bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Average Run Length of the Cumulative Sum Chart When a V-Mask is Used
Authors: Kemp K. W. 
Published: December 2018

SUMMARY
The use of a V-mask on a cumulative sum chart is shown to be equivalent to the simultaneous operation of two single-sided schemes with horizontal decision boundaries. A method for obtaining the average run length (A.R.L.) of a V-mask is derived and some values are given from which a number of masks can be constructed with known values of the A.R.L.’s at two specified quality levels.
Some Stochastic Processes with Absorbing Barriers
Authors: Saaty Thomas L. 
Published: December 2018

SUMMARY
Models for growth distributions of biological organisms are investigated in this paper. They are specializations of the birth–death equations with two absorbing barriers. The solutions we seek are the distributions of the time to grow from an initial dose to an infective dose. Equations for these functions are simply obtained from the birth–death equations. Two main cases of interest are then examined. In the first case the birth and death rates are proportional to the number present and in the second case they are constant. Graphs are developed for the solution of the first case. Useful applications depend on this result.
Subsidiary Sequences for Solving Leser’s Least-Squares Graduation Equations
Authors: Joseph A. W. 
Published: December 2018

SUMMARY
Henderson’s method is applied to solve the equations which Leser uses for fitting a trend to a time series. In essence Henderson’s method depends on finding two quadratic factors for the symbolic expression 1+ϵ−1Δ4E−2. Two essentially different ways of factorizing this expression lead to two processes for fitting the trend, one of which is suitable when ε = 1 and the other when ϵ=13, 118 or 160. The methods are applied to an example considered by Leser for the cases ε = 1 and ε = ⅓.
A Note on a Generalized Inverse of a Matrix with Applications to Problems in Mathematical Statistics
Authors: Rao C. Radhakrishna 
Published: December 2018

SUMMARY
Some years ago the author defined a pseudo inverse of a singular matrix and used it in representing a solution of normal equations and for obtaining variances and covariances of estimates in the theory of least squares (Rao, 1955). This provided a unified approach to least squares theory, including the case when the normal equations become singular. This note attempts to collect a few mathematical results, some of which are known in literature, associated with the inversion of singular and rectangular matrices, and to indicate briefly their use in problems of mathematical statistics.
A New Asymptotic Expansion for the Normal Probability Integral and Mill’s Ratio
Authors: Ruben Harold 
Published: December 2018

SUMMARY
Mill’s ratio can be expressed, for positive values of the argument x, as the Laplace transform, with argument x, of the function e−12t2. This enables a new, and superior, asymptotic expansion for Mill’s ratio to be obtained with the aid of a recent result on the asymptotic expansions of a wide class of Laplace transforms. The new expansion is considerably more accurate than the usual expansion.
The General Bulk Queue as a Hilbert Problem
Authors: Keilson Julian 
Published: December 2018

SUMMARY
Bulk queues are those in which customers arrive and are served in groups, with the size of the groups governed by given probability distributions. A general theory for arbitrary group size distributions is developed for Poisson arrival epochs and arbitrary service-time distribution. Phase space methods and devices for solving the Hilbert problem on the unit circle play a key role. Treated are both the ordinary queue in which the server finding an empty queue waits for new arrivals and the transportation queue in which the service epochs form a renewal process. Formal expressions are given for the server busy period and the equilibrium waiting-time distributions for the general case. The formalism is applied to several queueing situations untreated in the literature.
On Queues in Heavy Traffic
Authors: Kingman J. F. C. 
Published: December 2018

SUMMARY
We say that a single server queue is in “heavy traffic” when the traffic intensity p is less than, but very near, unity. Then the equilibrium waiting time w will be large, and it is proved that, under certain conditions, the distribution of (1 – p)w tends, as p tends to 1, to a negative exponential distribution. The conditions under which this result holds are fairly weak, and, in particular, it is not necessary to make the assumption of independent inter-arrival times.
Control Charts and the Minimization of Costs
Authors: Bather J. A. 
Published: December 2018

