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 mathematisch model voor een reserveringsprobleem

A mathematical model for a booking problem
Air companies have several problems in connection with booking. Clients may book for a certain flight some time in advance and are also allowed to cancel their bookings.
As a result of this it is possible that an airplane leaves with some places empty or that the company, expecting some clients to cancel their booking, has sold to many places.
In both cases losses are the result. In this paper a booking policy that minimizes the expected losses is developed.     

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 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 model voor discreet verdeelde grootheden met negatieve correlatie

Summary
A model for negatively correlated variables.
A mathematical model is described with which a bivariate distribution of two negatively correlated binomially distributed variables can be constructed. Let be given a vase with W white, Z black and R red balls; N = W + Z + R; P1= W: N;P2 = Z: N.
Let be drawn a random sample with replacement of n balls. Let be w = number of white en z = number of black balls; w + z < n. Then and are binomially distributed variates, correlated according to (1).
At the end of the paper the author formulates the following statistical problem: let be drawn a finite number of times () such random samples of n balls. The pairs w, z furnish a correlation coefficient r, which itself is a stochastical variable. How is the distribution of? In particular what are the expectation (, N) and the standard deviation (k, n, N)     

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 .     

Een simpele grafische iteratiemethode voor het schatten van een betrekkingtussen kwantitatievestochastische variabelen.

A simple graphical iteration procedure for estimating a relation between quantitative stochastic variables.
For the estimation of a relation which will predict values of one stochastic variable from known values of a number of other ones, a simple graphical iteration procedure, applicable under rather general conditions, is demonstrated by means of an example. The method amounts to plotting the values of the dependent variable against one (or one pair) of the initial variables, after correction for the influences of the other initial variables as far as these have already been estimated. An approximation (or improved approximation) for the influence of the variable considered can then be made.     

Maxima voor de eenzijdige overschrijdingskans en voor de grootte van de gemiddelde overschrijding bij discontinue en continue, eentoppige verdelingen

The well-known inequality of Bienaymé-Tschébyschef (for short B-T), generalized by Camp and Meidell (for short C-M) for continuous, unimodal distributions gives specific limits for total probabilities outside the ± to limits.
In many cases however, especially in the field of industrial applications we are interested only in the probability of one tail of the distribution, which of course must be smaller than the limits given by the B-T and C-M formula.
For these cases the maximum probability of surpassing the to limit on one side equals under B-T conditions and under C-M conditions instead of the two-sided values of 1/t² and 47/9 · 1/t² respectively (cf e.g. Uspensky: "Introduction to mathematical probability", 1937, p. 198) These results set upper limits for the value of

Alternatively we may also set an upper limit for the integral

which measures in terms of σ the average amount by which the limit + tσ is exceeded. This problem is also discussed and under C-M conditions an upper limit

is derived.
Some practical applications of these results are considered.     

Een steekproef ter vaststelling van de verdeling van de hoenderstapel

A sample estimate of the poultry distribution
In 1954 a sample survey was carried out of the returns of the agricultural census, May 1954, in order to establish the distribution of the number of holdings and the number of poultry, by size-group of arable land and by size-group of number of poultry. A simple 10 per cent, sample was planned and the expected variances of the numbers of poultry in each size-group were estimated beforehand. The method of estimation is indicated in this paper. This resulted in comparatively high relative errors in the size-groups above 500 hens and also in the size-groups of arable land. Therefore holdings with 500 hens and over were enumerated completely. Some tests were performed with the sample results and finally the efficiency of the stratification is discussed.     

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.     

Tabellen en nomogrammen voor het onderscheidingsver-mogen van de 5% en 10%-F-toets voor het gebruik bij de gewarde blokkenproef

Tables and graphs of the power of 5% and 10%-F-tests for use in randomized block experiments.
As randomized block experiments occur so often in agricultural and other research, it was thought worth while to adapt existing tables of the power of 5% F-tests for this special case: The author hopes that in this way the design of experiments in terms of power will be facilitated. Moreover new tables were computed for the power of 10%-F-tests.
The tables have been summarized in graphs that greatly facilitate their use. Illustrations are given in practical problems.     

Een indelingsprobleem

Summary  A branch and bound algorithm is given to solve the following problem: To each pair of elements (i,j) from a set X ={l,…, n } a number r _ij with r _ij≥ 0, r _ij= r _ij and r _ij= 0 has been assigned. Find a prescribed number of disjoint subsets P ₁…, P _m from X , such that

Experiments indicate that an optimal solution is usually found in a small number of iterations, but the verification may be rather time consuming.
The algorithm may be used to find the minimum value of m for which a partitioning of X with z = 0 exists. The algorithm appears to be efficient for finding this 'chromatic number of a graph'.     

Een smaak-onderzoek

A comparison has been made between three designs for flavor testing. In the test-situation even a flavor-difference which might be noticed by only a few people was of practical importance. In addition not only the unjustified rejection of the null hypothesis (no flavor-difference), but also the unjustifed rejection of the alternative hypothesis might have important practical consequences.     

Een indelingsprobleem

Summary A branch and bound algorithm is given to solve the following problem: To each pair of elements (i,j) from a set X={l,…, n} a number r_ij with r_ij≥ 0, r_ij=r_ij and r_ij= 0 has been assigned. Find a prescribed number of disjoint subsets P₁…,P_m from X, such that Experiments indicate that an optimal solution is usually found in a small number of iterations, but the verification may be rather time consuming. The algorithm may be used to find the minimum value of m for which a partitioning of X with z= 0 exists. The algorithm appears to be efficient for finding this ‘chromatic number of a graph’.     

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.