bluuebunny/crossref_metadata_2025 huggingface dataset:
The distribution of the brightness of stars. A Poisson‐process with “time”‐dependent parameter
Authors: Prins H. J.
Published: April 2008

Samenvatting

Bij de optische waarneming van sterren uit een satelliet is het belangrijk voor het richtmechanisme te weten wat de verdeling van de helderheid van de helderste ster en van het verschil in helderheid van de helderste en op een na helderste is op de verzameling van alle mogelijke te kiezen gezichtsveldjes van de kijker.

Het model is een Poisson‐proces met “tijds” afhankelijke parameter. Een monotone transformatie voert dit proces over in een tijdsonafhankelijk proces, waarna toepassing van bekende eigenschappen tot de oplossing leidt.

Een dusdanige transformatie lijkt ook voor andere tijdsafhankelijke processen een nuttig middel om een oplossing te verkrijgen.
Transformatie van niet‐normale verdelingen
Authors: Flapper P.
Published: April 2008

In statistical analysis and operational research many techniques are being applied, which are based upon the fact that the phenomenon under consideration has a distribution, which is approximately normal. This distribution‐type has got a number of very nice properties and a constant pattern, so that “normal” phenomenona can be predicted. In case of non‐normal, but deviated or skew distributions, analysis and forecasting become much more complicated. In this article a method has been described in which some non‐normal variables can be transformed into normal ones, so that techniques based on normal distributions may be used.
Oneindige verwachting en de wet van de grote aantallen
Authors: MIJNHEER J. L.
Published: April 2008

Samenvatting

De beide wetten van de grote aantallen (de zwakke en de sterke) vormen een centraal punt van de kansrekening. In het onderstaande wordt op eenvoudige wijze aangetoond, dat zij ook gelden voor steekproeven uit verdelingen met oneindige verwachting. Een minder eenvoudig bewijs is te vinden in M. LOÈVE, Probability Theory, Princeton 1963.

Dehiergebruikte bewijsmethode werddeschrijver aanbevolen door dr. J. FABIUS.
Bepaling van de personeelssterkte op kostenbasis*
Authors: Knaap J. v. d.
Published: April 2008

Determining the optimal number of staff in a department using a method based on costs.

How many men do you appoint in a department of a firm?

This number can be determined in an optimal way, if the following data are known:

‐ The number of men required per unit of time (may be given as a stochastic quantity).

‐ The mean probability of absence per man in the department (due to illness, holidays etc.).

‐ Wages per man.

‐ Costs (proceeds), if in one unit of time there are less (more) men available than required.

Generally the solution will be obtained by an iterative method. However, when the parameters show a certain behaviour it is possible to find the optimum solution by analytical and graphical means.
Random division of an interval*
Authors: Steutel F. W.
Published: April 2008

The well‐known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easily.
Some goodness of fit tests for exponential distributions
Authors: Soest J. van
Published: April 2008

Summary This paper considers tests of exponentiality against unspecified alternatives. The test functions are modifications of those given by Kac, Kiefer and Wolfowitz [Ann. Math. Stat., Vol. 26 (1955) 189–211]. The distributions of these statistics are obtained with the aid of the Monte Carlo method, and the tables may serve to apply a test of exponentiality for the usual levels of significance (sample sizes n≥ 10).

A Monte Carlo comparison is also made with competing tests for exponentiality, namely with criteria arising from probability plotting and due to Shapiro and Wilk [(1964) in an unpublished manuscript, but recently described in “Statistical Models in Engineering” by Hahn and Shapiro (Wiley, 1967)], and with tests based on the conditional distribution of total lives and on a likelihood ratio.
De Wet en de kansspelen
Authors: Hamaker H. C.
Published: April 2008

In the Netherlands all gambling is forbidden except in a few cases specially mentioned in the law. Time and again specialists in probability theory or statistics are called upon to testify as experts in lawsuits against law evaders. This paper discusses the part played by the experts in such legal procedures. It is pointed out that according to Dutch jurisprudence there does not exist an exclusive distinction between games of chance and games of skill. A simple declaration by an expert that a given game is largely based on chance suffices to see the game sentenced as against the law. This and various other related questions are discussed in detail and illustrated by examples taken from personal experience in the courts.
Kans en behendigheid
Authors: Hemelrijk J.
Published: April 2008

“Skill and chance”.

According to Dutch law games of chance are forbidden. This leads to the exploitation of all kinds of mechanical plays where skill plays a part, but chance too. Opinions differ about the interpretation of the law, which does not give a clear definition of the kind of plays it wants to forbid. It is not even quite clear whether the distinction between games of chance and games of skill is relevant. In this paper, which is a reaction to Hamaker's paper about the same subject in this issue, the thesis is defended that the distinction is necessary if one does not want the law to imply too much or too little.

