bluuebunny/crossref_metadata_2025 huggingface dataset:
Lijnvereffening met behulp van orthogonale polynomia
Authors: van der Loan E. , Ignatius Ir J. G. W.
Published: April 2008

Summary  (Evaluation of a regression by means of orthogonal polynomials).

In our mathematical‐statistical literature the use of orthogonal polynomials in evaluating a regression is scarcely known.

The authors give a brief description of this method, which reduces the labour of calculation involved in economical‐ or biological‐statistical investigations. Orthogonal polynomials are so constructed, that the terms are independent from? each other, so that each coefficient of regression can be computed independently from the others. The method is illustrated by an example of price‐statistics (apples), published by M. D. Woodin in Bulletin 761, 1941 of the Cornell Univ. Agr. Exp. Station. It must be emphasized that evaluation is relevant only for values lying within the range of observation, so that extrapolation is most speculative; moreover the evaluation is only possible if the independent variables are equally spaced. In other cases interpolation is necessary.
De grondslagen der regressieanalyse, met een toepassing op een doseringsletaliteitproef
Authors: Nass C. A. G.
Published: April 2008

Summary  (The principles of the Analysis of Regression with an application to dosage mortality data).

The principles of the analysis of regression are explained to research workers. For advanced statisticians a mathematical treatment is given in the appendix (in English), which follows closely the practical procedure and differs markedly from those given by Kendall or Wilks. The suite of a previous article on dosage mortality data (Statistica 1: 257) is given by way of example.
Net probleem der waarnemingsfouten bij een massaal onderzoek *
Authors: Sittig L.
Published: April 2008

Errors of observation in a large‐scale statistical research.

In an investigation carried out on behalf of one of the large department stores in the Netherlands, 15 different body measurement were taken on a sample consisting of 5000 women, with a view to establishing, on a sound statistical basis, a sizing system for ready‐made clothes. The present paper describes the error analysis carried out as a part of this investigation.

The errors are classified into (1) clerical errors, (2) systematic errors, and (3) random errors.

Clerical errors—that is ‘slips of the pen’ in recording, re‐writing or card punching—were succesfully traced by plotting scatter diagrams of highly correlated dimensions; compare fig. 4 where the cross indicates an outlying observation probably resulting from such an error. Out of 75000 observations 264 clerical errors have been detected; of which 233 could be corrected, while 31 were discarded, with their concomitant records, since the source of error could not be determined with sufficient accuracy.

Systematic errors were traced by inter comparison of regressions in samples of 50 records of each of the 18 female students who performed the measurements. A significant difference found for one particular dimension and for one observer appeared to be due to a faulty method of observation, for which a correction could afterwards be applied.

Lastly by a series of replications the random errors were determined for each of the 15 measurements taken. The standard deviations, β1‘sβ2’s, and correlations coefficients computed from the data, have all been corrected so as to eliminate the systematic errors resulting from these random errors in the observations. The formulae needed for this purpose were separately derived. In some cases these corrections turned out to be by no means trivial; their omission would have led to serious errors in the final conclusions.
Een methode van contrôle tijdens de fabricage*
Authors: Willemze F. G.
Published: April 2008

A method of quality control during production.

This paper describes the use of control charts in general, and of the control charts for percentage defectives in particular. A discussion of the principles of the control charts and of methods to fix the sample size, the sample frequency, and the warning and stop lines is followed by practical hints concerning the use of the charts and their introduction in the factory. The necessity of computing the average percentage defective from the total number of defectives recorded in a series of successive samples is emphasized. It is also pointed out that an analysis of the frequency of the numbers of defectives found in the samples can sometimes furnish useful information regarding the trustworthyness of the inspector.
Een schattingsproef
Authors: Varangot V.
Published: April 2008

An experiment on estimation.

On ten pieces of card board a line was drawn 100 mm in length and divided by a vertical dash (the pointer) in two parts, in each case at a different point. 40 persons were asked to estimate the length of the left hand portion after they had been told that the total length was 100 mm. The problem discussed is how to decide which person is the ‘best’ estimator.

Three criteria are proposed: (I) the sum of the absolute values of the deviations; (II) a similar weighted sum, each deviation being multiplied with the inverse of its standard deviation, in order to account for the obvious differences in accuracy for different positions of the pointer; and (III) by adding for each of the ten readings of one person the proportions of the observers whose readings were worse. Applied to a set of four observers all three criteria indicate No. 20 as the ‘best’ and No. 5 as the ‘worst’. If however we judge the observers by their mutual correlation coefficients, according to a method of Spearman, No. 20 turns out to be the worst.

Hence in applying Spearman's criterion caution seems required. It is pointed out that there does not as yet exist a universally recognized and accepted method for determining the relative quality of a set of observers.
Het tweede congres van de Biometric Society
Authors: Nass C. A. G.
Published: April 2008

A survey of the transactions and discussions at the Second Congress of the Biometric Society held at Geneva from the 30th of August to the 2nd of September 1949.