SUMMARY
The behaviour of a machine or manufacturing process is represented by a simple model, in which two types of cost are considered: running costs and overhaul costs. Both types depend on the performance level of the machine, which changes stochastically and is tracked by means of a sequence of observations. It is assumed that the machine will run for an infinite period, interrupted by recurrent overhauls in which its performance level is modified. At any instant, it must be decided on the basis of the given observations whether or not an overhaul would be advantageous. The problem of finding an optimal decision procedure is described in terms of a control chart, and a certain functional equation is obtained, which relates the expected cost in any position and the decision procedure. Methods of approximation are considered and this leads to a reformulation of the problem in continuous time, which can be solved explicitly.
On the Randomization Distribution and Power of the Variance Ratio Test
Authors: Atiqullah M. 
Published: December 2018

SUMMARY
A particular matrix representation is given for the usual sum of squares of treatments in some commonly used designs. This representation simplifies appreciably the calculation of randomization moments under null and non-null hypotheses. Fisher’s Z-transformation is applied to study the randomization distribution of the F-criterion. The behaviour of power curves under randomization and normal theory conditions is studied.
Quadratics in Markov-Chain Frequencies, and the Binary Chain of Order 2
Authors: Good I. J. 
Published: December 2018

SUMMARY
Let nr be the frequency of the state r in a segment of a regular ergodic Markov chain. It is shown how to obtain the asymptotic distribution of any quadratic expression in the nr’s. The method is especially convenient where the Markov chain is produced by a random motion on a circle. An explicit formula is given for the asymptotic variance of the number of 0’s in a binary Markov chain of order 2.
The Correlated Unrestricted Random Walk
Authors: Seth Asha 
Published: December 2018

SUMMARY
A particle performs an unrestricted correlated random walk along a straight line with a velocity constant in magnitude but variable in direction. This direction remains constant for every time interval of unit length, and with probability p it is the same as in the previous interval and with probability 1 − p it is reversed. The object of this paper is to obtain probabilities for the first passage to position r, the jth. return to the origin and cognate results.
A Lower Bound for the Critical Probability in the One-Quadrant Oriented-Atom Percolation Process
Authors: Bishir J. 
Published: December 2018

SUMMARY
For a percolation process on a one-quadrant lattice let p denote the probability that each point or atom, independently of all other atoms, allows fluid to pass. For an oriented process of this type a lower bound is established for the largest or critical value of p for which the process remains confined to a finite region of the lattice.
The Diffusion Equation and a Pseudo-Distribution in Genetics
Authors: Ewens W. J. 
Published: December 2018

SUMMARY
The function obtained by formally solving a differential equation is shown to describe, in a sense, the transient behaviour of a diffusion process. Interpretations of other solutions of the equation (obtained by a different allocation of constants) are mentioned. An analogous function for the case of a certain discrete process is exhibited.
Competitive Queueing: Idleness Probabilities Under Priority Disciplines
Authors: Gaver Donald P. 
Published: December 2018

SUMMARY
If (i) customers belonging to two (or more) classes are served at a single facility, and if (ii) the facility experiences orientation delay when a change is made between classes served, then a priority service rule may be more efficient than the “first come, first served” discipline. Efficiency here refers primarily to the facility's capacity to handle traffic without being saturated. This paper shows how busy-period distributions and long-run idleness probabilities may be determined for a system with stationary Poisson arrivals from two classes. Arrival, service and orientation times are independently but otherwise arbitrarily distributed. Illustrative numerical comparisons are made between various disciplines.
Stationary Amplitude Fluctuations in a Random Series
Authors: Herbst Laurence J. 
Published: December 2018

