bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Simple Stochastic Processes
Authors: Ramakrishnan Alladi 
Published: December 2018

Summary
Recently Janossy in his treatment of the stochastic problem of cosmic radiation employed “the method of regeneration points”—a method used earlier by Bellman and Harris and by C. Palm. In this paper, we consider some simple stochastic processes using this method. The simplified statistical problem of cosmic radiation is discussed in detail.
Estimation Methods for Evolutive Processes
Authors: Moran P. A. P. 
Published: December 2018

Summary
The logic of estimating the parameters in evolutive processes is considered with reference to a simple Poisson process and to the process resulting from using a counter with a non-zero resolving time. A complete solution of the problem of estimating the parameter in a simple birth process is followed by a partial solution of the problem of estimating the two parameters in the simplest birth and death process. The same method is applied to logistic processes without, however, obtaining exact distributions.
The Expression of the Complementary Outputs of Two Products in Terms of a Common Unit of Production Effort
Authors: Jowett G. H. 
Published: December 2018

Summary
Sometimes the output of an industrial process includes more than one kind of product, and the unit in terms of which this output is measured differs from one product to another. It is shown how an index of output may sometimes be constructed with the aid of an analysis, based on maximum likelihood methods, of the joint variation of the output of the products, and without prior information about the relationship between the different units. Discussion is confined to the case of two products and steady output. The solution is discussed in relation to the general problem of fitting a linear functional relationship for two variates.
Quantal Responses to Mixtures of Poisons
Authors: Plackett R. L. , Hewlett P. S. 
Published: December 2018

Summary
Various models for the joint action of poisons are examined. An attempt is made to clarify the differences between similar and dissimilar physiological actions; in similar action, the poisons act at a common site, whereas in dissimilar action each acts at a different site. In order to allow for the influence of one poison upon the action of another, the concept of interaction is defined on a physiological basis. Relations between mortality and dose are constructed for each model, and methods of estimation and tests of significance are put forward. These are illustrated by data from insecticidal experiments. The set of models considered is by no means exhaustive, and it may sometimes be found that others are required to give a satisfactory description of comparable data.
Application of the Theory of Stochastic Processes to the Study of Irreproducible Chemical Reactions and Nucleation Processes
Authors: Singer K. 
Published: December 2018

Summary
The irreproducibility of some chemical reactions is due either to (A) the inherent mechanism of the process or (B) extraneous factors (e.g., impurities). The purpose of this paper is to show that mathematical techniques developed in recent years permit the quantitative calculation of statistical properties of reactions of the type (A). An exposition of some general methods is given; their application to some typical chain mechanisms shows that conditions for the experimental observation of inherent fluctuations can occur. The distinction between the two types of irreproducibility is briefly discussed.
An Approximate Treatment of the Properties of the Correlogram and Periodogram
Authors: Sargan J. D. 
Published: December 2018

Summary
M. G. Kendall (1946) has shown that the correlogram is unsatisfactory in that it has a characteristic undamped oscillation even when the generating auto-regressive relationship is highly damped, and that the periodogram is misleading in indicating spurious cyclical periods when applied to series generated by a known auto-regression relationship. This paper gives an approximate treatment of the problem designed to explain these features of the correlogram and periodogram.
It is shown that the correlogram of an auto-regressive series can be regarded as though it were derived from an auto-regression equation of double the order of the equation generating the original series. Some properties of the periodograms of time series generated by linear stochastic equations are investigated, and the results are applied to the study of Beveridge’s wheat price index.
The Power of Wilcoxon’s 2-Sample Test
Authors: Sundrum R. M. 
Published: December 2018

Summary
Pitman’s formula for the variance of a distribution-free test of two samples, due to Wilcoxon, is evaluated for some special cases. The upper bound of this variance is derived, and a population is constructed in which this upper bound is attained. The value of the variance is then used to find the power of the test against normal and rectangular alternatives for large samples and to compare this test with certain distributional tests.
Confidence Intervals for Parameters in Markov Autoregressive Schemes
Authors: David S. T. 
Published: December 2018

Summary
An investigation is made of two suggested methods by which confidence intervals might be indirectly obtained for the autocorrelation in a stationary first-order Markov series. The suggestions were to use in the one case the distribution of the mean of the disturbance terms, and in the other case the distribution of their serial correlation. It is shown that both methods give meaningful results if the observations do not diverge too greatly from the characteristics of a Markov series.
Permutation Theory in the Derivation of Robust Criteria and the Study of Departures from Assumption
Authors: Box G. E. P. , Andersen S. L. 
Published: December 2018

