bluuebunny/crossref_metadata_2025 huggingface dataset:
Parasite in peril? A new species of mite in the genus Ophiomegistus Banks (Parasitiformes: Paramegistidae) on an endangered host, the pygmy bluetongue lizard Tiliqua adelaidensis (Peters) (Squamata: Scincidae)
Authors: Derne Bonnie T. , Hutchinson Mark N. , Weinstein Philip , Gardner Michael G. , Halliday Bruce
Published: December 2018

Host‐parasite relationships are generally understudied in wild populations but have a potential to influence host population dynamics and the broader ecosystem, which becomes particularly important when the host is endangered. Herein we describe a new species of parasitic mite from the genus Ophiomegistus (Parasitiformes: Mesostigmata: Paramegistidae) of an endangered South Australian skink; the pygmy bluetongue lizard (Tiliqua adelaidensis). Adult mites were observed on lizard hosts in three different host populations, among which prevalence varied. No temporal trend in prevalence was evident over two spring‐summer seasons of monitoring. We hypothesise that the reliance on burrows as refuges by T. adelaidensis may be essential for the completion of the mite life cycle and also for horizontal transmission. The conservation implications of not only its effect on the host, but also its potential status as an endangered species itself, are considered.
Racial Code Words, Re‐Memberings and Black Kids’ Civic Imaginations: A Critical Race Ethnography of a Post‐Civil Rights Leader
Authors: Woodson Ashley N.
Published: December 2018

This article uses the construct ofracial code wordto advance theory about unspoken, racialized expectations that accompany seemingly neutral historical concepts. Critical race ethnographic methods were used to examine how eight black teenagers made sense of the term “civil rights leader” and the assumptions that supported their sense‐making. Data from this eighteen‐month study reveals tension between ideals of whiteness in popular stories about black activism and the possible and desired civic identities of participants.
Gender differences in mental health and substance use disorders and related healthcare services utilization
Authors: Brand Evelyn , Rodriguez‐Monguio Rosa , Volberg Rachel
Published: December 2018

Background and Objectives

Pathological gambling often co‐occurs with other psychiatric disorders. Gender differences in treatment‐seeking behaviors among patients with pathological gambling diagnosis remain poorly understood. This study assessed gender differences in healthcare services utilization in patients seeking treatment for pathological gambling, substance use, and mental health co‐occurring conditions.

Methods

Study data were derived from a representative sample of the Massachusetts All Payers Claims Database for the period 2009–2013. Descriptive analyses were performed by gender using group t‐tests and Pearson's chi‐square tests. Bootstrap analysis was used to account for skewed distribution of healthcare services utilization data. Multiple linear regressions were used to evaluate the association between healthcare services utilization and gender while controlling for patient's age, county, and ICD‐9‐CM diagnosis codes.

Results

Over two‐thirds of the patients were males. Moreover, two in five patients seeking treatment had pathological gambling as principal or primary diagnosis. Females had a significantly greater number of three or more co‐occurring psychiatric conditions than males. Having a diagnosis of episodic mood disorder, neurotic disorder, or adjustment reaction significantly increased the utilization of healthcare services for both genders. Females had a greater utilization of healthcare services than males for the same psychiatric diagnosis.

Discussion and Conclusions

Healthcare services utilization significantly varies by gender and type of mental health and substance use diagnosis. There are significant differences by gender in the utilization of healthcare services for the same psychiatric disorders.

Scientific Significance

There is a need to address gender differences in psychiatric conditions and their related healthcare needs. (Am J Addict 2018;XX:1–7)
Leucine regulates slow‐twitch muscle fibers expression and mitochondrial function by Sirt1/AMPK signaling in porcine skeletal muscle satellite cells
Authors: Chen Xiaoling , Xiang Lu , Jia Gang , Liu Guangmang , Zhao Hua , Huang Zhiqing
Published: December 2018

