bluuebunny/crossref_metadata_2025_split huggingface dataset:
Coordination of a two‐echelon supply chain in presence of market segmentation, credit payment, and quantity discount policies
Authors: Taleizadeh Ata Allah , Rabiei Naghmeh , Noori‐Daryan Mahsa 
Published: December 2018

AbstractIn today's competitive business markets, a revenue optimization method is always one of the most crucial issues ahead of commercial supply chains so that it is utilized by the managers to improve their profitability. On the other hand, enhancing coordination and collaboration between the chains’ members has taken a vital role in increasing their efficiency and profitability. Thus, managers tend to employ/design marketing and coordinating incentive mechanisms using the revenue optimization method, as the most influential tools, to motivate the purchasers to order more and subsequently increase their market share. Here, this issue is studied in a two‐echelon supply chain by designing incentive contracts in order to evaluate the profit of organizations and enterprises and assess the best contract, which causes the highest profit, as the main goal of the businesses. In this study, a pricing‐inventory model is developed for a single‐item two‐echelon supply chain consisting of a manufacturer and a retailer in the presence of three different scenarios. In the first scenario, a credit payment (delay‐in‐payment) contract is considered between the chain members. In the second scenario, we studied a market segmentation policy in which the market demand is divided into price and quality oriented customers’ demand while a quantity discount contract is assumed as the third one. The profit of supply chain under these new conditions is computed by some numerical examples and then the effects of cost parameters on the decision variables and the profit are analyzed.
Part II: An Evaluation of Factor Analysis from the Point of View of a Psychologist
Authors: Smith B. Babington 
Published: December 2018

Summary of Contents
The need for such a method—Some historical points—What goes in and what does not—Some aspects of method—Q and R techniques—Burt’s reconciliation of Q and R and their relationship to analysis of variance—Stephenson’s treatment of trait universes—The importance of factors—Conclusions.
The Productivity of Machines Requiring Attention at Random Intervals
Authors: Benson F. , Cox D. R. 
Published: December 2018

Summary
In many industrial processes an operative attends a number of machines which stop from time to time. Each time a machine stops the operative has to do a certain amount of work before it can be restarted. If at any time two or more machines are stopped simultaneously, there will be a loss of production due to the period the machines have to wait for attention. In this paper we derive methods of estimating this loss of production when the operative has no duties away from the machines and discuss modifications to the theory when the operative has other duties.
Computation and Interpretation of Multiple Regressions
Authors: Woolf Barnet 
Published: December 2018

Summary
Full practical directions are given for the expeditious calculation of regression equations, which are built up by successive insertion of additional variates. The computer can readily measure the contribution made by each new variate to the goodness of fit, omit variates which do not make a significant contribution, and select that group of independent variates which together give the lowest residual mean square in the dependent variate. The statistical properties of the regression equation, and of the successive reciprocal matrices from which it is derived, are discussed in detail, with special reference to the proper interpretation of the equation and its associated tests of significance. In dealing with experimental or observational data it is rarely necessary to work to more than four or at most five significant figures.
On Certain Probability Distributions Arising from Points on a Line
Authors: Sukhatme B. V. 
Published: December 2018

Summary
The paper discusses for m points of k different colours on a line, the distributions for the number of (i) joins between points of different colours, (ii) triplets, quadruplets and s-plets, and (iii) runs of length r and total number of runs of lengths r1 and r2 of a specified colour. The expressions for the first four cumulants for all these distributions are given and found to be linear in m. It is shown that the distributions tend to the normal form when m tends to infinity, except when the probability of the points taking a specified colour is very small. In the latter case the distributions tend to the Poisson form.
Some New Designs of Latin Square Type
Authors: Pearce S. C. 
Published: December 2018

Summary
A study is made of certain designs of Latin square type, namely, Latin squares with (a) a column added, (b) a row and a column added, and (c) a column added and a row omitted.
Recommendations are given for the analysis of data by a method leading to an unbiased test. It is shown that sufficient randomization is obtained by writing down a possible configuration of plots and permuting rows and columns at random.
Some Recent Work on Systematic Experimental Designs
Authors: Cox D. R. 
Published: December 2018

Summary
An experimental design in which there is no randomization by the experimenter, except possibly in naming the treatments, is called systematic. Recent work is reviewed on systematic designs for use when the residual variation is (i) autocor-related and (ii) formed from a trend plus a random error. An example is given of the application of the second type of design in wool textile research.
Second Order Autoregressive Schemes with Time-Trending Coefficients
Authors: Hartley H. O. 
Published: December 2018

Summary
It has been suggested that the departure of certain time series from a fitted second order autoregressive scheme is due to time-trending coefficients in the generating differential equation. If coefficients with linear time-trends are introduced into the scheme the correlogram of the resulting non-stationary series can, in special cases, be evaluated exactly in terms of Airy integrals and is found to be approximately of the form sin s/s where s is proportional to the lag.
The Analysis of Multiple Stationary Time Series
Authors: Whittle P. 
Published: December 2018