Genève, 30 Augustus‐2September 1949.
De bovengrens van het gemiddeld doorgelaten uitvalpercentage bij enkelvoudige keuringsschema's met c = 0
Authors: Sittig J.
Published: April 2008

(The average outgoing quality limit for single sampling plans with c = o). The average outgoing quality limit occurs at

P
i= 1/(1 + n)

Its exact value is given by (6) and two approximations by (7) and (8), of which the more simplified formula (8) gives better results (see Table 1).
Statistiek in Suid‐Afrika
Authors: de Loor B.
Published: April 2008

Statistics in South Africa

A survey of the present status of statistics in South Africa treating successively of (I) classical administrative statistics, (2) modern statistics arid industrial applications, (3) teaching, and (4) terminology.
Die probleem van die aanpassing van polinome aan ‘n reeks ewewydige gegewens
Authors: Schumann T. E. W.
Published: April 2008

The adjustment of polynomials to a series of equidistant data.

If a quantity Ux has been observed for a set of equidistant values of x, and if we wish to adjust a polynomial

to these data by the method of least squares, the coefficients kp can be computed in the form

where the Ep(x) are functions of x and p, the values of which may be taken from a table.

Tables for this purpose for 1 ≦ N ≦ 6 and for series of observations up to 50 were computed and edited by the Weather Bureau in Pretoria. In this paper formulae for the computation of the functions Ep(x) are deduced from the analogous development in orthogonal plynomials. In a final section the method is illustrated by a particular example, namely the representation of average air pressure as a function of geographical latitude.
Over de herleiding van B tot F
Authors: IJzeren J. v.
Published: April 2008

The usual deductions of the well known relation between B‐ en T‐functions have some disadvantages. In this article a simple straightforward method is given.
Het uitzetten van waarnemingen op waarschijnlijkheids‐papier1
Authors: Benard A. , Bos‐Levenbach E. C.
Published: April 2008

The plotting of observations on probability paper

The mathematical foundation of probability paper for a variate with a cumulative distribution function F (αx+β) is explained as well as its purpose.

To plot the observations it is necessary to use an estimate cf F (xi, xi being the 1 th order statistic in the sample.

Several methods are described and compared, and a new one is developed, having the property that with a very good approximation the medians of xi are situated on a straight line.

The derivations are given separately in an appendix.
Proefopzetten in de Industrie
Authors: Hamaker H. C.
Published: April 2008

Experimental designs in industry.

It is pointed out that in industry owing to the greater speed of modem mass‐production we have a greater need for simple experimental designs than in agriculture. The paper makes a special and extensive study of the simplest of all designs: the two‐way classification.

A distinction is made between qualitative and quantitative factors; factors for which we do not, and for which we do know the levels. Three cases must then be distinguished: (1) two qualitative factors, (2) one qualitative and one quantitative factor, and (3) two quantitative factors. To these, different methods of variance analysis must be applied; in (1) the customary analysis according to rows and columns is adequate, but in (2) we can effectively use polynomial regression analysis in one direction, and in (3) we can do so in both directions. Examples of each of these types of analysis are provided.

The opinion is expressed that the analysis of variance serves to pick out from among a number of conceivable models, the simplest model that will adequately describe the observations, and further to provide an estimate of the residual fluctuations. The result of an analysis of variance is of no use for technical purposes; the model chosen expressed in the form of a numerical equation is the information to be used in the factory.
Tien jaar ontwikkeling van de industriële statistiek *
Authors: van Ettinger J.
Published: April 2008

A decade of industrial statistics

This paper deals with a review about the development of industrial statistics in the Netherlands during the last ten years.

Different factors influenced this development: a great need of statistical treatment of problems caused by the evolution of modern industry; the availability of useful statistical tools; the activity of a number of competetent industrial statisticians; the greater openness for new ideas and the better climate with reference to industrial statistics. A detailed discussion of these factors is given.
Gebruik van multi‐momentopnamen
Authors: Sparnaay K. F.
Published: April 2008

Application of the ratio‐delay method.

The ratio‐delay method affords a much quicker insight in the relation between direct‐productive and indirect‐productive times of a group of machines than the classical time study method.

Especially with cyclical and a‐cyclical work the ratio‐delay method is the most efficient and sometimes the only means to obtain a justified rate at short notice. This also holds for serial piece‐production.

Much attention will have to be paid to improving and accelerating ratio‐delay methods.
Experiment en waarneming in de economische statistiek *)
Authors: de Vries M.
Published: April 2008

In the design of experiments for scientific purposes it is assumed that the sample elements do not interfere with the experiment and do not influence the observations. In economic research, however, these assumptions are not always fulfilled.

In this field of investigation the sample elements are for the major part human beings. It might be expected that human subjects will not submit passively to any experiment.