A previous study demonstrated that leucine upregulates the slow myosin heavy chain mRNA expression in C2C12 cells. However, the role of leucine in slow‐twitch muscle fibers expression and mitochondrial function of porcine skeletal muscle satellite cells as well as its mechanism remain unclear. In this study, porcine skeletal muscle satellite cells cultured in differentiation medium were treated with 2 mM leucine for 3 days. Sirt1 inhibitor EX527, AMPK inhibitor compound C, and AMPKα1 siRNA were used to examine its underlying mechanism. Here we showed that leucine increased slow‐twitch muscle fibers and mitochondrial function‐related gene expression, as well as increased succinic dehydrogenase (SDH) and malate dehydrogenase (MDH) activities. Moreover, leucine increased the protein levels of Sirt1 and phospho‐AMPK. We also found that AMPKα1 siRNA, AMPK inhibitor compound C, or Sirt1 inhibitor EX527 attenuated the positive effect of leucine on slow‐twitch muscle fibers and mitochondrial function‐related gene expression. Finally, we showed that Sirt1 was required for leucine‐induced AMPK activation. Our results provide, for the first time, evidence that leucine induces slow‐twitch muscle fibers expression and improves mitochondrial function through Sirt1/AMPK signaling pathway in porcine skeletal muscle satellite cells.
Intangibles Disclosure on Entrepreneurial Small Businesses’ Websites to Influence Stakeholders’ Impressions
Authors: Abeysekera Indra
Published: December 2018

This study examines the ways in which entrepreneurs influence stakeholders to form perceptions using intangibles disclosed on business websites. Interviews were conducted with 10 entrepreneurs, each representing an entrepreneurial business, and 17 intangible capabilities disclosed to impress three stakeholder groups using five impression‐management tactics were uncovered. The study uses an entrepreneurship perspective to investigate entrepreneurs’ motivation to share their beliefs with stakeholders, and resource‐based theory to posit that intangibles combined with business capabilities are competencies for such communication, in addition to stakeholder theory for targeting specific stakeholders.
Distance‐based multicriteria group decision‐making approach with probabilistic linguistic term sets
Authors: Wang Xiaokang , Wang Jianqiang , Zhang Hongyu
Published: December 2018

Probabilistic linguistic term sets (PLTSs) are an important expression for hesitant linguistic preference information under group decision‐making circumstances. This study investigates problems of multicriteria group decision making (MCGDM) with PLTSs. A novel and rational comparison method is first proposed, and two distance measures for PLTSs are defined. The weight of each criterion is then obtained via maximum deviation method. Subsequently, extended Techniques for Order Preference by Similarity to Ideal Solution (TOPSIS) ‐ VIseKriterijumska Optimizacija I Kompromisno Resenje a Serbian name (VIKOR) and TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) methods are developed as decision support models to handle MCGDM problems. An illustrative example is also analysed to demonstrate the rationality and feasibility of the proposed methods.
Structural and mechanistic insights into polymyxin resistance mediated by EptC originating from Escherichia coli
Authors: Zhao Yanqun , Meng Qiang , Lai Yujie , Wang Li , Zhou Dan , Dou Chao , Gu Yijun , Nie Chunlai , Wei Yuquan , Cheng Wei
Published: December 2018

Gram‐negative bacteria defend against the toxicity of polymyxins by modifying their outer membrane lipopolysaccharide (LPS). This modification mainly occurs through the addition of cationic molecules such as phosphoethanolamine (PEA). EcEptC is a PEA transferase from Escherichia coli (E. coli). However, unlike its homologs CjEptC (Campylobacter jejuni) and MCR‐1, EcEptC is unable to mediate polymyxin resistance when overexpressed in E. coli. Here, we report crystal structures of the C‐terminal putative catalytic domain (EcEptCΔN, 205–577 aa) of EcEptC in apo and Zn2+‐bound states at 2.10 and 2.60 Å, respectively. EcEptCΔN is arranged into an α‐β‐α fold and equipped with the zinc ion in a conserved mode. Coupled with isothermal titration calorimetry (ITC) data, we provide insights into the mechanism by which EcEptC recognizes Zn2+. Furthermore, structure comparison analysis indicated that disulfide bonds, which play a key role in polymyxin resistance, were absent in EcEptCΔN. Supported by structural and biochemical evidence, we reveal mechanistic implications for disulfide bonds in PEA transferase‐mediated polymyxin resistance. Significantly, because the structural effects exhibited by disulfide bonds are absent in EcEptC, it is impossible for this protein to participate in polymyxin resistance in E. coli.