SYNOPSIS
In the practical circumstances in which statistical procedures are applied, little is usually known of the validity of assumptions such as the normality of the error distribution. Procedures are required which are “robust” (insensitive to changes in extraneous factors not under test) as well as powerful (sensitive to specific factors under test). Permutation theory, which provides one method for deriving robust criteria, is discussed and applied to the problem of comparing variances.
Pivotal Quantities for Wishart’s and Related Distributions, and a Paradox in Fiducial Theory
Authors: Mauldon J. G. 
Published: December 2018

Summary
An infinity of sets of pivotal quantities (with a remarkably simple distribution) is found for Wishart’s distribution, leading to an infinity of different “fiducial distributions” for the parameters, all derived from the same data. §7 is entirely independent of the rest of the paper, and provides the simplest case of the paradox discussed here.
Pivotal quantities for the distribution of the second-order moments of a sample from a multivariate normal population are also found in the cases when the second-order moments are taken about the population mean and/or the sample is too small for the usual theory to apply.
A Unified Theory of Sampling from Finite Populations
Authors: Godambe V. P. 
Published: December 2018

Summary
The most general type of linear estimate is defined for a general sampling design. It is demonstrated that an unbiased linear estimate with least variance does not exist uniquely for the entire class of linear estimates. A slightly modified criterion for best estimate, with reference to certain given prior information is proposed. Some sampling designs have been analysed accordingly.
The Asymptotic Powers of Certain Tests Based on Multiple Correlations
Authors: Hannan E. J. 
Published: December 2018

Summary
Pitman (1948) has proposed a criterion of the relative power of two tests of an hypothesis specified by a single parameter, based on the estimating efficiencies of the two test statistics, in case these test statistics are asymptotically normal. This criterion can be immediately generalized to many cases where the two statistics have limiting distributions of the same analytical form and, in particular, enables two tests based on statistics which are asymptotically distributed as chi-square to be compared, provided the numbers of degrees of freedom are the same. This was already recognized by Andrews (1954) who showed that the efficiencies of certain rank tests for analysis of variance could be compared in this way. Bradley (1955) also used the concept of asymptotic relative efficiency in relation to rank tests based on statistics which are asymptotically distributed as chi-square. The first section of this paper is therefore merely a slight generalization of Andrew’s and Bradley’s work.
The asymptotic powers of multiple correlations may then be compared since these statistics are asymptotically equivalent to statistics distributed as chi-square. In some cases which have arisen the two multiple correlations to be compared have not been based on the same numbers of regressors. In such cases the comparison requires the use of tables of non central chi-square and Pitman’s criterion is no longer directly applicable. However the distances, on which the asymptotic powers of the tests depend, can be simply expressed in terms of the covariance matrix of the regressors on the null hypothesis and in some instances clear-cut results may still be simply derived.
The applications in this paper relate to previous work by the author (Hannan (1955a), (1955b), (1956)).
Note on an Article by Sir Ronald Fisher
Authors: Neyman Jerzy 
Published: December 2018

Summary
(1) Fisher’s allegation that, contrary to some passages in the introduction and on the cover of the book by Wald, this book does not really deal with experimental design is unfounded. In actual fact, the book is permeated with problems of experimentation. (2) Without consideration of hypotheses alternative to the one under test and without the study of probabilities of errors of the two kinds, no purely probabilistic theory of tests is possible. (3) The conceptual fallacy of the notion of fiducial distribution rests upon the lack of recognition that valid probability statements about random variables usually cease to be valid if the random variables are replaced by their particular values. The notorious multitude of “paradoxes” of fiducial theory is a consequence of this oversight. (4) The idea of a “cost function for faulty judgments” appears to be due to Laplace, followed by Gauss.
Comment on Sir Ronald Fisher’s Paper: “On a Test of Significance in Pearson’s Biometrika Tables (No. 11)”
Authors: Bartlett M. S. 
Published: December 2018

Summary
It is pointed out that the conditional distribution claimed by Fisher to throw doubt on Welch’s solution of the Behrens-Fisher problem was already given in my 1936 paper, but has no relevance to the validity of Welch’s result.
Confirming Statistical Hypotheses
Authors: Bulmer M. G. 
Published: December 2018

Summary
This paper distinguishes between the acceptability and the confirmation of a statistical hypothesis. A hypothesis is called acceptable if it is accepted by a significance test or some similar procedure and unacceptable if it is rejected. The likelihood ratio criterion of acceptability is discussed. In order to define confirmation, a distance function is introduced in the hypothesis space which reflects the size of the departure of any hypothesis from the null hypothesis. All admissible hypotheses are tested and classified as acceptable or unacceptable. If none of the acceptable hypotheses are “near” the null hypothesis, the latter is disconfirmed; if all the acceptable hypotheses are “near” the null hypothesis, it is confirmed; otherwise the experiment is inconclusive and the null hypothesis is unconfirmed. In the second part of the paper these ideas are applied to some common statistical techniques.
Sequential Confidence Intervals for the Mean of a Normal Population with Unknown Variance
Authors: Ray W. D. 
Published: December 2018