In this paper methods of observation and experimentation are discussed in which the human influence has been largely eliminated. Some topics of sample design have been elucidated by means of an example.
Een algemene methode tot leemtevulling
Authors: Corsten L. C. A.
Published: April 2008

An exposition of the missing plot technique often applied in analysis of variance is given in very general terms.

Non‐orthogonality mostly implies heavy computations. If the scheme of observations is almost orthogonal this technique, however, supplies in a simple way unbiassed and efficient estimates of the expectation values which occur in a linear hypothesis underlying an analysis of variance. Moreover the correct residual sum of squares required for a test or a confidence interval estimation is obtained without difficulty.

A correct test of an effect or an interaction will be provided by two estimates, the first under the null‐hypothesis, the second under the alternative hypothesis. In the case of non‐orthogonality this may imply two separate applications of the discussed technique. The difference between the two residual sums of squares will be used for the numerator of a valid F‐criterion.

The technique is illustrated by an example.
Economische toepassingen van factoranalyse*
Authors: van Eijk C. J.
Published: April 2008

Economic applications of factor analysis.

The following is a brief, non‐technical exposition of the application of factor analysis to some problems of model building.
Enkele opmerkingen over de intensiteit van lokaal berichtenverkeer *
Authors: van der Putten A. , Swaagman H. C.
Published: April 2008

Some remarks on the intensity of local telephone and postal traffic.

In this paper a method is described to explain the trend of the intensity of the local telephone traffic in a certain area by means of the number of exchange lines, the telephone density (number of exchange lines per 1000 inhabitants), and the real national income per head of the population as explanatory variables. In connection with the intercorrelation between the number of exchange lines and the density, which would make the regression coefficients unreliable, the exponent of the number of exchange lines has been fixed by means of a cross section of telephone networks.

The method was applied to the Amsterdam telephone network; it appeared that the development of the local telephone intensity over a long period could be explained satisfactorily. Further, extrapolation offers the possibility to estimate future investments.

For the local postal traffic, too, it was examined whether the trend could be explained. It appeared, however, that it was not very well possible to do so because the basic data (which are nery difficult to collect in practice) were not sufficiently accurate. It was possible, however, to determine the relation, in a cross section, between the intensity of the local letter mail and the number of inhabitants per community.
Optimale betrouwbaarheid van parallelle meervoudige systemen
Authors: van Hees R. N. , Meerendonk H. W. v. d.
Published: April 2008

In this paper the reliability of parallel multi‐component systems will be considered.

The number and kind of spare components wil be determined for maximum improvement in reliability under the assumption that limited funds are available for the purpose.
Optimal allocation in J‐stage sampling with stratification from finite population
Authors: ELANDT‐JOHNSON REGINA C.
Published: April 2008

Summary  The known results of optimal allocation in two‐stage simple random sampling with stratification from finite population are generalized for J‐stages. The optimalization is treated by minimizing the cost function for given variance as well as by minimizing the variance for given cost. It turns out that for both cases the optimal values differ only for the first‐stage units and are the same for all the subsequent. The general formula for minimum variance of the unbiased estimator of the population mean per element is given.
Statistische eigenschappen van een vlambeveiliging met behulp van een gasontladingsbuis welke gevoelig is voor ultraviolet licht
Authors: ADRIAANSE R. P. , VAN DER LAAN P.
Published: April 2008

Summary  The output voltage of a detector circuit containing a gas‐filled tube sensitive to ultraviolet radiation can be used to indicate whether a flame is still burning or not. As long as the flame is burning the random nature of the discharges of the tube leads to random fluctuations in the output voltage, which can be considered as a Markov‐process with dependent increments. The problem is to select an alarm level for the output voltage with a suitable chosen probability of exceedance while the flame is burning, in order to limit the probability of false alarm. In this article a method is given for determining upper and lower bounds for the distribution function of the output voltage at any moment, answering the question of the alarm level to be chosen. Results are given for a special circuit.
Tabel en nomogram voor het aflezen van jaarlijkse groeipercentages van grafieken op semi‐logaritmisch papier
Authors: TILANUS C. B.
Published: April 2008

Summary  A table and a nomogram are given to find the growth rate of a regression line drawn on so‐called semi‐logarithmic graph paper. The growth rate is determined by: a) the slope of the regression line, b) the length ratio between the logarithmic and the metric unit, in other words, the number of years on the time axis (if a year is the time unit) corresponding in length to one cycle on the logarithmic axis (say, 1 to 10, or 100 to 1000). With an example, the use of the table and nomogram is explained.
Orde en wanorde*
Authors: Freudenthal H.
Published: April 2008

Order and disorder

Order is a quite definite notion as long as it means a special kind of order. Disorder in the sense of absence of any order is a vague notion. Statistical notions do not depend on notions like order and disorder. Instead of disorder independency is the fundamental statistical notion. Statistical independency can be obtained by creating disorder. But pseudo‐random‐material shows that it can also be obtained by suitable strictly causal methods. It is not possible to test whether a given material is produced by stochastic devices. It is dangerous to try disorder as a null hypothesis in order to refute it by showing some regularities in the underlying material. This is shown by analyzing of statistical sham proofs for the impossibility of generatio spontanea, such as tried by some biologists.
Enige punten uit de wiskunde der informatietheorie*
Authors: Stam A. J.
Published: April 2008

Some mathematical remarks on information thery

This paper is the eleboration of a lecture given by the author at the “Statistische Dag 1960”. It contains the definitions of entropy and amount of information as given by Shannon, some remarks on their interpretation, and their generalizations to abstract probability spaces. Some remarks are made on the mathematical problems arising from these definitions.