Rapport S 409 (SP 113) van de Afdeling Mathematische Statistiek van het Mathematisch Centrurn, Amsterdam.
Discussie bijdrage
Authors: Cohen Ir. J. W.
Published: April 2008

An analysis is given of the character of games of chance and games of skill. It is shown that every game is influenced by stochastic effects. Whether a game should be classified as a game of pure skill or as a game of chance depends on the rules of the game, on the evaluation of the outcomes of the game and on the possibilities the player has by applying his skill to cope with the random effects of the particular game situations.
Percentiles and approximations of the sample median over the sample range for samples of size 3, 5, 7 and 9 from a standard normal distribution
Authors: Bouma N. , Vehmeyer A.
Published: April 2008

A table of the distribution function of the quotient of sample median and sample range of small samples from the normal distribution is given which is based partly on theoretical results published by L. de Haan and J. Th. Runnenburg, partly on numerical results obtained with Monte Carlo methods. Moreover an approximation of this distribution by Students distributions is introduced.
De chi‐kwadraat‐toets voor aanpassing van continue verdelingen
Authors: Hermans J.
Published: April 2008

SummaryA description is given of the version of the chi‐square test of goodness‐of‐fit proposed by G. S. Watson(1957, 1958). This version is applicable if one has a full samplex1, x2,…xnfrom a (under the null‐hypothesis) continuous distribution. To estimate the unknown parameters it uses (as will be general practice in this situation) the sample valuesxand not the class‐numbersn1,n2,…,nk. To calculate the asymptotic distribution of the test statistic a more detailed description is given of a method originally proposed by Harperand MacDonald(1960). Some numerical calculations in case of the normal distribution lead to the conclusion that the asymptotic distribution may be well approximated by ax2distribution.
Invariantie in de schattingstheorie
Authors: Sander P. C.
Published: April 2008

Summary A number of methods of estimation have been proposed on relatively intuitive grounds. A “best” method does not exist. Sometimes the principle of invariance or, better termed, equivariance is very useful. By use of the group structure on hand it is possible to characterize equivariant estimators.

Lezing gehouden op de Statistische Dag 1969.
A fractile programming approach with extreme sample estimates of parameters
Authors: Sengupta J. K. , Sanyal B. C.
Published: April 2008

Abstract This paper investigates the implications of extreme value estimates of net prices in the objective function of a linear programming problem. Analytically, our approach suggests interesting points of comparison between different measures of sensitivity of a linear programming problem, when a specified fractile of the distribution of profits is optimized.

Work done under the National Science Foundation Project GS‐1810–420–21–17 at the Department of Economics, Iowa State University.
An input system for linear programming problems *
Authors: Anthonisse Jac. M.
Published: April 2008

Summary This report contains a description of an input system for linear programming. In this system the mathematical formulation of a LP problem serves as input for a computer. The coefficients of the problem are generated from the formulas. Some examples are presented.
On the Kuiper test for normality with mean and variance unknown
Authors: Louter A. S. , Koerts J.
Published: April 2008

Summary If one wants to test the hypothesis as to whether a set of observations comes from a completely specified continuous distribution or not, one can use the Kuiper test. But if one or more parameters have to be estimated, the standard tables for the Kuiper test are no longer valid. This paper presents a table to use with the Kuiper statistic for testing whether a sample comes from a normal distribution when the mean and variance are to be estimated from the sample. The critical points are obtained by means of Monte‐Carlo calculation; the power of the test is estimated by simulation; and the results of the powers for several alternative distributions are compared with the estimated powers of the Kolmogorov‐Smirnov test.
Herinneringen dt het losse geheugen
Authors: Enters J. H.
Published: April 2008

It isn't so astonishing, the number of things that I can remember, as the number of things I can remember that aren't so
The Neyman‐Pearson theory for testing statistical hypotheses
Authors: Schaafsma Willem
Published: April 2008

SummaryThis is an attempt to write an introduction to some aspects of the present state of the Neyman‐Pearsontheory. The object is to interest the reader who has some knowledge of modem probability theory and statistics. We try to emphasize the main ideas, “unnecessary” mathematics is avoided.

In our opinion, the Neyman‐Pearsontheory (or, more generally, the objectivistic approach to statistics) is a vigorous attempt to statisfy some weakened form of the philosophical principle of the “intersubjective verifiability”. This attempt is considered successful in those situations where “various different objectivistic optimum properties are satisfied by the same optimal test”. Unfortunately, these conditions are not satisfied for many situations from actual practice (testing against restricted alternatives, non‐parametric problems). Thus we arrive at a dilemma: for many problems from practice different “optimum” tests are available. There is no easy way out of this dillemma (see the last section).

We have tried to emphasize the motivation and to aim at readability while minimizing the overlap with e.g. Lehmann'sbasic textbook. Thus many basic tools are disregarded: exponential families, completeness and sufficiency of statistics and many other subjects are missing, the restrictions by similarity, unbiasedness or invariance are only mentioned. The references constitute an incomplete apology for deleting so many important contributions.
A generalization of Cochran's procedure for the combining ofr×ccontingency tables*
Authors: Hopkins Carl E. , Gross Alan J.
Published: April 2008

AbstractCochran[3] derives a test of association whenk2 × 2 contingency tables are combined. We show in this paper how to extend Cochran'stest to the combiningof k r×ccontingency tables using a multiple comparison technique similar to the one presented by Dunn[4]. An example is included.
A procedure to estimate relative powers in binary contacts and an application to Dutch Football League results
Authors: Leeflang P. S. H. , Praag B. M. S. van
Published: April 2008