Database

Structural data are available in the PDB under the accession numbers 6A82 and 6A83.

Enzyme

EC 2.7.8.43
Subsistence migration: Smallholder food security and the maintenance of agriculture through mobility in Nicaragua
Authors: Carte Lindsey , Radel Claudia , Schmook Birgit
Published: December 2018

Research on Central American migration has revealed the importance of journeys to the global North for rural sending communities. The outcomes of south–south journeys to nearby countries are less explored, although they are commonplace. We examine Nicaraguan rural residents’ migration to other Central American countries, especially El Salvador, to understand this migration's impacts on agricultural systems and food security. Based on mixed‐methods fieldwork in north‐western Nicaragua, we find that rather than produce remittance landscapes, or an abandonment of agriculture, south–south migration is linked to the maintenance of small‐scale agricultural systems and thus food production. “Subsistence migration,” or mobility to maintain small‐scale agriculture as a food security strategy, draws attention to how these less explored forms of migration in Central America help families to persist in agriculture in a context of worsening environmental and structural conditions.
Ballade of Multiple Regression
Authors: Corlett Tom
Published: December 2018

These verses were used by Tom Corlett as a summary of the points which he made in opening the discussion on a paper entitled ‘Multiple Regression and Marketing’ read by John Clemens and Paul Duncan-Jones at the Market Research Society's Annual Conference at Eastbourne, 13th-15th February 1964.
Factorial Designs in Small Blocks Derived from Orthogonal Latin Squares
Authors: Thompson H. R. , Dick I. D.
Published: December 2018

From a basic p × q design in blocks of q plots (q < p, p a prime or power thereof) three factor designs with the same block size are obtained, the number of levels being p, q or factors of q.

When multifactorial experiments are used in the field they often need too many plots per block for ordinary randomized blocks to be used, so that a design in which there is a degree of confounding is necessary to control the experimental error. In certain other applications the block size may be limited naturally to a very small number of plots and a further degree of confounding is required. Particular instances occur in pig nutrition experiments where litters form the blocks, and in plant inoculation work where there may be only a small number of leaves per plant on which to place treatments. Designs to suit such cases are derived in this note, the block size in every case being equal to or less than the number of levels in the leading factor.
Change-Over Trials
Authors: Patterson H. D.
Published: December 2018

A number of designs for experiments in which sequences of treatments are applied to experimental units are considered. These experiments are described as change-over trials. The arrangements are such that estimates can be obtained of direct and first residual effects of treatments. The total number of units is kept as low as possible consistent with a neat analysis.

It is found that confounding in factorial arrangements and incomplete block designs can be introduced by an adaptation of the methods of single period experiments. Only 3 and 4 period designs are included, but the extension to larger numbers of periods where this is practicable presents little difficulty.

The statistical analysis of data from change-over trials is discussed. The ordinary method based on a straightforward application of the least squares principle is subjected to some criticism and a modification suggested.
The Statistical Theory of Bacterial Populations Subject to Mutation
Authors: Armitage P.
Published: December 2018

This paper is a study of the growth of a mixed bacterial population composed of two types of organisms, and subject to mutation from one type to the other, in one or both directions. The bacteria divide by binary fission, but the rates of division for the two types may differ. The paper is intended as a unified and critical presentation of statistical results previously published by other authors, together with a number of new results.

The first part presents a mathematical theory, from both the deterministic and the stochastic viewpoints. The definition of a mutation rate is discussed in some detail. Particular attention is directed to the situation in which the proportion of organisms of one type remains negligible throughout the period of growth (so-called short-term experiments); the effects of delayed phenotypic expression and of the sampling of replicate cultures are considered. For the more general situations, approximate expressions are obtained for the first few cumulants of the joint distribution of the numbers of organisms of each type present at any time.

The second part is concerned with methods of estimation of the parameters of a mutation process. In particular I examine the suitability of various methods of estimating the mutation rate in short-term experiments, when phenotypic delay is present. Methods based on the upper portion of the distribution of the number of mutants in replicate cultures, such as the upper quartile, are preferable.