Shannon's definition is compared with the concept “instrinsic accuracy” or information used in statistics that was defined by Fisher. Some properties these different kinds of “information” have in common are mentioned.
Residuen als bron van informatie bij regressie‐analyse*
Authors: Barten A. P.
Published: April 2008

Residual terms—a source of ordered information in regression analysis

Although in regression analysis residual terms seem to represent chaos, they can be used to complement the original hypothesis in a theoretically acceptable way. This is demonstrated with an example: the construction of a wage rate equation for the Dutch economy 1923—1938 and 1949—1957. Extrapolation of the equation for the years 1958 and 1959 and its application to the United States economy 1931—1958 provide a primitive test.
On a metric in the space of random variables
Authors: Kuiper Nicolaas H.
Published: April 2008

Samenvatting

Van een metriek d(x,y) gedefinieerd op de ruimte Ω van alle stochastische variabelen worden twee interessante eigenschappen bewezen. Deze kunnen soms met vrucht onder meer worden toegepast voor de beoordeling of bij een gegeven monotone functie f, en een benadering y van x, ook f(y) een goede benaderende stochastiek is voor f(x).
Enkele opmerkingen over de opzet van onderzoekingen naar de werkzaamheid van cytostatica in de kliniek1)
Authors: Rümke Chr. L.
Published: April 2008

Some remarks on the design of clinical trials of cancer chemotherapeutic agents.

After a general introduction on the aim of clinical trials, some factors are discussed, which are of special importance in clinical trials of cancer chemotherapeutic agents. The effects of these agents on specified tumor types should be compared concurrently with those of placebos in equivalent groups of patients.
Project‐planning methoden
Authors: Reith P. F.
Published: April 2008

Project planning methods

The purport of the article is to give a general survey of methods of project planning such as Pert, Critical path method, etc. In the first place a definition is given of what is understood by project in this respect.

The possibility to represent such a project by a network of certain characteristics is specified more closely and it is examined what restrictions this imposes in practice.

With regard to the planning of such projects three possibilities, dependent on the available data for and the objectives of the planning, are to be distinguished, i.e.:

The activity durations are supposed to be fixed and given numbers and the planning aims at minimal total project duration.

The activity durations are supposed to be stochastic variables having given distributions and the planning aims at a total project duration which is to be realised with satisfactory probability.

The activity durations are supposed to be variables that can move within certain given limits and a cost function for each of these variables is given; this time the planning aims at activity durations which are such that the total project cost is minimal.

For each of these three possibilities we discussed solution methods. Some flow‐diagrams are added as a demonstration of the fact that the numerical procedures are greatly apt to be executed with the help of an electronic computer.
Twintig jaren Studiekring voor Statistische Techniek*
Authors: Kuiper N. H.
Published: April 2008

A survey is given of the history {twenty years) of the study group for statistical techniques of the Landbouwkundig Genootschap, and in connection herewith the history of the relevant parts of statistics and of the teaching of statistics in particular at the Agricultural University of Wageningen is touched upon.
Besliskunde, een vlag die de lading dekt?*
Authors: Monhemius W.
Published: April 2008

Does operations research teach, how to make decisions?

Some confusion seems to exist with regard to the subject of taking decisions. Decision making is not restricted to the field of management decisions; in every field of life we take decisions and branches of applied science exist to help us.

Operations research is primarily research of operations, which means that it is both more and less than “the knowledge of decision making”. It is less, because only decisions about operations are concerned and because the decision itself is taken by a manager. This manager uses partly as a basis: conclusions drawn by staff people or consultants.

It is more, because the element of research is not sufficiently stressed by the expression “knowledge of decision making”. Research in the field of methods of linear programming for example is called mathematical research; it is needed by Operations Researchers but also by other scientists and engineers.

As far as decision theory is concerned, the point of view of Arrow (1957) is underlined.

As a sideline it is pointed out, that a decision theory cannot be developed without help of psychologists and that leadership is much more than just taking decisions.
Gegist bestek*
Authors: Bakker A.
Published: April 2008

A method is given to determine the consistency of an inspector, who is judging a number of non‐measurable properties of a product.