Summary In this paper a simple model is developed to explain and to predict the results of “binary contacts” in a set of n subjects with different powers where couples meet each other in binary contacts. The outcome is explained by a comparison of the respective powers and the random influences. The problem is to estimate the powers of the subjects from observations in the past and to predict the outcomes of future contacts. The model is relevant in many economic and Sociological settings. Here it is applied to the Dutch Football League results to estimate the relative powers of the teams and to predict the outcomes of future matches.
De frequentistische opbouw van de waarschijnlijkheids‐rekening volgens R. von Mises
Authors: Daal J. van
Published: April 2008

Samenvatting

R. von Mises publiceerde zijn frequentistische opbouw van de waarschijnlijkheidsleer voor het eerst in 1919. De daarbij naar voren gebrachte inzichten verschilden zeer van de in die tijd algemeen geaccepteerde ideeén omtrent de grondslagen van de waarschijnlijkheidsleer. Onder invloed van (zowel opbouwende als abrekende) kritieken, alsmede door eigen gewijzigde inzichten, evolueerde zijn theorie zich, via diverse publikaties, tot die, weke wij aantreffen in zijn in 1964 posthuum verschenen, laatste werk.

In dit artikel wordt nader ingegaan op de theorie van Von Mises, zoals die in het zojuist genoemde werk behandeld wordt. Hiertoe is het soms nodig in te gaan op vroegere publikaties van zijn hand.

In vele boeken en artikelen (zie bijv. Cramer (1966) p. 150 en Hemelrijk (1968) p. 13) worden enige zinnen gewijd aan het feit, dat Von Mises zich met de grondslagen van de waarschijnlijkheidsleer heeft bezig gehouden. Bijna nooit krijgt men echter te lezen, wat hij precies gezegd heeft.
On residuals and their autocorrelations in fitted time series models
Authors: Pierce David A.
Published: April 2008

Summary When discrete autoregressive‐moving average time series are fitted by least squares, both the residuals and their autocorrelations are for large n representable as singular linear transformations of the true errors (or white noise) and their autocomlations, respectively, and the matrices of these transformations arc both of the form I‐X(X'X)‐1X, where the rank of X is the number of parameters estimated. However, the large‐sample properties of these two sets of statistics are fundamentally different, a phenomenon which is of considerable importance for the use of the residual autocorrelations in performing tests of fit of these models.
On the Kuiper test for normality with mean and variance unknown
Authors: Srinivasan R.
Published: April 2008

Summary A modified form of the Kuiper statistic Vn is developed for testing the composite hypothesis that a sample of size n comes from a normal population with unspecified mean and variance. Its distribution is derived using Monte Carlo methods. Power comparison with the adjusted Kuiper test proposed by Louter and Koerts [6] indicates that our test is superior with respect to certain alternatives.
Skew probability curves with negative powers of time and related to random walks in series
Authors: Wise M. E.
Published: April 2008

Summary The well known probability distribution of first arrival times of a particle undergoing random walk or Brownian movement in one dimension is extended to allow for steps in series each in a different medium. Previously this led to considering a certain distribution defined by its cumulants, which form a simple series generalising that for the known distribution. This is illustrated by the particular case of two first passages in series. Approximations to the probability (density) curves are found, each of which consists of a sharp peak followed by a long tail where the ordinates are very nearly proportional to t‐W, W ≥ 3/2. A generalisation can yield smaller W down to ca. 0.1. It is concluded that this explains why negative powers of time are found in so many physiological clearance curves of all kinds. Numerical tables are based on distributions with very smal step times, and give ones built up from the sum of a varying number of steps. The parameters 01 the triangle formed by the inflection tangents are given in order to describe the peaks.
Some results for the dynamic (s, S) inventory model *
Authors: Tijms H. C.
Published: April 2008

Summary The periodic review, single item, stationary (s, S) inventory model is considered. There is a fixed lead time, a linear purchase cost, a fixed set‐up cost, a holding and shortage cost function, a discount factor 0 < α≤ 1 and backlogging of unfilled demand. The solution for the total expected discounted cost for the finite period (s, S) model is found. In addition the time dependent behaviour of the inventory process is found. Further a limit theorem is given, which relates the total expected cost for the finite period (s, S) model with no discounting to the average expected cost per period for the infinite period (s, S) model. As a by‐product we obtain known results for the infinite period (s, S) model.
Simplified estimation of parameters in a cauchy distribution
Authors: Raghunandanan K. , Srinivasan R.
Published: April 2008

Simplified estimators of the location and scale parameters of a Cauchy distribution are constructed along the lines developed by Dixon [3, 4]. Symmetrically censored samples are considered. The efficiency of these estimators is shown to be high enough to make them useful in practice.
Probability distributions of two‐component soil samples
Authors: Stol Ph. Th.
Published: April 2008