The verification of the theory by certain data published by other authors is considered in the third part. An attempt is made to fit some observed distributions of the number of mutants in replicate cultures, using a particular model for phenotypic delay; the fit is unsatisfactory, the fitted distributions having too high a frequency of cultures with two or three mutants.
Greenwood’s “Problem of Intervals”: An Exact Solution for N = 3
Authors: Gardner A.
Published: December 2018

The probability integral of the sum of squares of four random intervals is derived geometrically. The probability density is obtained by differentiation and the appropriate substitution given whereby the distribution of the variance of the intervals can be derived, as required by Greenwood.
A Study of Queues and Appointment Systems in Hospital Out-Patient Departments, with Special Reference to Waiting-Times
Authors: Bailey Norman T. J.
Published: December 2018

An investigation, based on the use of random numbers, has been made into the kind of queueing process occurring in hospital out-patient departments. Special attention has been paid to the patients’ waiting time and also to the time which a consultant may waste waiting for the next patient. As compared with many appointment systems at present in use, it is concluded that by suitable choice of the system to be adopted a substantial amount of the patients’ waiting time may be eliminated without appreciably affecting the consultant. A recommended procedure is to give patients appointments at regular intervals, each equal to the average consultation time; the consultant commencing work when the second patient arrives. The effect of variations in the appointment interval, the number of patients attending the clinics, and the distribution of queue-size are discussed. The precision of the results obtained is also considered.
On the “Transition Probabilities” Corresponding to any Accident Distribution
Authors: Irwin J. O.
Published: December 2018

From any known distribution of accidents in a fixed exposure time T, the expected number of other accidents sustained by a person who has x accidents is obtained. It is the ratio of the x + 1th to the xth factorial moment of the distribution. its limiting value when the exposure time tends to zero gives the transition probabilities.
A Note on the Time-Homogeneous Birth Process
Authors: Armitage P.
Published: December 2018

Some simple limiting properties of the time-homogeneous birth process, valid for small exposure times, are obtained.
Grading with a Gauge Subject to Random Output Fluctuations
Authors: Mandel L.
Published: December 2018

A study is made of the errors arising in grading a normal population into classes with a gauge subject to output fluctuations. This involves evaluating the bivariate normal integral when the correlation coefficient is close to unity and series for this are developed. Curves are derived showing the dependence of the errors on the population variance and on the instrumental noise level. Means of reducing some errors by small adjustments of the gauging limits are also examined. The results have a direct bearing on the industrial applications of β-ray thickness gauges.
The Analysis of a Factorial Experiment (with Confounding) on an Electronic Calculator
Authors: Rowell J. G.
Published: December 2018

(a) The analysis of a 24 factorial experiment confounded into blocks of two carried out on an electronic computer (the EDSAC) is described. Treatment effects were calculated in the factorial analysis and summarized. The factorial analysis, which would have taken 10 or 12 weeks with a desk machine, was carried out in about 13 days. The summary represented a greater saving of time, being carried out in 3 days.

(b) Three-quarters of the time needed for the computation of the factorial analysis was used in punching the data tapes; calculators capable of reading from punched cards are available and may be more suited to statistical calculations of this type. No data tape had to be punched for the summary analysis since the input for this was the output of the factorial analysis.

(c) The total machine time needed for the factorial analysis was about four hours.

(d) About 450 orders were used in each part of the analysis leaving storage space for about 190 numbers of 10 decimal digits.
Moments of Negative Order and Ratio-Statistics
Authors: David H. A.
Published: December 2018

A simple method is considered of obtaining the moments of the sampling distribution of a ratio, when the numerator and denominator are independent.
Some Distribution and Moment Formulae for the Markov Chain
Authors: Whittle P.
Published: December 2018

An exact formula (8) is derived for the probability distribution of an observed set of transition totals. This expression furnishes asymptotic expressions for the likelihood (24), for the covariances of transition totals (27), and for the distribution of Bartlett’s goodness-of-fit statistic (31). Formulae are also derived for the expectations of some sample functions related to the factorial moments of the transition totals (34) and for the lower moments of the estimated transition probabilities (42), (44). It is shown that the Markov chain has properties similar to those of a. set of independent multinomial distributions.
A Note on Equalising the Mean Waiting Times of Successive Customers in a Finite Queue
Authors: Bailey Norman T. J.
Published: December 2018