This method can also be used to compare the results of a judgment by several inspectors.
Het maken van een schaal voor niet meetbare kenmerken*
Authors: van den Toorn J. W.
Published: April 2008

When no scale is available, it is hardly possible to come to a well‐founded judgment on the basis of evaluations of immeasurable characteristics.

A description is given of an investigation from the results of which a scale (of photographs) is prepared of the immeasurable characteristics by means of the method of paired comparisons.
Produktiebesturing: beslissen zonder gissen?*
Authors: van Hees R. N.
Published: April 2008

The problem of controlling productionlevels, productionseries and stocks can be solved in different ways.

In many cases, however, it is necessary to realise that both production and deliveries are stochastic variables.

Therefore it is impossible to make exact forecasts of the number of products that will be produced per unit of time and the quantities demanded by the customers.

In spite of these facts the whole chain of activities (consisting of production, inventories and demand) must be kept under control.

This can be done by using the inventory‐level as a useful source of information concerning the cumulative deviations which occur both in production and sales. The feedback of this stock‐level‐information is necessary in practical planning‐procedures.

This can be proved easily.
De methoden van De Wolff en Van Heerden voor het nemen van aselecte steekproeven bij accountantscontroles*
Authors: Kriens J.
Published: April 2008

The procedures suggested by De Wolff and Van Heerden for random sampling in auditing.

In recent years two different methods were suggested for taking random samples in typical auditing problems. In this paper these two methods are critically reviewed and compared.

In De WoIff's method all large entries in a register are checked, whereas a sample is taken from the smaller ones. Van Heerden does not consider the register as a population of entries, but, if all entries total up to B guilders, as a population of B guilders. He selects guilders randomly and checks the entries to which the selected guilders belong. Both authors only use probability statements if no {severe) mistake is found in the sample. De Wolff uses confidence intervals with a confidence‐level 1‐txfor the fraction p of incorrect small entries and states that, except for a probability α, B will not surpass the correct total value with a fraction ϕ. Van Heerden formulates his conclusions, using the probability β(ϕ) that no mistake will be found in the sample if a fraction ϕ of B is incorrect.

In this paper (§ 3), it is shown that the intervals for p, if no mistake is found, cannot be ordinary confidence intervals. However, it is possible to give a somewhat unusual interpretation of De Wolffs results and then it turns out that his conclusions regarding a and ϕ actually are rather pessimistic upper‐limits for the probability of a wrong statement and for the maximal fraction of incorrect guilders respectively.

Very often, a priori information is present in auditing problems; § 4 shows how to use this information in order to get shorter intervals for p or smaller values for a. In § 5 a suggestion by V an H e er den to find the optimal sample size is discussed. The suggestion boils down to applying the minimax method to the sum of the checking‐costs nc, c being the costs of checking one entry, and the expected loss if a sample of size n is taken and the fraction tp of incorrect guilders has a probability distribution G(ϕ). For a special case, the optimal value of n is proved to be either the largest integer, smaller than , or the smallest integer, larger than this value. Table 5.III gives these values of n and the corresponding values of β for some values of B/c and ϕ.
Uitbijternegerende schatters bij duplobepalingen
Authors: Keuls M.
Published: April 2008

Outlyer‐ignoring estimators for measurement in duplo.

By hypothesis a measurement u is the sum of two independent random variables, the normal random variable with expectation μ, and standard error σ, and a random error φ:

Basically two independent measurements u1 and u2 over u are to give the estimate x=1/2(u1+ u2) over μ.

However, to reduce the effect of the error φ on a final estimate of μ, one adds, according to a common practice, a third or even a fourth measurement u3, u4, in the case that the basic pair differs by more than a number A. For this extended set of measurements two outlyer‐ignoring estimator y and z of μ are defined, and investigated against three specifications fo the error φ. Also an outlyer‐ignoring estimate of σ is considered, and its application is illustrated by an example.
Multimodality in a family of probability densities, with application to a linear mixture of two normal densities.
Authors: Wessels J.
Published: April 2008

Samenvatting

In dit artikel worden enige eigenschappen samenhangende met het aantal toppen van kansdichtheden afgeleid. Beschouwd wordt de situatie bij een dichtheid h(x, θ) (met θ parametervektor), die voor elke toegestaneparameterwaarde θɛθ tweemaal differentieerbaar is naar x, terwijl zowel h zelf, als zijn eerste en tweede afgeleide naar x, continu zijn in (x, θ). In paragraaf 2 worden enige eigenschappen afgeleid van de verzamelingen θk (k > o) van parameterwaarden waar strikt k‐toppigheid optreedt (definitie in paragraaf 1) en θo van die parameterwaarden, waarbijh(x, θ) voor geen enkele k (> o) aan de eisen voor strikte k‐toppigheid voldoet. In paragraaf 3 wordt h(x, θ) gespecialiseerd tot een lineair mengsel van twee kansdichtheden en in paragraaf 4 wordt gedetailleerd het geval van een lineair mengsel van twee normale dichtheden nagegaan.
Dimensionering van homogeniseringsinstallaties
Authors: von der Mooren A. L.
Published: April 2008

Designing of homogenizing equipment

The spread in quality in a large stream of granular material can be sufficiently reduced only by homogenization in mixing heaps and bunker installations. In this treatment each unit of consumption is composed of portions which, at given intervals, are taken from the stream.

