Inleiding over de verdeling van extremen

Summary This paper is an introduction to the exact and asymptotic distribution of univariate statistical extremes and gives the methods of estimation of the parameters of the double exponential distribution.     

Een lading van kraaltjes

Summary An urn containing 200 red beads and 1000 yellow ones is frequently used for demonstration of the hypergeometric or binomial distribution. Experiments show that the practical frequency distribution differs slightly but definitely from the theoretical one. This deviation turned out to be caused by electro-static forces.     

Steekproeven uit de halve cauchy verdeling

Summary  Let x₁…, x_n be a sample from a distribution with infinite expectation, then for n →∞ the sample average _n tends to +∞ with probability 1 (see [4]).
Sometimes _n contains high jumps due to large observations. In this paper we consider samples from the "absolute Cauchy" distribution. In practice, on may consider the logarithm of the observations as a sample from a normal distribution. So we found in our simulation. After rejecting the log-normality assumption, one will be tempted to regard the extreme observations as outliers. It is shown that the discarding of the outlying observations gives an underestimation of the expectation, variance and 99 percentile of the actual distribution.     

Een toepassing van "importance sampling"

Summary  This paper describes an experiment with "importance sampling", to show how much reduction of the computation time and sample size can be achieved in comparison with the usual Monte Carlo method. A comparison is made between each of the three methods of "importance sampling" and the usual Monte Carlo method by the determination of the expression

Of the three methods A, B and C the first one uses the shifted exponential distribution, the second one uses the gamma distribution, and the third one uses the exponential distribution with modified parameter. These three methods have all smaller variances, ranges and sample sizes than the usual Monte Carlo method. Their order of preference is A, B, C. With respect to computing time only the method A is significantly better. So only the method A is an improvement in respect of both the sample size and the computing time.     

Een criterium voor het kiezen van een proefopzet

A characterization of D-optimality is given together with several examples where D-optimal designs are computed.     

Een berekeningsmethode voor de logistische curve

Summary “Simple estimation of the parameters of the logistic curve.” By means of an appropriate transformation of the dependent variable Y_t into a simple function of Y_t, which depends only linearly on time, one of the parameters can be estimated in the usual way. A second transformation leads to the estimation of the two remaining parameters. As a numerical illustration two examples are presented.     

Een Monte-Carlo-bepaling van overschrijdingskansen, in verband met een keuzetest

A Monte-Carlo method for a test of significance, applied to points on a lattice, in connection with a vocational preference test, by C. A. G, Nass.
Appendix by Constance van Eeden.
A periodical rectangular lattice, with a period of k.m, is considered. Thus there are N = k.m points on the lattice, repeated in the two perpendicular directions. Two points are said to be "connected" if they are adjacent in a straight or diagonal way. Thus, if k and m 3, every point is connected with 8 other pooints. Out of the N points of the lattice, n points are selected and the total number of connections x, of all possible pairs of those n points is considered for a vocational preference test with k = m = 9, N = 81, n = 10. The problem is to test whether the sum y = x₁+…+ x*** from a sample of h values of x, is significantly small, under the hypothesis that in the h cases the n points are selected at random with equal chance. A Monte-Carlo sample of 100 values of x was taken, using random numbers. For h = 1, the problem was solved by the determination of P( y x₁), assuming that y is taken at random from the 101 values of x, supplied by the Monte-Carlo sample and x₁ for fixed values of x₁. For h - 2, a similar solution is given. For greater values of h, Student's two-sample test, with correction for continuity is suggested. For h = 2 the results of Student's test are compared with those of the solution mentioned above.
In the appendix a summary is given of results found by P.A.P Moran and P. V. Krishna Iyer for some closely related problems. Further some results concerning exact distributions, moments and asymptotic distributions for C. A. G. Nass' problem are given. The proofs of these results may be found in a paper by C. van Eeden and A. R. Bloemena (1959).     