Summary
After some preparatory work, the least square estimation equations are derived for a purely nondeterministic stationary multiple process (Th. 6). The asymptotic covariances of the parameter estimates are calculated for a normal process (Th. 9) and a test of fit derived (Th. 10). The testing of a sunspot model provides an illustration of the methods developed.
The Errors of Lattice Sampling
Authors: Patterson H. D. 
Published: December 2018

Summary
Lattice samples are samples selected from a multiple classification of units with one unit in each subclass in such a way that they include equal numbers of units from each main class or from each combination of two, three or more main classes in different classifications. The present paper provides a discussion of the errors of such samples.
Methods for determining the sampling variances from the complete data, when these are available, for purposes such as a comparison of different sampling methods, are described for several methods of selection. The estimation of the sampling variances from the sample data is also considered. In general estimates of error can be obtained (a) from samples consisting of special patterns of units or (b) from random samples of several mutually exclusive sets each of which itself constitutes a lattice sample. If suitable elements of randomization are introduced method (a) is satisfactory for selecting samples of 2p units from a p × p lattice, samples of 2p2 units from a p × p × p lattice and, in general, 2pn–1 units from a pn lattice. In other cases, however, the estimated means and errors may be inaccurate. Method (b) is most useful when several lattices have to be sampled.
The case of the square lattice is considered in detail and rigorous proofs of the various formulae are given. In the section on cubic lattices a method is given whereby the required expressions can be written down immediately in terms of components of variance. This method is extended to the general case of sampling a pn lattice. Examples of rectangular lattices and multistage sampling are also briefly considered.
Limits for the Ratio of Means
Authors: Creasy Monica A. 
Published: December 2018

Summary
Limits for the ratio of the means of two normal distributions are obtained by a method which appears to be analogous to that used in finding fiducial limits for the difference of two means with possibly unequal variances (the Fisher-Behrens problem). The properties of these limits are compared with those obtained using Fieller’s solution of this problem, for the case of known variances and zero correlation. The extension to more general cases is also discussed.
Problems of Sample Allocation and Estimation in an Agricultural Survey
Authors: Church B. M. 
Published: December 2018

Summary
A sampling method which has been used in fertilizer surveys in England and Wales is described. The relative efficiencies and biases of several methods of estimating average fertilizer dressings are determined from the results of eight surveys carried out in 1950. The unbiased method of estimation is found to be 65 per cent efficient relative to the unweighted mean of the field observations; this latter method is only slightly biased. An alternative method of estimation, eliminating any gross bias which might occur in the unweighted mean, has a relative efficiency of 90 per cent.
The size and most appropriate form of sample for given accuracy are discussed and compared with those adopted in recent surveys. The advantage of revisiting the same farms when estimating trends in fertilizer practice is examined.
Least Squares Regression Analysis for Trend-Reduced Time Series
Authors: Jowett G. H. 
Published: December 2018

Summary
The difficulties of obtaining a valid estimate of the standard error of a regression coefficient between two time series are discussed. It is shown how a preliminary trend-reducing operation on the series, using a moving average, makes it possible to obtain such a valid estimate. A method of analysis is described, along with considerations which affect the best choice of moving average for the purpose, which is applicable when the local variational properties of the series resemble those of Markoff series.
Some Applications of Zero-One Processes
Authors: Lomnicki Z. A. , Zaremba S. K. 
Published: December 2018

Summary
Zero-one processes are defined as discrete-parameter stochastic processes in which the random variables take the values 0 and 1 only. Various processes of this kind can be derived from any discrete-parameter stochastic process; they include, in particular, the upcross and peak processes. Apart from the intrinsic interest of some of them, the study of these processes yields reasonably accurate methods of estimating the parameters of a Gaussian primary process by means of mere counting. The consistency proofs are based on an elementary lemma concerning the normal probability integral over the positive orthant of the four-dimensional Euclidean space. Applications to autoregressive schemes are discussed.
On a Test of Significance in Pearson’s Biometrika Tables (No. 11)
Authors: Fisher Ronald 
Published: December 2018

Summary
The publication by Pearson and Hartley of numerical values for the proposed solution of Behrens' problem developed by Welch, affords an opportunity of clarifying in concrete terms, ideas which have in the past been disputed in perhaps a too abstract an atmosphere. Behrens' problem was to find a test of significance suitable for testing the hypothesis that two normal populations with unknown variances had a common mean. The fact that an unknown variance-ratio entered into the test was a comparatively novel feature, and has led to the problem being described as a test-case for examining different views of the process of testing hypotheses.
An Elementary Method of Solution of the Queueing Problem with a Single Server and Constant Parameters
Authors: Champernowne D. G. 
Published: December 2018