Summary
A modified sequential procedure is put forward for the problem of estimating the mean of a normal population by a confidence interval of prescribed width and confidence coefficient, when the population variance is unknown. Certain problems akin to the latter are discussed and wherever possible comparison is made with some results of Anscombe based on his asymptotic theory.
The Efficiency of N Machines Uni-Directionally Patrolled by One Operative When Walking Time and Repair Times are Constants
Authors: Mack C. , Murphy T. , Webb N. L. 
Published: December 2018

Summary
The solution is given to the problem of determining the efficiency of N machines looked after by an operative who walks round them in one direction, always taking the same time to walk to a given machine from the previous one and to inspect it and service it (we call this overall time the “walking time”), and then, if the machine has stopped, taking a fixed time to repair it.
The Efficiency of N Machines Uni-Directionally Patrolled by One Operative When Walking Time is Constant and Repair Times are Variable
Authors: Mack C. 
Published: December 2018

Summary
The solution is given to the problem of determining the efficiency of N machines looked after by an operative who walks round them in one direction taking a constant time to walk from one machine to the next, inspect and service it (this overall time we call the walking time), and then, if the machine has stopped, repairing it, when the repair times have a probability distribution of a very general nature.
A Minimax Procedure for Choosing between Two Populations Using Sequential Sampling
Authors: Maurice Rita J. 
Published: December 2018

Summary
When a choice has to be made in favour of one of two populations the cost of sampling (experimenting) in order to obtain information on which to base the decision must be balanced against the cost of making the wrong choice. Wald’s (1950) minimax procedure is used to determine a sequential method of sampling when a decision is to be made between two normal populations on the basis of their sample means. It is assumed that the cost of making a wrong choice is given by the difference of the population means multiplied by a factor representing the use made of the chosen population. The population variances are taken as known and equal. It is found that this determines a sequential procedure defined by the ratio of the difference it is desired to detect to a function of the probability with which it is desired to detect that difference, therefore corresponding to a range of tests in which these constants are fixed for the statistician by the user of the results. The performance of this procedure is compared with that for a fixed sample size and found to result in smaller losses over all values of the difference between the populations. A comparison is also made with the double sample procedure of Grundy et al. (1956) on which it is also generally an improvement.
The Lindisfarne Scribes' Problem
Authors: Silvey S. D. 
Published: December 2018

SUMMARY
The Lindisfarne scribes' problem is one of estimating, from observations on an ordered set of random variables, the number of changes which occur in the distribution functions of these random variables as they are considered in order. This is a multiple decision situation and it is suggested that, in the absence of a loss function, the principle of controlling the probability of over-estimating the number of changes, which is a natural extension of the principle underlying many currently applied tests of significance, might be used. An estimation procedure, based on this principle, is suggested for the Lindisfarne scribes' problem, and some of its implications are discussed.
Dilution Series: A Statistical Test of Technique
Authors: Stevens W. L. 
Published: December 2018

SUMMARY
When only the presence or absence of a micro-organism can be ascertained, density can be determined by preparing a dilution series in geometrical progression, setting aside the same number of plates at each level and observing fertile and sterile plates. Sometimes, series of observations appear which suggest that some failure in technique has occurred. An example, in a ten-fold dilution series, with five plates at each level, is given by the following number of fertile plates:
… 5 5 4 1 5 5 5 4 2 0 0 …
To provide an objective criterion to measure the significance for a possible deficiency of technique, the writer proposes the range, defined as the number number of levels, counted inclusively, from the first where not all plates are fertile to the last where not all are sterile (in the above example, 7). The distribution of the range is found, and tables provided for making a test of significance.
Equally Correlated Variates and the Multinormal Integral
Authors: Stuart Alan 
Published: December 2018

Summary
An n-dimensional distribution with all correlations equal to p, called an equally correlated distribution, can very simply be constructed from a set of n + 1 one-dimensional variates; these variates are uncorrelated if p is non-negative, and n of them are uncorrelated if p is negative. From this, a general relation is deduced between any problem concerning an equally correlated distribution and an equivalent problem for uncorrelated variates. Applications are (i) to a t test due to Walsh (1947) and Halperin (1951); (ii) to Moran’s (1956) result for the probability that all the variates of an equally positively correlated normal distribution are positive and to a generalization of this; (iii) to the approximation of sampling distributions under randomization to the results of standard normal theory.
On Some Problems of Machine Interference
Authors: Nasr Saad K. 
Published: December 2018