Mixing of sand layers on top of peat soils is achieved by soil improvement machines. The result of the mixing process is studied by taking samples from a vertical cross‐section of the profile. The samples will have various values of the sand to peat volume‐ratio. These values can be plotted in emperical cumulative frequency distributions. The distributions for two types of machines were found to be quite different due to differences of mixing intensities. A method is proposed for the evaluation of the mixing effect expressed in the parameters of theoretical probability distributions of two‐component soil samples. The probability distribution of the volume‐ratios in the sample are derived and their properties are discussed. Moment estimators of the parameters are derived. The theoretical distributions are compared with two experimental results obtained with a mixing rooter and a rotary mixer respectively.
A comparison of two nonparametric k ‐sample slippage tests
Authors: Doornbos R. , Senden W. L. M. M.
Published: April 2008

The tests which are discussed here are Mosteller's k‐sample slippage test for an extreme population [8] and the k‐sample slippage analogue of the Wilcoxon two‐sample test proposed by Doornbos and Prins [3]. A comparison is made between both tests in respect of their consistency against normal, exponential and uniform shifts and against Lehmann‐alternatives. For some small sample sizes the powers of the two tests have been calculated.
The estimation of guaranteed fatigue life under random loading
Authors: Jaroš Frantšek , ŽAludová Agnes H.
Published: April 2008

Introduction and Summary

One of the pressing problems of mechanical reliability still requiring a satisfactory solution is that of ensuring the guaranteed fatigue life of a component or structure subject to random dynamic loading. In the past, this problem has generally been solved in technical practice by the choice of a sufficiently large “safety factor” when dimensioning critically stressed parts of a complex structure.

Application of probability and statistical methods now offers the possibility of developing a theory of reliability of mechanical systems, where the risk of failure can be expressed as a probability, taking into account effects of random loading processes, which characterize either the functioning of the system itself or external environmental operating conditions.

In the following paper we describe one method of approach to the solution of this problem. The solution consists of a combination of the Weibull‐Freudenthal‐Gumbel theory of fatigue estimation using (s̀, N, P) relations, the Palmgren‐Miner hypothesis of linear accumulation of damage and the theory of stationary random processes having a given autocorrelation function or spectral density. Several other stochastic models are discussed in [1]. The subject of this paper was chosen in acknowledgement of the fact that H. C. Hamaker in his applied theoretical work also dealt with a related problem concerning the breaking strength of glass [2].
An asymptotic problem in renewal theory
Authors: Klamkin M. S. , Lint J. H. van
Published: April 2008

A special problem in renewal theory is considered. The asymptotic behavior of the renewal function was studied by W. L. Smith. Here we show that his result with an exponentially small remainder term follows from a theorem of DeBruijnon Volterra integral equations.
Non‐normal bivariate densities with normal marginals and linear regression functions *
Authors: Ruymgaart F. H.
Published: April 2008

Summary It is well known that for a bivariate density in order to be bivariate normal, the possession of univariate normal marginal densities alone is not sufficient. In this paper it will be shown by means of some counterexamples that the additional requirement of linearity of the regression functions does not supply a sufficient condition either.
A maximin test for means
Authors: Lepage Yves
Published: April 2008

Summary Let X be a normal vector with mean μ and known covariance matrix. This note is concerned with the problem of showing that the test based on X‐1X is maximin most powerful for μ= 0 versus μ belongs to a given ellipsoid and uniformly most powerful for μ= 0 versus μ belongs to a family of ellipsoids.
Enige ervaringen met economisch‐technische bedrijfsmodellen
Authors: Ek J. L. P. van , Tilanu C. B.
Published: April 2008

Summary The raw material entering a factory at one end passes through 7 successive production stages; at the fifth stage a second raw material is added, and at each of the 7 stages a certain fraction of the material being processed has to be scrapped. Equations are developed for the yield and for the economic profit of this production process taking into account the production capacities of the various stages, the production costs, the cost of the raw materials, and the prices obtained for the final product and for the scrapped material. From these equations expressions for the elasticities are derived giving the relative changes in profit resulting from small relative changes in the influencing factors. Likewise an expression is developed for the overall operating efficiency of the production process. The use of the formulae is illustrated by a numerical example, for which the rigidities, that is the efforts required in order to increase the profit by a fixed amount through changes in the influencing factors, are also estimated.
On order statistics when the sample size has a binomial distribution
Authors: Buhrman J. M.
Published: April 2008

Raghunandanan and Patil [1] derived the density function of the i‐th order statistic from a sample with random size. For the case that the size has a bionmial distribution, a simpler derivation is given below.
Statistical inference and subjective probabilities
Authors: Koerts J. , Leede E. de
Published: April 2008

Summary “Learning by experience” is a well‐known part of the theory of subjective probabilities; the learning process is often derived from some prior distribution F(p) where p is a parameter of unknown value of a binomial process for instance. In this paper, the learning process is explicitly formulated and the corresponding prior distribution is derived from it. In this interpretation, subjective probabilities are part of an inference methodology, rather than a subjective evaluation of frequentistic probabilities. Implications are considered for a concept like the “non‐informative prior; the situation is considered in which the learning process seems to be in contact with some objectively determined prior.
Lineaire regressie‐analyse, ook bij gegevens in strijd met het model
Authors: van Montfort M. A. J.
Published: April 2008

Samenvatting Robuuste lineaire regressie‐analyse volgens Andrews (1973) wordt behandeld. Deze methode is bestand tegen enige fouten in zowel de verklarende variabele(n) als in de te verklaren variabele. Zij levert

i. een opsplitsing van de waarnemingen in begrijpelijke en onbegrijpelijke bij het gekozen model, en ii. parameterschattingen met nauwelijks verlies aan doeltreffendheid bij Gauss‐residuen ** en met grote winst aan doeltreffendheid bij residuen met langere staart. zulks vergeleken met de bekende kleinste kwadraten procedure, die optimaal is bij Gauss‐residuen.