Summary
The queueing problem, in which the input and service time have independent negative exponential distributions with constant parameters, is studied for the single server case. The “simple” problem with constant parameters, dealt with first by W. Ledermann and G. E. H. Reuter (1954), and by A. B. Clarke (1953) was considered by these writers in relation to far more general problems, and their solutions are accordingly less simple than is possible in the special case: This special case has recently been investigated by Bailey (1954) by means of a generating function technique. In view of its importance I propose to obtain the result directly: it will be found in terms of Bessel Functions in the form obtained by Dr. A. B. Clarke. He has pointed out there that this solution is easily adapted to the case where the ratio of the exponential parameters for the two waiting times is constant but where each parameter is not necessarily constant.
Note on Some Criticisms Made by Sir Ronald Fisher
Authors: Welch B. L. 
Published: December 2018

Summary
In a recent note Sir Ronald Fisher (1956) has commented upon some tables which were calculated under my direction and first published in Biometrika about seven years ago (Aspin, 1949). Fisher is concerned with what he supposes to be errors in the values given. The object of the present reply is to explain once more what the tables aim to do, and to maintain that there is no justification in Fisher’s criticism.
The Spectral Analysis of Time-Series
Authors: Jenkins G. M. , Priestley M. B. 
Published: December 2018

Summary
(i) A review has been made of spectral analysis and its relation with other branches of time-series analysis. A detailed account has been given of the methods available for estimating the spectral density, the band spectrum and the integrated spectrum; suggestions have also been made for confidence intervals for the latter two estimators. (ii) Emphasis has been laid throughout upon the difficulties which are met in practice and gaps in the theoretical structure have been indicated. In applications to physical problems, it is suggested that an empirical statistical approach is not enough by itself and that more realistic descriptions of each particular phenomenon should be attempted. (iii) Reference has already been made in Section 9 to a sampling investigation in which it is proposed to apply the techniques mentioned in this paper to a large number of artificially constructed series of the type given by (1).
On Estimating the Spectral Density Function of a Stochastic Process
Authors: Lomnicki Z. A. , Zaremba S. K. 
Published: December 2018

Summary
On the basis of an expected-mean-square-error criterion, the authors discuss the various hitherto proposed estimators of the spectral density function of a discrete-parameter process; they also introduce a new estimator. Any of these estimators depends on some parameter, and indications are given as to how this parameter should match those of the process in order to optimize the estimator. The alleged conflict between resolvability and statistical reliability is discussed. By way of illustration, the case of a first-order Markov process is treated in detail. Numerical applications are also given.
On the Use of the Normal Approximation in the Treatment of Stochastic Processes
Authors: Whittle P. 
Published: December 2018

Summary
A method of treating nonlinear Markov processes is discussed, based on the assumption that the variates are normally distributed. The method is applied to models of logistic population growth, plant competition, and animal predation. In the preparatory section (§2) an alternative form (9) of the Bartlett relation is deduced, which is relatively convenient if one wishes to derive equations for the cumulants of a Markov process; the relation is particularly useful in the case of normal processes. In order that one may treat the joint distribution of the variate values at several instants of time, the Bartlett relation is generalized to provide equations (40) and (41) for the characteristic functional of the process. The validity of the “normalization technique” is discussed in the final section, and a comparison made with other methods.
The Fitting of Markoff Serial Variation Curves
Authors: Davies Hilda M. , Jowett G. H. 
Published: December 2018

SUMMARY
The generalized least squares method is used to establish a practical method of fitting the function θ(1 — ρ |τ|) to the first few serial variation statistics of a time series for use as an approximation to the beginning of a serial variation function of more general type. A large-sample goodness of fit test is given, and also a method of testing the goodness of fit of a common or specified function, or functions with a common or specified value of ρ, to several series.
Bandwidth and Variance in Estimation of the Spectrum
Authors: Grenander Ulf 
Published: December 2018

SUMMARY
This paper deals with the uncertainty principle that governs the behaviour of bandwidth and variance in the estimation of the spectrum of a stationary stochastic process. Lomnicki and Zaremba (1957) have tried to show that this principle is not valid. It will be shown below that their reasoning is not correct. Further it will be shown, that not only is the uncertainty principle correct as it was originally stated, but that it can be extended in various directions. Guided by the uncertainty principle we discuss the basic questions in construction of estimates of the spectral density.
On a Multivariate Version of Fieller’s Theorem
Authors: Bennett B. M. 
Published: December 2018

