摘要:

SummaryPlayingAgainstNature.Human activity implies making decisions under partly unknown circumstances but backed by former experience.Modern theories of mathematical statistics enable us in certain cases to determine among all decisions under consideration those which have the greatest chance to lead to a given end. This is achieved by considering human activity as a combined game of brains and chance, with “nature” as a fictitious opponent.Though excessive mathematical difficulties are as a rule prohibitive for complete calculations, we nevertheless get a better idea of what the words “rational behaviour” stand for. In many cases, where a sufficient quantity of information in the form of statistical material is available, it is possible to arrive at concrete results. In particular this is the case when economic factors prevail; at the same time the statistical theory of testing hypotheses can be seen in a broader aspect.This paper, read at the Meeting of the “Vereniging voor Statistiek” on March 6, 1925, gives an elementary exposition of some of the principles of Wald's theory of Decision Functions and Von Neumann and Morgenstern's Theory of Games and Economi

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00583.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

SummaryAn application of the occupancy theory on a coding problemFor large scale registration of certain medical phenomena it is very useful to have the disposal of a coding system which enables the reconstruction of the code number of a given person at any moment from the smallest possible number of personals. For this purpose, place and date of birth and sex may be used. These items, however, are not sufficient as they do not permit to distinguish between persons of the same sex, born at the same day in the same place. For Amsterdam this number is about 20. Therefore the Inspector of Public Health considered the possibility of including the birthday of the mother in the data and requested the Municipal Bureau of Statistics of Amsterdam to estimate the percentage of duplications which would occur when this enlarged system of personals were used. A special investigation for September 1951 turned out a rate of 10% which seemed to be rather high even if the number of twins for which duplications by their very nature would occur was taken into account. So it became interesting to know which rate theoretically might be expected.If we suppose the birthdays of the mothers of the persons born on the same day and in the same place to be evenly distributed over the days of the year, it is easy to calculate the expected number of duplications.We are then led to consider the following occupancy problem: n objects (number of births on a given day) are distributed over N places (possible birthdays of the mothers), the probability to occupy a certain place is the same for all objects and independent of the place. What is the probability that noplaces will be empty, n1occupied by only one object, n2by two objects etc.? It is shown that this probability is equal toFrom this formula the expectation and the variance of the number of persons with equal code numbers can easily be derived.The empirical results for 4 different months of 1951 (including the already mentioned month of September) proved to be in good agreement with these theoretical calculations.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00584.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

SummaryParametric and non‐parametric methods and their applicationsThe rapid development of non‐parametric methods in statistics raises the question of the difference between these methods and the classical parametric methods and of their different fields of application. This paper, read at a meeting of the “Vereniging voor Statistiek” on March 6, 1952, attempts to throw some light on this problem by means of two examples. A short exposition of an application of the method of moments of K. Pearson to the estimation of a population is given for a case, where this method is quite adequate and where it would be difficult to find an equally adequate parameterfree method. On the other hand a method of determination of histamine in human blood is described, which is based on an application of the method of m rankings of M. Friedman and M. G. Kendall. In this case the transition from the classical methods to parameterfree methods constitutes a real gain in rigour and eff

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00585.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

SummaryTwo lectures on Wilcoxon's two sample test.This is an account of two lectures on Wilcoxon's parameterfree two sample test, held by H.R. van der Vaart en Prof. D. van Dantzig, for the mathematical statistic's section of the „Vereniging voor Statistiek”. Van der Vaart discussed the results of his studies about the power function of the test for very small samples, comparing it with the power function of Student's test. These results have been published completely in [1]. Although Wilcoxon's test is far more general than Student's test, its power is only slightly less. Prof. Van Dantzig then discussed the consistency of the test, indicating an exhaustive class of alternative hypotheses for which the test is consistent. These results have been published in

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00586.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00587.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00588.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY

摘要:

Book reviewed in this article:The Exchange Stability Problem, dr G. StuvelOntstaan en ontwikkeling van de spanning tussen lonen en prijzen, dr G. van der WalDe Juiste Maat, J. Sittig, en Prof. Dr H. FreudenthalSequential Analysis, A. Wald†First course in Probability and Statistics, J. NeymanAn introduction to probability theory and its applications, Vol. I, W. FellerIndexnumbers, Bruce MudgettStatistical Thermodynamics, R. H. Fowler&E. A. Guggenhe

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1951.tb00589.x

出版商:Blackwell Publishing Ltd    

年代:1951

数据来源: WILEY