Aan de hand van getallen‐voorbeelden wordt een en ander toegelicht.
Theory and numerical solution of a discrete queueing problem
Authors: Ponstein J.
Published: April 2008

Abstract  A queueing problem is considered with one server, independent discrete inter‐arrival times, and independent discrete service times. The steady state distribution of the waiting time is approximated by means of the solution of certain linear equations and applying a generalization of the Lin‐Bairstow method for finding quadratic factors of polynomials.
Discounted semi‐Markov decision processes: linear programming and policy iteration
Authors: Wessels J. , Nunen J. A. E. E. van
Published: April 2008

For semi‐Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal linear programming formulation of the problem.
Some models of truck allocation for household refuse collection*
Authors: Panne C. van de
Published: April 2008

A number of models is developed for the selection and allocation of trucks for household refuse collection. The models vary from a simple model related to the optimal batch‐size formula to a linear programming model. A minimum‐cost selection is made on the basis of time per pick‐up, weight per pick‐up, driving time from collection area to landfill site, capacity and costs of the relevant truck‐crew combinations and lengths of possible shifts. The models are equally applicable to other house‐to‐house collecting and distributing activities.
A test for randomness in behaviour
Authors: Snijders Tom
Published: April 2008

In biological analysis of behaviour, transition matrices occur of which the diagonal entries are essentially zero. For such transition matrices, a model of randomness is constructed, with a test for the hypothesis that this model holds.
Commentaar op “Lineaire regressie, ook bij gegevens in strijd met het model“
Authors: Baaij J. G.
Published: April 2008

Samenvatting Er wordt een voorbeeld gegeven waarbij de regressie‐analyse volgens Andrews zoals beschreven in het artikel van Van Montfort niet tot het gewenste resultaat leidt.
Nonlinearity measures: a case study
Authors: Linssen H. N.
Published: April 2008

SummaryAn important problem in applied statistics is fitting a given model functionf(β) with unknown parameters β to a data vectory.Minimizing the residual sum of squares provides the least squares estimates of β. Iff(β) is linear in β the precision of these estimates is well‐known. In a nonlinear case approximate (though asymptotically exact) confidence statements can be made. Beale[1] introduced measures of nonlinearity which can be used to indicate when approximate confidence statements are appropriate. Guttmanand Meeter[2] showed that in some, severely nonlinear, cases Beale's measures do not give the right indication. In this paper two new nonlinearity measures are introduced and their use is illustrated on a practical problem described by Witt[3]. A more detailed discussion of the theoretical background can be found in references [1] and [2].
Loten bij delicate vragen; een overzicht van “randomized response“‐technieken
Authors: Verdooren L. R.
Published: April 2008

Samenvatting

In een populatie wenst men de fractie personen te schatten, die een zeker kenmerk vertoont. Bij het interview krijgt men vaak een weigering of een ontwijkend of een bewust onjuist antwoord op vragen m.b.t. delicate kenmerken, waardoor de schatter van de fractie onzuiver kan worden. Door gebruik te maken van statistische technieken, die de laatste tien jaren in de V.S. zijn ontwikkeld, kan men deze fractie toch zuiver schatten.

Ook van kwantitatieve kenmerken, zoals de hoogte van het inkomen, kan men m.b.v. deze technieken het populatiegemiddelde zuiver schatten.

Een overzicht van deze “randomized response”‐technieken wordt behandeld. Een bibliografie van de tot nu toe verschenen publikaties wordt gegeven.
On Markov games
Authors: Wal J. van der , Wessels J.
Published: April 2008

In the paper it is demonstrated, how a dynamic programming approach may be useful for the analysis of Markov games or stochastic games. Markov games with finitely many stages are dealt with extensively. The existence of optimal Markov strategies is proven for finite stage Markov games using a shortcut of a proof by Derman for the analogous result for Markov decision processes. For Markov games with a countably infinite number of stages some results are summarized. Here again the results and the methods of proof have much in common with results and proofs for Markov decision processes. Actually the theory of Markov games is a generalisation. The paper contains short introductions into the theories of matrix games and tree games.
Merkkeuze bij consumenten
Authors: Wierenga B.
Published: April 2008

Samenvatting

Bij iedere aankoop van een produkt waarvan meer dan één merk wordt aangeboden, moet de consument een keuze doen uit de beschikbare merken. Welk merk wordt gekozen is afhankelijk van: eerder gekochte merken, de winkel waarin wordt gekocht en marketing variabelen zoals prijs en reclame.