The type of appointment system recommended in a previous paper (Bailey, 1952) for hospital out-patient departments suffered the disadvantage that a patient’s average waiting time was much longer at the end of the queue than at the beginning. It is shown here that a slight modification of the appointment system results in the patient’s average waiting time being nearly independent of his position in the queue.
Some Notes on Ordered Random Intervals
Authors: Barton D. E. , David F. N.
Published: December 2018

The joint probability distribution of several magnitudinally ordered intervals of a line is derived together with a moment generating function belonging to it. Some limiting distributions are given and the rate of convergence is examined. The distributions of some simple functions such as the ratio and difference of two ordered intervals are derived.
Generalizations of Tchebycheff’s Inequalities
Authors: Mallows C. L.
Published: December 2018

We may often obtain the lower moments of a sampling distribution when the distribution itself is intractable. Tchebycheff’s celebrated inequalities for the cumulative distribution function are of very little use in practice, being “much too wide”. The present work obtains generalizations of these inequalities by restricting the distribution function to be “smooth” in two senses: firstly, by restricting the number of changes of sign of some derivative, and secondly by also restricting the size of this derivative. These conditions lead to certain “extremal” distributions, and hence to the required inequalities. These have been proved correct only in the simpler cases, but are conjectured to hold in general. In Part I some of the simpler results are given explicitly.
Some Statistical Problems in Experimental Psychology
Authors: Cane Violet R.
Published: December 2018

The paper deals with some problems that arise in determining thresholds and in describing a learning process; it includes a comparison of three psychophysical methods, an interpretation of certain data from experiments on visual thresholds, and a discussion of the sort of models that might be useful in work on learning.
Some Methods of Estimating the Parameters of Discrete Heterogeneous Populations
Authors: Freund John E.
Published: December 2018

Methods of estimation are suggested and illustrated for estimating the distribution of a parameter within a heterogeneous population. If a parameter assumes a discrete set of values θj, estimators are obtained for the probabilities f(θj). It is assumed that certain values xi are observed with frequencies ni in a sample from the entire heterogeneous population and that the conditional probabilities f(xi | θj) are known.
Regression Analysis of Relationships between Autocorrelated Time Series
Authors: Wise J.
Published: December 2018

The properties of complete systems of linear regression equations, (in particular systems of the closed-loop and recursive type) are discussed in Part I, while least-square estimators and estimators of the Gauss-Markoff type are examined in Part II.
Some Experimental Designs of Use in Changing from One Set of Treatments to Another: Part II. Existence of the Designs
Authors: Freeman G. H.
Published: December 2018

Necessary conditions are given for the construction from two block designs of row and column designs, i.e., three-way classifications two of whose classifications are orthogonal. For all designs considered except those partially balanced both ways (type O:PP) the conditions for existence appear to be that the block designs exist separately. For O:PP designs, however, further conditions are necessary, these leading in practice to the exclusion of (i) certain singular group-divisible designs, (ii) all designs formed from unextended disconnected group-divisible designs and (iii) a small design not fitting into either of these categories. There may be other types of row and column design that are apparently possible but do not in fact exist, but none is known.
The Variance of the Mean of a Stationary Process
Authors: Hannan E. J.
Published: December 2018

A method of estimating the variance of the mean of a stationary process, proposed by Jowett (1955), is modified and extended and its relationship to the estimation of the spectral density is discussed.
On the Exact Distribution of a Test in Multivariate Analysis
Authors: Banerjee D. P.
Published: December 2018

By rearranging the factors of the complicated r  th moment of the distribution of a statistic in multivariate analysis and using Mellin’s Transformation it is possible to find the exact distribution of the statistic. This cannot be found easily by other methods.
The Inspection of a Markov Process
Authors: Broadbent S. R.
Published: December 2018

The output of a Markov process producing good and bad items in sequence is inspected for the bad items. A measure is proposed of the work involved, and the estimation required for this measurement is discussed.
The Continuous Time Solution of the Equations of the Single Channel Queue with a General Class of Service-Time Distributions by the Method of Generating Functions
Authors: Luchak George
Published: December 2018

