chosen values of (v 1, v 2).