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.     

De omvang van de steekproef bij een enkelvoudig steekproefsysteem

Summary  (Sample size for a single sampling scheme).
The operating characteristic of a sampling scheme may be specified by the producers 1 in 20 risk point ( p ₁), at which the probability of rejecting a batch is 0.05, and the consumers 1 in 20 risk point ( p ₂) at which the probability of accepting a batch of that quality is also 0.05.
A nomogram is given (fig. 2) to determine for single sampling schemes and for given values of p₁ and p ₂ the necessary sample size ( n ) and the allowable number of defectives in the sample ( c ).
The nomogram may reversedly be used to determine the producers and consumers 1 in 20 risk points for a given single sampling scheme.
The curves in this nomogram were computed from a table of percentage points of the χ² distribution. For v > 30 Wilson and Hilferty's approximation to the χ² distribution was used.     

Een noodzakelijke correctie van de overschrijdingsgrenzen voor steekproefgemiddelden bij toepassing van stratified sampling

Summary  (A necessary correction of the control chart limits for averages of samples in the case of stratified sampling).
Application of stratified sampling results in smaller fluctuations of sampling than where the same total number of individuals is drawn at random from the superposed strata.
The proportion of the standard errors of the averages obtained by these two sampling methods may be expressed by a factor φ (o ≤φ≤ 1). The probability limits, between which the random sampling results would be fluctuating normally, should be corrected according to this factor.
A few properties of φ are discussed. This is graphically illustrated. Remarks have been added about the relation between the shape of the population of the sampling averages and the population from which the individuals are drawn, and about the difficulties which arise when the populations are non-Gaussian.     

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.     

Statistisch onderzoek van contrôle-analyse cijfers: (De verdeling van het droge stofgehalte van het brood tijdens de tweede wereldoorlog)

Summary  (Statistical investigation of the distribution of data for the solids of bread (in loaves analysed in the Food Inspection Laboratory in Amsterdam))
The distributions of the data of the solids of bread as analysed during the years of the war are investigated. The means and the standard deviations are calculated, also χ², kurtosis and skewness supposing the distributions to be normal. An example of calculation is given in table I. Actual numbers for different years are given in table II and in table III. The distributions were tested on normality because former investigations showed that the distribution of under survey prepared loaves did not deviate significantly from the normal.
It is found that generally the investigated distributions cannot be regarded as normal. Though symmetric they show leptokurtosis and the χ²-test for the goodness of fit of normal equation gives values of P 0,01 (or a little more). Similar distributions were found by Clancey¹⁾ in his investigation of numbers of chemical analyses of industrial products (about 10% of the distributions showed this shape, some 10% were truncated leptokurtic curves) and by us for the fat percentage of meals from the governmental eating-houses. The distributions are represented on probability-paper. This way of representing results gives a clear view of the variations of the mean and the standarddeviation in the course of the years (fig. 1). The deviations of the shape of the normal straight line on probability paper by special causes is investigated (fig. 3, fig. 4, fig. 5, fig. 6 to be compared with fig. 2). With this "spectrum" of possibilities of deviations from the normal distribution in mind the special cause for the leptokurtic shape in our special case has been discussed.     

Een systeem van kostenbeheersende productieplanning

In this paper a system of cost-controlled production planning is described. This system considers all kinds of costs associated with a production in phases (e.g. production of units, production of subassemblies, assembly) which may be affected by the planning, such as set-up costs, costs of transport, control, inventories, capacity and changes in capacity.
The mathematical model leads to a linear or mixed discrete-linear programming problem whose solution gives for each time period considered the size of the capacities which should be used and of the series of different products which should be produced. Practical recommendations are given for obtaining a sufficiently satisfying solution.     

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.     

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 x?_n tends to +∞ with probability 1 (see [4]). Sometimes x?_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.     

Het vergelijken van twee verschillende schatters voor een percentiel P van een normale verdeling

A comparison is made between two different methods to estimate the probability that a normally distributed observation is less than a certain value. One method is based on the binomial distribution, the other one on HALD'S maximum likelihood estimates of the parameters of a censored normal distribution. For large sample sizes a graph of the relative efficiency of these two estimates is constructed. A sampling experiment was performed in order to investigate for one particular situation the possible bias of HALD'S maximum likelihood estimate, which is only asymptotically unbiassed.     

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 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).     

De bewerking van de resultaten van veldproeven door herleiding van de opbrengstcijfers in beide richtingen van het proefveld

Summary  (The treatment of the results of field experiments by reducing the yields in two directions)
Ir J. J. Dijkveld Stol has shown that good results have been obtained by reducing the yields of field experiments both in columns and in rows.
The mathematical foundation of this method is discussed in the preceding article and it is shown, that the method gives good results if the same supposition may be made as necessary for the application of the methods of Fisher, Knut Vik and the method of the differences.
The variance of Dijkveld Stol's method is identical with Fisher's error variance.     

Een nomogram voor betrouwbaarheidsgrenzen van quantielen en overschrijdingskansen bij normaal verdeelde grootheden

A nomogram for confidence intervals and exceedance probabilities.
In this paper two problems are considered regarding the probability β that an observation on a normally (μ, σ²)-distributed random variable exceeds a given value W:

If μ and σ² are unknown, the two problems are as follows:
1)if Wis given, to determine a confidence interval for β and
2)if β is given, to determine a confidence interval for W.
For these two essentially equivalent problems graphs are given from which the confidence intervals can be determined. The graphs are given in terms of:

and are based on an approximation for the distribution of x¯ +k s .     

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.