Equations describing a single channel queue with random arrivals and a general class of service-times are solved for time-dependent state probabilities. Solutions for a Pearson type III service-time and a “double” Pearson type III service-time are given in terms of the Ik  n function. Corresponding results for the distribution of busy periods are also obtained.
Interval Analysis and the Logarithmic Transformation
Authors: Moore P. G.
Published: December 2018

The intervals between random events have an exponential distribution. The use of the logarithm of the intervals leads to possible tests for homogeneity that are independent of the average interval. This paper considers the distribution of the logarithm and discusses possible approximations.
Renewal Theory and its Ramifications
Authors: Smith Walter L.
Published: December 2018

This is an expository article on the theoretical and some computational aspects of renewal theory. §1 describes basic theory, including Blackwell’s theorem; renewal density theorem; cumulants and asymptotic normality of the number of renewals in (0, t); and the integral equations of renewal theory. §2 is concerned with asymptotic behaviour of processes having an embedded renewal process: regenerative stochastic processes; semi-Markov processes; cumulative processes. §3 discusses infinite sums and products connected with a renewal process which arise out of the study of electronic particle counters, and an integral equation connected with the infinite products. §4 describes some generalizations of renewal theory that have been proposed by different writers, and also “infinitesimal” renewal processes. Illustrative examples are drawn from biology and from the theories of queues, dams, and electronic counters; a table summarizing some of the papers on the last subject is given.
Experiments with Mixtures
Authors: Scheffé Henry
Published: December 2018

A theory is developed for experiments with mixtures of q components whose purpose is the empirical prediction of the response to any mixture of the components, when the response depends only on the proportion of the components and not on the total amount.
The Information in an Experiment
Authors: Mallows C. L.
Published: December 2018

A measure is derived of the information obtained in an experiment; it is shown to have close connections with previous measures. It leads to a comparison of experiments which is intermediate between those of Blackwell and Lindley.
The Dispersion of a Number of Species
Authors: Barton D. E. , David F. N.
Published: December 2018

The problem of dispersal of one-coloured balls in boxes is generalized for the case of a number of colours. An approximation is obtained for the distribution of the number of colours per box.
The Logistic Process: Tables of the Stochastic Epidemic Curve and Applications
Authors: Mansfield Edwin , Hensley Carlton
Published: December 2018

The logistic process is a simple stochastic process often used to represent the spread of an epidemic. Some recent studies (Bailey, 1950; Haskey, 1954) provided information regarding the stochastic epidemic curve for this process. In this paper, we present much more extensive tables of this epidemic curve, and we note some potential uses for the logistic process in the behavioural sciences.
Consistency in Statistical Inference and Decision
Authors: Smith Cedric A. B.
Published: December 2018

It is suggested that the strength of a person’s beliefs may be tested by finding at what odds he is prepared to bet on them. This leads to a system of numerical “medial personal probabilities” obeying the classical laws of probability. However, these do not have precisely defined values, but are contained within specified intervals. The appropriate method of inference is Bayes’s Theorem. This leads to generally accepted statistical procedures in large samples, except that the “weight of evidence” and not significance level is the measure of conviction in a significance test. Under very general conditions decisions are made by maximizing expected utility.
The Solution of Queueing and Inventory Models by Semi-Markov Processes
Authors: Fabens Augustus J.
Published: December 2018

In this paper we set forth an approach to queueing and inventory problems which is based on the theory of semi-Markov processes. The method is applicable to a wide variety of models in continuous or discrete time. After developing two basic theorems, we illustrate the method by determining the limiting distribution of a “batch service” queue, in which K customers are always served at a time. The batch service queue is also shown to be equivalent to a classical single-server queue with gamma interarrival distribution and general service distribution, and to an inventory model of the popular “s, S” type. Waiting-time distributions and expected lengths of busy periods are shown for the queues, and the application of the method to finite queues is indicated.
The Asymptotic Efficiency of Daniels’s Generalized Correlation Coefficients
Authors: Farlie D. J. G.
Published: December 2018

The asymptotic efficiency of the generalized correlation coefficient devised by Daniels, used as a test of association in the bivariate function