The paper indicates how to choose the number and size of the portions and the intervals between them in order to achieve the required reduction in spread at minimum costs.

This determination, elucidated by means of an example, is based on the correlo‐gram of the stream referred to thin slices.
The correlation theory for stationary stochastic processes applied to exponential smoothing
Authors: Grunwald H.
Published: April 2008

Samenvatting

Er wordt aangetoond dat tijdreeksen x(t), die stationaire eerste incrementen y(t) met een zeer speciale correlatiefunctie (φyy() hebben, d.m.v. exponential smoothing optimaal in de zin van Wiener geëxtrapoleerd worden.

De smoothing parameter a. is gemakkelijk met behulp van (φyy() te berekenen. Het blijkt bovendien dat deze parameter soms ook groter dan één kan zijn. Een aantal generalisatus worden gediscussieerd en voor een daarvan wordt de extra‐polatie formule berekend.
The hypergeometric, the normal and chi‐squared*
Authors: Hemelrijk J.
Published: April 2008

This note describes a numerical investigation of the normal and χ2‐approximations to the hypergeometric distribution, which leads to a surprisingly simple foot rule. If n and r are the two smaller marginal totals, then for the tails of the distribution up to about a probability of 0.07, the normal approximation will in nearly all cases be better than the χ2 if n+r1/2N (where N is the grand marginal total) and worse otherwise. Although the two approximations are nearly equivalent, thisfootrule is so simple that it seems worth publishing.
The optimality of (s,S) inventory policies in the infinite period model*
Authors: Tijms H. C.
Published: April 2008

Summary The infinite period stationary inventory model is considered. There is a constant lead time, a nonnegative set‐up cost, a linear purchase cost, a holding and shortage cost function, a fixed discount factor β, 0 < β < 1, and total backlogging of unfilled demand. Both the total discounted cost (β < 1) and the average cost (β= 1) criteria are considered. Under the assumption that the negatives of the one period holding and shortage costs are unimodal, a unified proof of the existence of an optimal (s.S) policy is given. As a by‐product of the proof upper and lower bounds on the optimal values of s and S are found. New results simplify the algorithm of Veinott and Wagner for finding an optimal (s, S) policy for the case β< 1. Further it is shown that the conditions imposed on the one period holding and shortage costs can be weakened slightly.
From univariate‐ to multivariate analysis
Authors: Bosch A. J.
Published: April 2008

This paper is intended for those who are interested in the didactics of multivariate analysis. The problem studied is: how can the transition from univariate ‐ to multivariate analysis be made as simple as possible? Here we provide a simple “codingkey”, which works logically and is easy to remember and to handle. Some of the notations are adopted from lecture‐notes by L. C. A. Corsten.
Inventory control with unknow demand distribution: a slow‐mover case
Authors: Wessels J.
Published: April 2008

In this paper some tools will be developed for analysing a simple inventory problem of the slow‐mover type with the special feature that the probability distribution of the demand interarrival times is unknown. The role of sufficient statistics in decision making is analysed for an arbitrary optimality criterion and particularly for the Bayesian criterion. A computational approach for the case of a Bayesian criterion is presented together with some numerical results.
A generalization of the logistic growth function and its estimation
Authors: Levenbach Hans
Published: April 2008

SummaryThis paper presents a generalization of the logistic growth function based on a model for relative growth rates. The basic relative growth rate model is based on the Riccati differential equation, which has a solution that closely resembles the familiarS‐shaped logistic curve. For estimation purposes, a statistical version of this model is developed in which linear, exponential, and modified exponential growth in addition to logistic growth arise as special cases under various statistical hypotheses. The growth of yeast cells, population growth of the Netherlands and an example from the telephone industry are provided as illustrations of the model.
The inverse hypergeometric ‐ a useful model
Authors: Guenther William C.
Published: April 2008

The inverse hypergeometric random variable is defined. Properties of the distribution, in particular the relationship to the hypergeometric, are discussed and a number of important applications are reviewed. Finally, an alternative definition which permits an easy extension to the multivariate case is given.
Distribution‐free confidence intervals
Authors: Noether Gottfried E.
Published: April 2008

Summary  A general approach for converting a certain class of nonparametric tests into confidence intervals for suitably defined parameters is discussed. The class of tests comprises but is not limited to lineair rank tests for the one‐sample, two‐sample, and linear regression problems.
The moments of products of quadratic forms in normal variables*
Authors: Magnus Jan R.
Published: April 2008

Abstract  The expectation of the product of an arbitrary number of quadratic forms in normally distributed variables is derived.
Mean, median, mode II
Authors: Zwet W. R. van
Published: April 2008