Summary
A previous model leading to periodicity in the variance of a random series was of the form Xt = σt ηt (t = 1, 2, …, N), the ηt being independently, normally, distributed with zero means and unit variances (N.I.D. (0,1)), and σt, σt, σt2 possessing short Fourier series. It was argued that periodogram analysis of Xt2 could be used to detect the fixed oscillatory frequencies contributing to σt2. Following the path of Yule, the deterministic multiplier σt above is replaced by a stationary Gaussian second-order autoregressive scheme Yt, independent of ηt, such that Yt has quasi-oscillatory realizations. The resulting series Xt = Yt ηt will have zero means, zero correlations and constant variances, yet its amplitudes will tend to follow a quasi-oscillatory pattern. The process Yt ηt is then generalized to Xt = Wt ηt, where Wt=∑j=0∞ajvt−j(∑aj2&lt;∞), the vt being N.I.D. (0,1) and independent of ηt, leading to purely non-deterministic amplitude fluctuations in a series of uncorrelated random variables with zero means and constant variances. It is suggested that statistical spectral analysis of Xt2 is a suitable technique to detect the important frequency bands contributing to the purely non-deterministic amplitude fluctuations.
A Bivariate Signed Rank Test
Authors: Bennett B. M. 
Published: December 2018

Summary
Wilcoxon (1945, 1947) proposed a signed rank test for the hypothesis of equality of means in samples of n matched pairs of observations from a bivariate population in (x, y). He stated the exact distribution of the sum (= U +) of the signed ranks of the positive differences z = x - y, as well as providing some tables of the significant values Uϵ+. The present paper gives a generalization of the Wilcoxon test using the sums of the signed ranks for two correlated or matched bivariate populations. An approximate test using the signed ranks is also proposed.
Derivation of a Class of Frequency Distributions Via Bayes's Theorem
Authors: Särndal Carl-Erik 
Published: December 2018

Summary
Being in some respects expository in character, this paper uses Bayes's theorem to derive a k-variate discrete probability distribution which is fundamental inasmuch as it proliferates, under various sets of asymptotic conditions, to yield as its limiting forms an array of other k-variate distributions including the multinomial, independent Poisson, independent negative binomial, independent gamma, Dirichlet and multivariate normal. A systematic arrangement of these distributions thereby suggests itself, and a number of properties pertaining to the distributions are discussed within the framework created by this arrangement.
On the Busy Period of a Facility Which Serves Customers of Several Types
Authors: Welch P. D. 
Published: December 2018

Summary
Customers of a finite number of types are attended by a single server. The input for each type is Poisson and these inputs are mutually independent. The service times are general, and a function of the customer type. The service discipline is subject only to minimal restrictions. This paper contains a discussion of the phenomenon of the busy period for the above queueing model. The main result obtained is the determination of the joint distribution of the length of the busy period and the number of each type of customer served during it.
Asymptotic Sequential Design of Experiments with Two Random Variables
Authors: Abramson Lee R. 
Published: December 2018

Summary
Given two independent random variables with densities f1 and f2, we test H1: f1 = f11, f2 = f12 versus H2: f1 = f21, f2 = f22, where the fij are known densities (i,j = 1,2). We study asymptotic Bayes sequential procedures as the cost of each observation approaches zero. An asymptotic expression for the Bayes risk is found, and necessary and sufficient conditions for a decision rule to be asymptotically Bayes are derived. We study a class of tests which we call tandem tests and construct an asymptotically Bayes set of tandem tests. (A tandem test is a sequence of at most two sequential probability ratio tests, the first performed on one of the random variables and the second performed on the other.)
A Note on the Asymptotic Efficiency of Bennett's Bivariate Sign Test
Authors: Bhattacharyya G. K. 
Published: December 2018

Summary
Asymptotic power properties of Bennett's bivariate sign test are studied by computing its Pitman efficiency relative to Hotelling's T2 test corresponding to the translation family of alternatives. The behaviour of the Pitman efficiency in some important special cases is also discussed.
On Streams of Events and Mixtures of Streams
Authors: Leadbetter M. R. 
Published: December 2018