H(x, y) = F(x) G(y) {1 + αA(x) B(y)},

is shown to depend in a simple way on the score-matrices used to define the coefficient. Two coefficients for which the corresponding row sums of the two score-matrices, written in a standard form, are proportional are shown to have the same asymptotic efficiency. In particular, this is shown to be true for Spearman’s rank correlation coefficient and Kendall’s alternative coefficient, τ. For alternatives of the above type, maximum efficiency can be obtained within Daniels’s family of coefficients; for a more general class of alternatives a weighted combination of Daniels’s coefficients is necessary to attain maximum asymptotic efficiency.
A Bulk-Service Queueing Problem with Variable Capacity
Authors: Jaiswal N. K.
Published: December 2018

The bulk-service queueing problem solved by Bailey (1954) has been extended to the case in which the maximum number of units to be taken for service is not constant, but depends upon the number of units already present with the server as well as upon the capacity. This extension has been made to study queues at lifts, bus stops, etc. The problem is first solved by applying the phase method used by Jaiswal (1960a) to solve Bailey’s problem, and then by the imbedded Markov chain technique. A comparison of the two methods has been made at the end.
The Average Run Length of the Cumulative Sum Chart When a V-Mask is Used
Authors: Kemp K. W.
Published: December 2018

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

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.
Some Simple Wear-Dependent Renewal Processes
Authors: Mercer A.
Published: December 2018

The probability that a component fails is assumed to be linearly dependent on a physical wear variable, which can be measured, as well as on the age of the component. A wearing mechanism is represented by the extended Poisson process. The alternative strategies of replacement after a given time or when the wear reaches a scheduled level are compared.
Subsidiary Sequences for Solving Leser’s Least-Squares Graduation Equations
Authors: Joseph A. W.
Published: December 2018

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

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

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

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

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.
Note on a Paper by Ray and Pitman
Authors: Gurland John
Published: December 2018

Ray and Pitman recently gave some results on the distribution of two statistics introduced by Welch in connection with the two-sample problem with unequal variances. In the present note a theorem is given subsuming Ray and Pitman's work.
Control Charts and the Minimization of Costs
Authors: Bather J. A.
Published: December 2018

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

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

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

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

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

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

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.
On Local Unbiased Estimation
Authors: Fraser D. A. S.
Published: December 2018

A concept of local unbiasedness is derived from an investigation by Fisher (1956, p. 145) of consistency for a neighbourhood of a parameter point θ0. Connections are made with Cramér-Rao type inequalities and conditions obtained under which the local estimates propagate to provide globally-unbiased estimates.
Comments on a Posterior Distribution of Geisser and Cornfield
Authors: Stone M.
Published: December 2018

No asymptotic justification based on convergence in probability can be found for the Fisher-Cornish density as a posterior density for the mean of a multivariate normal distribution in contrast to the univariate case.
Stationary Amplitude Fluctuations in a Random Series
Authors: Herbst Laurence J.
Published: December 2018

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<∞), 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

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.
On Comparisons between Confidence Point Procedures in the Case of a Single Parameter
Authors: Welch B. L.
Published: December 2018

In a recent paper (Welch and Peers, 1963) formulae were obtained for confidence points depending on the distributional properties of certain integrals of weighted likelihoods. Some comparisons are made here with the corresponding formulae derived by other methods.
Moment Crossings as Related to Density Crossings
Authors: Marsaglia G. , Marshall A. W. , Proschan F.
Published: December 2018

In this paper we show how the number of moment crossings of two symmetrical densities is related to the number of crossings of the densities. This generalizes a result of Fisher recently proved by Finucan (1964).
Derivation of a Class of Frequency Distributions Via Bayes's Theorem
Authors: Särndal Carl-Erik
Published: December 2018

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

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.
On a Fiducial Example of C. Stein
Authors: Pinkham R. S.
Published: December 2018

The fiducial example supplied by Stein (1959) is reviewed and criticized.
Asymptotic Sequential Design of Experiments with Two Random Variables
Authors: Abramson Lee R.
Published: December 2018

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

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.
Corrections and Comments on the Paper “A Branching Process Allowing Immigration”
Authors: Heathcote C. R.
Published: December 2018

A discrete time branching process is considered in which migration into the system is permitted. The present note corrects an error in a previous paper (Heathcote, 1965), and discusses an application of the model in genetics.
On Streams of Events and Mixtures of Streams
Authors: Leadbetter M. R.
Published: December 2018

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.