Summary  In a delightful note Runnenburg [2] has recently discussed the celebrated mean‐median‐mode inequality. The present note continues this discussion.
Bounds for the variance of an inverse binomial estimator
Authors: Sahai Ashok , Buhrman J. M.
Published: April 2008

Summary  Best [1] found the variance of the minimum variance unbiased estimator of the parameter p of the negative binomial distribution. Mikulski and Sm [2] gave an upper bound to it, easier to calculate than Best's expression and a good approximation for small values of p and large values of r (the number of successes). In this paper both lower bounds and closer upper bounds are derived.
M‐estimation in the presence of unequal scale
Authors: Cressie Noel
Published: April 2008

Abstract  The class of weighted M‐estimators is defined. The ratio of the asymptotic variance of the weighted estimator to the asymptotic variance of the optimally weighted estimator is defined as the inefficiency. A Kantorovich inequality is proved, its implications are investigated for the misweighted mean and misweighted median, and the results are applied to a batch of demographic data.
Asymptotic power of the two‐sample test of Wilcoxon for Logistic shift alternatives, and comparison with simulation results
Authors: van der Laan P. , Weima J.
Published: April 2008

In this paper the power of the two‐sample test of Wilcoxonfor Logistic shift alternatives is computed by using two approximations, based on the asymptotic Normality of the test statistic. The sample sizes considered are m = n = 6,m = n=10 andm = n = 15. These approximations are compared with the results of an experimental determination by Monte Carlo techniques.
On the unimodality of passage time densities in birth‐death processes
Authors: Keilson J.
Published: April 2008

It has been shown [2] that for any ergodic birth‐death process the p.d.f. of Ton, the passage time from the reflecting state 0 to any level n is log‐concave and hence strongly unimodal. It is also known (cf [2]) that the p.d.f. of Tn, n+1 or Tn+1, n for such a process is completely monotone and hence unimodal. It has been conjectured that the p.d.f. for the passage time Tmn between any two states is unimodal. An analytical proof of the result is presented herein, based on underlying renewal structure and methods in the complex plane. It is further shown that the p.d.f. of Tmn can always be written as the convolution of two p.d.f.s, one completely monotone and the second PF and hence log‐concave.
Measuring pairwise interobserver agreement when all subjects are judged by the same observers
Authors: Schouten H. J. A.
Published: April 2008

Abstract  An experiment is considered where each of a sample of subjects is rated on an L‐point scale by each of a fixed group of observers. Weighted kappa coefficients are defined to measure the degree of agreement among the observers, between two particular observers, or between a particular observer and the other observers. Attention is paid to the selection of one or more homogeneous subgroups of observers. A linearized Taylor series expansion is used to derive explicit formulas for the computation of large sample standard errors. The procedures are illustrated within the context of a study where seven pathologists separately classified 118 histological slides into five categories.
A generalization of Friedman's rank statistic
Authors: Kroon J. de , Laan P. van der
Published: April 2008

Abstract  In this paper a very natural generalization of the two‐way analysis of variance rank statistic of Friedman is given. The general distribution‐free test procedure based on this statistic for the effect of J treatments in a random block design can be applied in general two‐way layouts without interactions and with different numbers of the continuous observations per cell provided the design scheme is connected. The asymptotic distribution under the null hypothesis of the test statistic is derived. A comparison with the method of m rankings of Benard and van Elteren is made. The disadvantage of Benard and van Elteren's test procedure is that the number of observations per block does influence the statistic twice, namely firstly by the number itself, as it should, and see ondly by the level of the ranks which will be different in different blocks if the numbers of observations per block are different. The proposed test statistic is not sensitive to differences in the levels of the ranks caused by the different numbers of observations per block. The test is derived from considerhg the Kruskal‐Wallis statistics per block.

Finally, the results of simulation experiments are given. The simulation is carried out for three designs and a number of normal location alternatives and gives some information about the power of the suggested test procedure. A comparison is made with Benard and van Elteren's test and with the classical analysis of variance technique. For some simple orthogonal designs the exact null distributions of Benard and van Elteren's test and the proposed test are compared.
ANTITHETIC VARIATES FOR MONTE CARLO ESTIMATION OF PROBABILITIES
Authors: Snijders Tom A. B.
Published: April 2008

This paper explores some possibilities for variance reduction by the use of antithetic variates when estimating probabilities.
CURRENT STATISTICAL ISSUES IN AGRICULTURAL RESEARCH
Authors: CORSTEN L.C.A.
Published: April 2008