SUMMARY
The problem of interference arises when a team of operatives is attending a set of machines, these being assumed to have a certain servicing factor. In this paper an estimator of the servicing factor and a simple expression for the machine efficiency are introduced. A loss function is also given, with a method for the determination of an appropriate number of operatives to be applied for the attendance of the machines.
The Efficiency of Automatic Winding Machines with Constant Patrolling Time
Authors: Howie A. J. , Shenton L. R. 
Published: December 2018

Summary
The problem is that of maximizing the average efficiency of a machine which (i) stops when its total running time has reached a fixed value a, (ii) has accidental stops, and (iii) is patrolled for servicing (i.e. re-starting if necessary) at a fixed interval p which may be less than a, efficiency being defined as the ratio of the running time to the total time under consideration. The probability distribution of the number of patrols required to exhaust the total running time of the machine is derived in the case where the accidental stops have uniform probability, and is found to be expressible in terms of Laguerre polynomials. The properties of the distribution are illustrated by an example. its asymptotic normality as a increases is established. The properties of the average efficiency are discussed.
Confidence Regions in Non-Linear Estimation
Authors: Beale E. M. L. 
Published: December 2018

Summary
The statistical properties of the approximate confidence regions for nonlinear estimation based on the likelihood ratio criterion are considered, assuming normal variation of errors. It is suggested that these approximate confidence regions are preferable to any known exact confidence regions for this problem, provided that the model is only moderately non-linear.
A numerical measure of the non-linearity of a model (as a function of the experimental design and the parameter values) is proposed. This can be used to indicate: (a)the accuracy of these approximate confidence regions, and a simple method of modifying the regions to avoid exaggerating the significance of the experimental data in doubtful cases; and(b)the effectiveness of a non-linear transformation of parameters as a device for making the model approximately linear.
Methods of computing the non-linearity so defined, either empirically or theoretically, are indicated.
Discrete Stochastic Processes in Population Genetics
Authors: Bodmer W. F. 
Published: December 2018

SUMMARY
The application to population genetic models of the approximate treatment of a non-linear discrete stochastic process by linearizing near an equilibrium point is discussed. The value of the dominant characteristic root for approximate linear changes near an initial equilibrium can be used to estimate the chances of survival of newly occurring genotypes. These methods are illustrated on the classic population genetic model for a balanced polymorphism and also on a model for a simple incompatibility system. A method is developed for the complete stochastic treatment of a linear process. This makes it possible to fit observed changes to those expected from theoretical models when it is assumed that the changes are near an equilibrium point. It is also possible to estimate the chance of losing a gene segregating with a given selective advantage in a small population of known size and in certain cases to obtain estimates of the selective advantage when a certain proportion of fixations has been observed. A general treatment of a complex model for the evolution of homostyly in primroses using these methods is given. Numerical methods, using an electronic computer, are applied to both deterministic and stochastic study of this model.
Estimation of Parameters of a Multivariate Normal Population from Truncated and Censored Samples
Authors: Singh Naunihal 
Published: December 2018

SUMMARY
This paper is concerned with the problem of estimation of means and variances of a k-variate normal distribution from a sample doubly truncated or censored on s-variates (s ≤ k), when variates are uncorrelated. Maximum likelihood equations are derived which, with the help of normal probability tables, can readily be solved by iteration. The information matrix is given from which the asymptotic variances and covariances of the estimates can be determined. to illustrate the practical application of these results a numerical example is added.
The Wilcoxon Test and Non-Null Hypotheses
Authors: Wetherill G. B. 
Published: December 2018

SUMMARY
The two-sample Wilcoxon test provides an exact test of location when the two parent populations are identical in shape. The research recorded in this paper is an investigation into the behaviour of the test, and a comparison with the behaviour of the t-test, when the two distributions differ slightly in shape.
A Simple Method of Trend Construction
Authors: Leser C. E. V. 
Published: December 2018

SUMMARY
The principle adopted here in the construction of a trend for a time series consists in minimizing a linear combination of two sums of squares, of which one refers to the second differences of the trend values, the other to the deviations of the observations from the trend values. Properties of the general solution are deduced, and the solution is explicitly obtained for up to 7 observations.
In the special case in which the sum of the two sums of squares is minimized, the exact solution is derived for up to 15 observations. An approximation formula, suitable for practical use when there are 8 or more observations, is also given. The method is illustrated by examples, in which it is applied to an artificially constructed and to an actual time series.