Summary
Distribution functions for streams of events (and, in particular, for the length of the interval “between successive events”) are defined within the framework of the theory of Khintchine (1955). Relationships such as that between the distributions for the length of an “arbitrary interval” between successive events, the interval containing a fixed point and that of the time to the nth event after t = 0 are discussed briefly in this context. The definitions and results are extended to deal with mixtures of two streams, in which the events are alternately of opposite type. An important application concerns upcrossings and downcrossings of a level by a stationary stochastic process.
On the Distribution of the F-Type Statistics in the Analysis of a Group of Experiments
Authors: Caliński T. 
Published: December 2018

Summary
Particular matrix representations are given for the usual sums of squares in the analysis of a group of experiments. Box's theorems on quadratic forms in normal variables are applied to study the distributions of the sums of squares and of the usual variance ratio statistics. The behaviour of these statistics under heterogeneity of the error variance and of the interaction variance is considered and approximate F-tests are suggested.
A Generalization of Fieller's Theorem to the Ratio of Complex Parameters
Authors: Halperin Max 
Published: December 2018

Summary
By an elementary argument, essentially identical to that given by Fieller (1940) to obtain confidence limits for a ratio of real parameters, it is shown how one can obtain confidence regions for the real and imaginary parts of a ratio of complex parameters. An exact confidence region (under assumptions of normality) is developed based on Hotelling's T 2 distribution. A conservative region which allows a considerable simplification of computations is also suggested; this region is based on the joint distribution of two correlated Student t-variates.
Asymptotic Renewal Results for a Natural Generalization of Classical Renewal Theory
Authors: Heyde C. C. 
Published: December 2018

Summary
A generalization of the classical renewal theory for non-negative summands is suggested which involves the maxima of the partial sums instead of the partial sums themselves. It is shown that the generalization is a natural one and that most of the classical properties are preserved. In addition, methods are developed for obtaining asymptotic expansions for the moments of the random variable whose expectation is the new renewal function.
Non-Homogeneous Branching Poisson Processes
Authors: Lewis Peter A. W. 
Published: December 2018

Summary
The properties of non-homogeneous branching Poisson processes are derived, using some particular conditional distributional results for the non-homogeneous Poisson process. The properties derived include the Laplace-Stieltjes transforms of the cumulant generating functions of the number of events by time x and of the state of the process at time x.
On the Choice of a Strategy for the Ratio Method of Estimation
Authors: Rao T. J. 
Published: December 2018

Summary
Three sampling strategies are considered: (i) H(M, R 1) consisting of the Midzuno (1952)–Sen (1952) sampling scheme and the estimator R1=X(∑i∈sYi)/(∑i∈sXi) of the population total Y, where the symbol ∑išs indicates that the summation is over all units Ui contained in the sample s; (ii) H(M, ŶHT) consisting of the Midzuno–Sen sampling scheme and the estimator ŶHT = ∑išs(Yi/πi), where πi is the probability of inclusion of the ith unit in the sample; (iii) H(πps, Rn) consisting of the πps sampling scheme (Hanurav, 1965; 1967) and the estimator Rn = (X/n) ∑išs(Yi/Xi) of Y. It is shown that the strategy H(πps, Rn) is suitable for the method of ratio estimation. A direct application to cluster sampling is given at the end.
The Combination of Information in Generally Balanced Designs
Authors: Nelder J. A. 
Published: December 2018

Summary
A general method is proposed for combining information in generally balanced designs when estimates of treatment effects are available from more than one stratum. Estimates of stratum variances are obtained by equating residual sum of squares in each stratum to their expectations, using the ML estimates of treatment effects. Weights may be given, the solution then being explicit, or fitted, in which case iteration is required. The results of a Monte Carlo study are given for a BIB design to test the distribution of the variance estimates.
An Application of Biorthonormal Expansions in Theory of Stochastic Processes
Authors: Mehr C. B. 
Published: December 2018

Summary
Markov processes (with the exception of Gauss-Markov processes) are not in general Markov in the wide sense. Using a biorthonormal expansion of the second-order density function, it is shown that a class of Markov processes (not necessarily Gaussian) are Markov in the wide sense. These processes share some of the nice properties of Gaussian processes.
Note on X2 Tests for Matched Samples
Authors: Bennett B. M. 
Published: December 2018