De invloed van eerder gekochte merken kan worden weergegeven door merkkeuzemodellen, waarvan er in het artikel enkele worden besproken. Deze modellen worden vervolgens toegepast op empirische gegevens. Hierdoor wordt inzicht verkregen in de aard van het merkkeuzeproces. Voor dezelfde empirische gegevens wordt ook de invloed op de merkkeuze onderzocht van winkelkeuze en marketing variabelen.
On the Continuity Correction
Authors: Schouten Hubert J. A.
Published: April 2008

A simple, and fairly general, analytical derivation of the “one‐half” continuity correction is presented.
Bacteriological assay: the best motley row
Authors: Weima Jan
Published: April 2008

Summary Different culture media can be used in bacteriological assay. In this paper criterions are given for selecting subsets of the available set of culture media. First the selection is made in a nonsequential way. Later on this is done in a sequential way.
Regen, een toepassing van dynamische programering
Authors: Wijngaard J.
Published: April 2008

Inleiding

Veel mensen zal het wel eens overkomen zijn dat ze tijdens een wandeling overvallen werdcn door een regenbui. De eerste reactie in zo'n situatie is in de regel, hard te gaan lopen teneinde zo droog mogelijk thuis te komen. Bij sommigen echter zal ongetwijfeld wel eens de vraag zijn opgekomen hoeveel effect dat harde lopen nu heeft; als je hard loopt ben je weliswaar eerder thuis maar je vangt ook meer regen per tijdseenheid, en stel je voor dat het al gauw ophoudt met regenen.

In dit verhaaltje wordt het probleem van de optimale strategie aan de orde gesteld, wat is de optimale snelheid in verschillende omstandigheden. Als criterium gebruiken we de (verwachte) totale hoeveelheid opgevangen regen. Daarbij gaan we er van uit dat de regen recht naar beneden valt en homogeen verdeeld is over de ruimte.

In paragraaf 1 wordt aangenomen dat het blijft regenen. In paragraaf 2 wordt rekening gehouden met de mogelijkheid dat het ophoudt met regenen en daarna droog blijft. In paragraaf 3 nemen we aan dat het steeds opnieuw kan gaan regenen.
Latent structure models applied to the joint distribution of drivers' injuries in road accidents
Authors: HUTCHINSON T. P.
Published: April 2008

The joint occurrence of the seventies of injury sustained by the two drivers in collisions between two vehicles of equal mass is considered. The positive correlation between them is explained by the speed of the accident, which is not recorded in national accident statistics and thus is ‘latent’.
Stochastic programming in production planning: a case with none‐simple recourse
Authors: PETERS ROBERTJ. , BOSKMA KLAAS , KUPPER HENDRIKA. E.
Published: April 2008

Abstract  In modeling real world planning problems as optimization programs the assumption that all parameters are known with certainty is often more seriously violated than the assumption that the objective function and the constraints can be approximated sufficiently accurate by lineair functions. In this paper we discuss the concrete application of stochastic programming to a multiperiod production planning problem in which the demand for the products during the various periods is assumed stochastic with known probability distribution. Since the resulting stochastic program does not possess the property of “simple” recourse no direct use can be made of existing methods that have been proposed in literature for solving problems of this type.
Overflow traffic from the viewpoint of renewal theory
Authors: WALLIN J. F. E.
Published: April 2008

In this paper some known formulae concerning overflow traffic have been derived in a simpler way than is generally done in literature, i.e. by using simple results obtained from elementary renewal theory.

After the model has been introduced, the distribution of intervals between overflows is calculated by means of a recurrence relation. A generalization of Erlang's formula for the call congestion follows almost immediately. The last section the special case of Poisson input is discussed.
Recursive Filtering*
Authors: Willems Jan C.
Published: April 2008

The purpose of this paper is to give an exposition of the theory behind the Kalman filter and its application to the so‐called LQG‐problem. This problem is concerned with the stochastic optimal control of a linear system with respect to a quadratic cost in the presence Gaussian disturbances.
The discrete Kalman filter applied to linear regression models: statistical considerations and an application
Authors: Otter Pieter W.
Published: April 2008

In this paper we show how the Kalman filter, which is a recursive estimation procedure, can be applied to the standard linear regression model. The resulting “Kalman estimator” is compared with the classical least‐squares estimator.

The applicability and (dis)advantages of the filter are illustrated by means of a case study which consists of two parts. In the first part we apply the filter to a regression model with constant parameters and in the second part the filter is applied to a regression model with time‐varying stochastic parameters. The prediction‐powers of various “Kalman predictors” are compared with “least‐squares predictors” by using Theil‘s prediction‐error coefficient U.
Mean, median, mode
Authors: Runnenburg J. Th.
Published: April 2008

Summary This note is an attempt to avoid doing the same search for the third time. It happened twice in my life that I wished to prove that the median is located between mean and mode for certain B‐distributions: first in 1953, next in 1976. For arbitrary distributions the result is sometimes referred to as Fechner's theorem. Of course it does not hold in general. In order to prove the result for particular distributions one can often use an elegant theorem of Timerding. There is a nice relationship with the standardized third central moment.
A test for equality of two exponential distributions
Authors: Perng S. K.
Published: April 2008