SUMMARY
The use of Fieller’s theorem for determining confidence limits for a ratio α of bivariate normal means is a standard procedure in biological assay problems (Fieller, 1940, 1944; Finney, 1952, Chapter 2). Occasionally situations arise wherein several successive samples of correlated measurements are involved, and then particular interest attaches to the corresponding problem of confidence limits for the common ratio of multivariate means based on successive samples. For example, in clinical trials on experimental subjects concerning the effectiveness of a certain therapeutic substance as compared with a control or placebo, correlated clinical measurements may be obtained at a number of participating research laboratories. An approximate method is also discussed by Clarke (1956) for an example in microbiological assay.
Contagious Occupancy
Authors: Barton D. E. , David F. N. 
Published: December 2018

SUMMARY
In the Occupancy theory of distribution of elements into a set of “boxes” (alias intervals, cells, groups, categories, subsets, compartments, etc.) the random distribution (a) is contrasted with distributions reflecting (b) heterogeneity, (c) limitation on the number of elements which may be contained in a box, or (d) a mixture of these. The following models are proposed, n balls being assumed dropped into N boxes. The distribution of the number of boxes containing no balls is obtained assuming the individual distribution in a single box is (a) Poisson, (b) Negative Binomial, (c) Positive Binomial, (d) Positive Binomial with varying probability. The large sample powers of the Index of Dispersion and the Zeros Test are compared in regard of these alternatives and the question of optimum cell size is dealt with.
The Limiting Frequencies of Integers with a Given Partitional Characteristic
Authors: Bodmer W. F. 
Published: December 2018

SUMMARY
The integers can be classified according to partitions characterizing their prime decompositions. Formulae are obtained for the limiting frequencies of integers of a given type, and a table of the frequencies greater than 0·001 per cent. is given. The calculation is made possible by developing certain symmetric function product sums, which reveal a proof of the validity of the rule given by Sukhatme for evaluating the bipartitional function Gs(P, Q). It is possible, using the results given, to investigate the association between integers with different partitional characteristics, and also to give values for the quantity dk considered by Renyi. The classification of 330 integers according to their partitional characteristics is discussed.
A Renewal Problem with Bulk Ordering of Components
Authors: Cox D. R. 
Published: December 2018

SUMMARY
Suppose that k components are in use simultaneously, that batches of n items are ordered, and that all items in use at one time must be from the same batch. After n — k + 1 failures have occurred the remaining k — 1 items are wasted. Properties of the system are investigated and different strategies of use compared.
A Different Loss Function for the Choice between Two Populations
Authors: Maurice Rita 
Published: December 2018

SUMMARY
In previous discussions of the problem of balancing sampling costs against the cost of choosing the wrong population it has been assumed that the cost of sampling is equal to the sample size multiplied by a constant known unit cost. In the present paper the cost of sampling is assumed to be the cost of an incorrect choice for half of the sample programme (which is divided evenly between the two populations). The resulting loss function is considered when the choice is between two normal populations of known equal variance, the standard of performance being determined by the mean. Wald's (1950) minimax principle is used to determine fixed size and sequential sampling procedures, and the performance of these procedures is examined.
Optimum Experimental Designs
Authors: Kiefer J. 
Published: December 2018

Summary
After some introductory remarks, we discuss certain basic considerations such as the nonoptimality of the classical symmetric (balanced) designs for hypothesis testing, the optimality of designs invariant under an appropriate group of transformations, etc. In section 3 we discuss complete classes of designs, while in section 4 we consider methods for verifying that designs satisfy certain specific optimality criteria, or for computing designs which satisfy such criteria. Some of the results are new, while part of the paper reviews pertinent results of the author and others.
Necessary Restrictions for Distributions A Posteriori
Authors: Sprott D. A. 
Published: December 2018

SUMMARY
The combining by the method of Bayes of two samples each yielding a fiducial distribution, does not often yield a unique result. Necessary restrictions are given which it seems reasonable to impose on a posteriori distributions. If, in combining two samples having sufficient statistics following the same continuous distribution, the a posteriori distributions obtained by Bayes’s method satisfy these conditions, they are identical with the fiducial distribution based on the combined sample. The same result seems to hold for samples having sufficient statistics following two different continuous distributions. The paper is confined to single parameter distributions in which the range is independent of the parameter.
Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments
Authors: Good I. J. 
Published: December 2018

SUMMARY
The main purpose of this paper is to consider what explicata are possible for corroboration and explanatory power of a hypothesis. The work is intended to sharpen some previous work by Popper. It will be found, for example, that the only possible explicatum for explanatory power, satisfying the desiderata, is a monotonic function of amount of information (without expectations). Corroboration has a wider variety of explicata, one of them being “weight of evidence”. This, too, is essentially unique if probabilities of hypotheses are not to appear explicitly in the formula.
In the choice of an experimental design we may have difficulty in judging the relevant utilities. In such cases it may be reasonable to base the choice on a knowledge of the probability distribution of some measure of corroboration, and especially on the expectation.