Summary
This note represents an extension of the author's results (Bennett, 1967) on the problem of tests for matched samples. These were shown to be equivalent to tests of linear hypotheses H0 concerning multinomial probabilities. Solutions for the goodness-of-fit and modified minimum chi-square tests and an explicit relation between the two tests are presented. The power function is discussed under certain alternatives to H0.
On the Linear Control of a Linear System Having a Normal Stationary Stochastic Input
Authors: Dowson D. C. 
Published: December 2018

Summary
This paper deals with the linear control of a linear system subject to a random error in the form of a stationary stochastic input. It is shown that when the error is normally distributed, the problem of finding stationary points of the expected value of almost any function of the input Yt and the output Xt is, in general, equivalent to that of finding stationary points of the quadratic control function Q = var Xt + φ cov (Xt, Yt) + θ var Yt, provided that θ and φ are suitably chosen. This leads to a procedure for finding the optimal linear control for all loss functions likely to be met in practice.
Some Applications of Multiple-Type Branching Processes in Population Genetics
Authors: Ewens W. J. 
Published: December 2018

Summary
Multiple-type branching processes are used in this paper to derive survival probabilities of mutant genes in a number of situations in population genetics. Specifically, we apply the theory in the following cases. (1) Bisexual populations. In a population allowing (say) far more males than females, a favourable new mutation will have far greater survival probability if it occurs initially in a female; use of weighted survival probabilities will allow derivation of an optimum sex ratio. (2) Two locus problems. The selective advantage of a gene is not a fixed quantity but depends on the “genetic background”, that is on the genes present at other loci in the individual in question. Here we suppose that the selective advantage depends, in this way, only on a second interacting locus. Attention will be concentrated on the effect of linkage between the two loci. (3) The extension to three locus problems. (4) In a model introduced by Kimura (1957) it is assumed that a chromosome consists of a number k of sub-units, or strands, in any one of which a mutation may occur. The mode of inheritance is such that each strand duplicates itself and the daughter chromosome is made up of a random collection of k of the 2k strands so obtained. This model allows a wide field of possible investigations, only a few of which are considered here.
Apart from questions of genetical interest, it is shown that a multiple-type branching process may not possess the close relationship with the corresponding deterministic process that is enjoyed by a single-type process. This means that some caution may be needed in drawing conclusions about the stochastic behaviour from the deterministic behaviour.
A Queue with Random Arrivals and Scheduled Bulk Departures
Authors: Mercer A. 
Published: December 2018

Summary
The distributions of queue length and waiting time of a customer are considered for the queue where customers arrive at random, wait in the order of arrival and are scheduled to be served in batches by a single server during equal intervals. A general lateness distribution is assumed but a service either takes place in the scheduled interval or not at all; no overlapping of services is allowed.
The Bayesian Estimation of a Linear Functional Relationship
Authors: Lindley D. V. , El-Sayyad G. M. 
Published: December 2018

Summary
The purpose of this note is twofold. First, to demonstrate by means of an example that a statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method yields sensible results. Second, to develop the Bayesian method and apply the results to the problem of estimating a linear functional relationship. In Section 1 we discuss the likelihood approach. Section 2 concerns the Bayesian method, which is applied to the functional relationship situation in Section 3: it is shown that the asymptotic behaviour of the distributions exhibits a novel form. In Section 4 the posterior distributions derived in Section 3 are considered in more detail: in particular, a standard error for the estimate of slope is provided. Section 5 contains various comments on the method, and, in particular, indicates other fields of application.
On Extremal Factorization and Recurrent Events
Authors: Heyde C. C. 
Published: December 2018

Summary
Associated with any recurrent event there is a Markov chain whose distributions possess what can be called an extremal factorization property. The important role which this property plays in the general theory is briefly indicated and the behaviour of the probability of occurrence of the recurrent event, in some specified time interval, is discussed using the property as a tool.