Abstract Let X1., Xn1 and Y1., Yn1, be two independent random samples from exponential populations. The statistical problem is to test whether or not two exponential populations are the same, based on the order statistics X[1],.X[r1] and Y[1],.Y[rs] where 1 r1n1 and 1 r2n2. A new test is given and an asymptotic optimum property of the test is proved.
A numerical planning model for a central bank's bank notes operations
Authors: Fase M. M. G. , Hoeven D. van der , Nieuwkerk M. van
Published: April 2008

Abstract  This paper discusses a numerical planning model for the bank notes operations at a central bank. The operation of the model is demonstrated by four examples taken from the present day situation in the Netherlands. The major aim of this effort has been towards developing a new tool for the assessment of the performance of the bank note process from a central banker's point of view. Thus the thrust has been towards the description of the bank notes operations at a central bank, utilizing a comprehensive quantitative model. In a sense, this effort exemplifies long‐term corporate planning of a central bank's issue department.
An efficient variant of the product and ratio estimators
Authors: Sahai Ashok
Published: April 2008

Abstract  This article presents a variant of the usual ratio and product methods of estimation, with the intention 10 improve their efficiency. The first order large sample approximations to the bias and the mean square error of the proposed estimator are obtained and compared with those of the well‐known methods (simple expansion, ratio, product, difference and linear regression methods). For a special case, the accuracy of the first order approximation (terms up to the order n‐1) is examined by including terms upto the order n‐2. With suitable choice of a design parameter, the proposed estimator turns out to be superior to the three methods mentioned first. The relation to the other two methods is examined; if the design parameter can be chosen near to the optimal value, the proposed method is seen to be approximately as efficient as the linear regression estimator. Finally some extensions are indicated.
Beware of averages!
Authors: Smit J. C.
Published: April 2008

Summary  Let X1,.,., Xm, and Y1, Yn, be two independent samples from the same distribution and let X and Y be the means of these samples. What is the maximal value of P(X < Y)?
The expectation of products of quadratic forms in normal variables: the practice
Authors: Magnus Jan R.
Published: April 2008

Summary  A table is presented to simplify the computation of the expectation of a product of quadratic forms in normal variables. Some peculiarities of the table are discussed.
The rate of convergence in law of the maximum of an exponential sample
Authors: Hall W. J. , Wellner Jon A.
Published: April 2008

Summary  We derive a uniform rate of convergence of (1–n‐1x)n to e‐x(x < 0). It provides a uniform rate of convergence for the distribution of the largest order statistic in a sample from an exponential distribution to the “double exponential” extreme value distribution. It likewise provides a rate of convergence for the distribution of the smallest order statistic from a uniform distribution.
An alternate development of conditioning
Authors: Winter B. B.
Published: April 2008

Abstract  The “classical” development of conditioning, due to Kolmogorov, does not agree with the “practical” (more intuitive, but unrigorous) way in which probabilists and statisticians actually think about conditioning. This paper describes an alternative to the classical development. It is shown that standard concepts and results can be developed, rigorously, along lines, which correspond to the “practical” approach, and so as to include the classical material as a special case. More specifically, let Xand Y be random variables (r.v.‘s) from (Ω, f, P) to (x, fx) and (y. fy.), respectively. In this paper, the fundamental concept is the conditional probability P(AX = x), a function of xε x which satisfies a “natural” defining condition. This is used to define a conditional distribution Py/x, as a mapping x × fy‐R such that, as a function of B, Pylx=x,(B) is a probability measure on fy. Then, for a numerical r.v. Y, conditional expectation E(Y/X) is defined as a mapping x →r̄ whose value at x isE(Y/X = x) = ydPY/x=i(y). Basic properties of conditional probabilities, distributions, and expectations, are derived and their existence and uniqueness are discussed. Finally, for a sub‐o‐algebra and a numerical r.v. Y, the classical conditional expectation E(Y) is obtained as E(Y/X) with X = i, the identity mapping from (Ω, f) to (Ω).
Mean, Median and Mode in Binomial Distributions
Authors: Kaas R. , Buhrman J.M.
Published: April 2008

Summary  While studying the median of the binomial distribution we discovered that the mean median‐mode inequality, recently discussed in. Statistics Neerlandica by Runnen‐burg 141 and Van Zwet [7] for continuous distributions, does not hold for the binomial distribution. If the mean is an integer, then mean = median = mode. In theorem 1 a sufficient condition is given for mode = median = rounded mean. If median and mode differ, the mean lies in between.
Inequalities compared
Authors: Hoekstra A.H. , Runnenburg J. Th.
Published: April 2008

We know that the partial means mrof a sequence of i.i.d. standardized random variables tend to 0 with probability 1. If we want P{mk≥εfor some k ≥r}≤δ for given positive ε and δ, how large should we take r? Several (strong) inequalities for the distribution of partial sums providing an answer to this question can be found in the literature (Hájek‐RényiRobbins, Khan). Furthermore there exist wellknown (weak) inequalities (Bienaymé‐Chebyshev, Bernstein, Okamoto) that give us values of rfor which P{mr≥ε}≤δ. We compare these inequalities and illustrate them with numerical results for a fixed choice ofε and δ.