Four topics, selected from the range of statistical subjects with current relevance for agricultural research are considered. The first is concerned with the need and usefulness of efficient incomplete block designs for any number of treatments, either equireplicate or with different number of replicates. The second one is a presentation of linear prediction procedures for phenomena with spatially random behaviour and its generalization towards kriging. Next, a reparametrization of a general four–parameter family of growth curves is recommended, leading to numerically stable parameter estimation for RICHARDS' functions and additional special cases. Finally, the modelling of factorials with continuous response and of log–linear relationships for frequencies is proposed to be handled on the same footing, with preference for an alternative criteria of model deviance over test critera or Cp–like measures.
INDUSTRIAL STATISTICS
Authors: UPPERMAN P.M.
Published: April 2008

Statistical methods are indispensable tools for management and play a key role in Total Quality Control. Statistical methods in process control, experimental design and life testing are considered. Some aspects of tecbing statistics in industry are discussed. The successful application of statistical methods very much depends on the proper collection of data. Applying and teaching experimental design is therefore strongly recommended.
ON THE ESTIMATION OF POPULATION MEANS AND RATIOS USING SUPPLEMENTARY INFORMATION
Authors: Upadhyaya L.N. , Singh H.P. , Vos J.W.E.
Published: April 2008

In this paper we discuss the problem of estimating population means and ratios of population means using supplementary information on an auxiliary variable. Two classes of estimators are proposed, depending on two parameters. The bias and mean square error of each of the involved estimators is obtained to the first order of approximation. It is shown that, with a proper choice of the values for the parameters, the estimators are more efficient than the conventional estimators. Numerical examples are provided.
AGREEMENT ON A TWO–POINT SCALE
Authors: Fidler V. , Nagelkerke N.J.D.
Published: April 2008

Consider m observers each classifying n objects into one of two disjoint categories. The problem of measuring agreement among m observers is discussed. A new approach, based on a specific parametric model, is recommended. The approach is applied to data on agreement in judging biopsy slides.
The sieve method, a sampling method for audit practice
Authors: Driessen S.
Published: April 2008

The sieve method is a new sampling method which may, under certain conditions, be validly used even though the statistical evaluation is based on random sampling. The method is described in both one‐phase and multi‐phase sampling schemes.
The Misspecification of Arma Models
Authors: Pollock D.S.G.
Published: April 2008

The object of this paper is to assess the effects of fitting a model of the wrong order to a time series which is generated by an autoregressive moving–average process. The method is to examine the spectral density functions which are indicated by the probability limits of the least–squares estimators of the misspecified models. The least–squares estimates are asymptotically equivalent to the maximum–likelihood estimates.

The experiments reported in this paper suggest that, if the spectral density function of the data–generating process displays prominent modes, then there is a danger of being seriously misled about the nature of the process whenever one fits a model with too few parameters. It also transpires that, in such cases, the criterion function is liable to have several local minima.

Autoregressive moving–average models are being used increasingly in object detection applications where the spectrum of a signal serves to identify the nature of its source. Our results suggest that radical misidentifications can result from the use of incorrectly parametrised models.
A Note on Properties of Iterative Procedures of Asymptotic Inference
Authors: Paardekooper H.C.H. , Steens H.B.A. , van der Hoek G.
Published: April 2008

This note deals with the article ‘On iterative procedures of asymptotic inference’ by K.O. DZHAPARIDZE (1983), in which an informal discussion is given on performing an unconstrained maximization or solving non–linear equations of statistics by iterative methods with the quadratic termination property. It discusses the theorem that if a maximized function, e.g. the likelihood function, is asymptotically quadratic, then for asymptotically efficient inference finitely many iterations are needed.

It is argued here that the theory still applies if certain well specified inexact (hence computationally cheaper) line searches are used in the optimization.
Measurement error and panel data1
Authors: Wansbeek T.J. , Koning R.H.
Published: April 2008

The underidentification of linear models with measurement error does not necessarily extend to panel data models, as has been shown by GAiliches and Hausman (1986). We discuss and extend some of their results for a simple case and address particular issues concerning identification and asymptotic variances.
An application of approximate finite sample results to parameter estimation in a linear errors‐in‐variables model
Authors: Friedmann R. , Mittag H. J. , Brandtstater A.
Published: April 2008

In the simple errors‐in‐variables model the least squares estimator of the slope coefficient is known to be biased towards zero for finite sample size as well as asymptotically. In this paper we suggest a new corrected least squares estimator, where the bias correction is based on approximating the finite sample bias by a lower bound. This estimator is computationally very simple. It is compared with previously proposed corrected least squares estimators, where the correction aims at removing the asymptotic bias or the exact finite sample bias. For each type of corrected least squares estimators we consider the theoretical form, which depends on an unknown parameter, as well as various feasible forms. An analytical comparison of the theoretical estimators is complemented by a Monte Carlo study evaluating the performance of the feasible estimators. The new estimator proposed in this paper proves to be superior with respect to the mean squared error.
Restricted maximum likelihood estimation under Eisenhart model Ill
Authors: Lee K.R. , Kapadia C.H.
Published: April 2008

For a balanced two‐way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non‐negativity requirements of the variance components by Lee and Kapadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non‐negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.