Aantekeningen bij de herziening van de methodiek der prijsindexcijfers van het levensonderhoud

Momentarily (fall 196o) the Netherlands Central Bureau of Statistics is revising its price indexnumbers of family living. Some features of this revision are summarized below.
The old series is based on an expenditure pattern of 1951, whereas the new series will be calculated according to an expenditure pattern of 1959/'60. The latter data will be derived from a budget survey held among 250 households of manual and clerical workers consisting of 4 persons and grossing between four and eight thousand guilders a year (para. 6). The period covered was April 1959 till April i960.
The author indicates the way in which the varieties of the budget items to be covered by the monthly price surveys are chosen (para. 7). He discusses the principles and results of determining the number of price quotations (para. 8).
The choice of the municipalities in which price data will be collected is explained. An outline is given of the organisation of the new surveys apparatus (para. 14).     

Practische [berekening van de standaardafwijking van de constante term bij regressie-analyse

The formula arrived at in a previous article [1] is adapted to the usual computation schemes of regression analysis.     

Een opmerking over het aanpassen van functies aan een groot aantal waarnemingsuitkomsten

Note on the fitting of a function to a large number of observations.
The paper deals with various ways in which a set of functions may be chosen to describe a given body of observations, the parameters determining the function being determined by the data.
The special case when the functions of the set are given in the form of a table or a graph is emphasized.     

De invloed van de keuze der gewichten op de hoogte van een gewogen indexcijfer

The influence of the choice of the weights on the value of an indexnumber.
Price and quantity indexnumbers are weighted averages of groups of price and quantity ratios and they are convenient instruments to indicate the general tendency of such groups, especially if the number of basic ratios is considerable. The frequent use of indexnumbers is due to the fact that they can often be applied to problems for which, strictly speaking, an indexnumber had to be used derived from the same group of ratios but based on a different set of weights.
Two typical examples of such problems are given.
The use of a set of weights differing from the appropriate one is only justified, however, when the indexnumber is rather insensitive to changes in the set of weights. A simple formula is derived showing that the relative change of an index-number due to a change in the set of weights is equal to the product of the (weighted) coefficient of variation of the basic ratios, the (weighted) standard deviation of the relative changes of the weights and the (weighted) coefficient of correlation of the ratios and of the relative changes. The system of weights used in the calculation of these three factors is the same and is equal to the set of true weights belonging to the problem under consideration.
The practical use of the formula is demonstrated at the problem of index-numbers of costs frequently encountered in the practice of cost accounting.     

De bewerking van veldproeven volgens de methode van Knut Vik

Summary  (The treatment of field experiments by Knut Vik's method).
Agriculturists and statisticians have studied the problem, how to free the yields in a field experiment from the inequality of the soil. The method of the analysis of variance, due to the English statistician R. A. Fisher has taken an important place in the study of field experiments, so that other methods fell in the background.
The Norwegian agriculturist Knut Vik has suggested a method, which leads to good results without complicated calculations and without the knowledge of a great part of the mathematical statistics.
The mathematical foundation of this method is discussed in this article, which concludes, that the method of Knut Vik is of great importance for agriculturists, who don't want to perform intricate calculations.     

Oneindige verwachting en de wet van de grote aantallen

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.     

Opmerkingen over de standaardafwijking van de constante term bij regressie-analyse

Some remarks on the standard error of the constant term in regression analysis.
In this article a formula for the standard error of the intercept — when applying least squares — is derived for the case of two explanatory variables. This is done without using matrix algebra. The result is compared with the corresponding formula in matrix algebra, after which a design for computation is indicated.     

Toespraak door de directeur van de Stichting "Kwaliteitsdienst voor de Industrie"

Adress of the Director of the Foundation Industrial Quality Service.
The increasing of productivity also has an important qualitative aspect, To promote the qualitative increase of productivity the "Kwaliteitsdienst voor de Industrie" (Industrial Quality Service) wants to organize courses through which the statistical quality control methods can for each separate branch of industry be made available to those who are able to apply these methods, but who cannot spare the time and the energy required to take fully note of the mathematical and statistical backgrounds.     

De statistiek van de Militair Geneeskundige Dienst

The author gives a review of the origin and use of the statistical material used in the medical corps of the Dutch army. He points out the value of employing the data in a statistical manner for planning the medical care of the troops.