After a general survey and introduction in section 1, the normal and the binomial distribution are considered in more detail in the sections 2 and 3, while in section 4 it is shown that the strong inequality essentially due to Robbinscan give an inferior result for particular distributions.
On estimation of variance components*
Authors: Verdooren L.R.
Published: April 2008

In this survey paper the estimation of variance components is given. The least squares approach in variance component estimation is a unifying principle which includes the analysis of variance estimators and the MINQUE. When normality is assumed the maximum likelihood estimators can be used. Many variance component estimators are not permissible because they are not non‐negative. The development of non‐negative variance component estimators is indicated.
Consistent selection of explanatory variables
Authors: Bierens Herman J.
Published: April 2008

We consider a linear regression model where some explanatory variables are unknown members of sets of alternative explanatory variables. It will be shown that under weak conditions the minimum residual variance criterion for selecting these explanatory variables has the property that the probability of selecting wrong explanatory variables vanishes if the number of observations increases to infmity. Moreover, the O.L.S. estimator of the resulting “specified” model turns out to be consistent, while in the case that all the parameters are nonzero it can be shown that this O.L.S. estimator has the same limiting distribution as the O.L.S. estimator of the true model.
Admissibility Considerations in the Finite State Compound and Empirical Bayes Decision Problems*
Authors: Boyer JohnE. , Cilliland DennisC.
Published: April 2008

In the compound decision problem the same decision problem. called the component decision problem, occurs repeatedly. Data from all repetitions are used to reach decisions concerning the parameter values in each component; such rules are called compound decision rules. The compound risk is the average risk across all component decisions. In the analogous empirical Bayes problem the parameters are taken to be independent and identically distributed with unknown distribution. This paper explores the relationship between compound risk admissibility and component risk admissibility in these problems. The definitions are general and the results are fairly obvious and proved for the finite parameter set component only.
Small sample behaviour of some nonparametric multi‐sample location tests in the presence of dispersion differences
Authors: Fung Karen Yuen
Published: April 2008

This paper describes the small and moderate sample behaviour of three studentized non‐parametric statistics by Sen and a modified Wilcoxon statistic by Potthoff for testing the equality of location parameters in the presence of dispersion differences. Based on the agreement between the asymptotic and small sample distributions of the statistics as well as a comparison of their power under heteroscedasticity, the studentized Wilcoxon and the studentized Brown and Mood tests arc preferred in the two‐sample and c‐sample situations, respectively.
Mixing of direct, ratio, and product method estimators
Authors: Vos J.W.E.
Published: April 2008

In a paper by SrivenkataramanaTracy[4], four methods of estimating a population total Ywith the use of an auxiliary variable were introduced, given a random sample without replacement from that population. These methods were “built around the idea that estimating the population total is essentially equivalent to estimating the total corresponding to the non‐sample units, since that corresponding to the sample units is known once the sample is drawn and measurements are made on it.”

However, in the case of small sampling fractions the nonsample units constitute most of the population and no great improvement over the traditional estimators is to be expected. Therefore the methods are compared with the existing estimators and it turns out that they are special cases of the “mixing estimators”, introduced in this paper. The latter estimators can be made asymptotically equivalent to the regression estimator and are therefore asymptotically superior to all other estimators. An exact comparison is carried out on the artificial example given in [4]. The statement in this paper that “the proposed estimators are to be preferred to the regression estimator for., superiority of performance in the case of small samples” is evidently misleading. Finally a comparison is made with other “mixing‐type” estimators, that can prove very useful in practice.
Some Comments on Latent Structure Analysis, Arising Out of a Paper by R.D. Gill
Authors: Altham P.M.E.
Published: April 2008

The model of latent structure analysis forkdiscrete‐valued variates was explained and illustrated by R.D. Gill[5], Here the latent structure model is related to a condition for a covariance matrix, as in factor analysis theory, and a word of warning is given for the interpretation of a factor analysis from discrete valued variables.
Explicit steady state solution for a Markovian inventory system*
Authors: Ramanarayanan R.
Published: April 2008

Abstract The explicit steady state probability vector for the inventory level is presented for a Markovian system.
Trimmed means and M‐estimates
Authors: Jewett R.I. , Ronner A.E.
Published: April 2008

Summary  In this paper we show that HUBER‐estimates and more general M‐estimates are bounded by the smallest and the largest trimmed mean of a sample.
Properties of a distribution‐free two‐stage two‐sample median test
Authors: Orban John , Wolfe Douglas A.
Published: April 2008

Abstract  In this paper we consider a class of distribution‐free two‐stage two‐sample median tests. These procedures are based on a fixed size sample from one population, while the observations from the second population are collected in a truncated sequential fashion. Necessary tables are provided enabling us to select a particular member from the class such that arbitrarily preset power levels are approximately obtained. We also present asymptotic expressions and tables for the expected number of observations from the second population. Finally, comparisons between the asymptotic version of this two‐stage median test and the binomial sequential probability ratio test due to Wald (1947) are discussed.