摘要:

Summary “Stratificationprocedures for a typical auditing problem”.During the past ten years, much experience was gained in The Netherlands in using random sampling methods for typical auditing problems. Especially, a method suggested by VAN. HEERDEN [2] turned out to be very fruitful. In this method a register of entries is considered to be a population ofTguilders, if all entries total up toTguilders. The sample sizen0is determined in such a way that the probability β not to find any mistake in the sample, if a fractionp0or more ofTis incorrect, is smaller than a preassigned value β0. Son0should satisfy (l‐p)n0≤β0forp≥p0. A complication arises if it is not possible to postpone sampling until the whole populationTis available. One then wants to take samples from a population which is growing up toT. Suppose one is going to take samplesnifrom e.g.rsubpopulationsUsing the minimax procedure, it is shown, that in this case one should choose the sizesniequal to (Ti/T)n0. The minimax‐value of the probability not to find any incorrect guilder in thersamples, taken togethe

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00628.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary The output voltage of a detector circuit containing a gas‐filled tube sensitive to ultraviolet radiation can be used to indicate whether a flame is still burning or not. As long as the flame is burning the random nature of the discharges of the tube leads to random fluctuations in the output voltage, which can be considered as a Markov‐process with dependent increments. The problem is to select an alarm level for the output voltage with a suitable chosen probability of exceedance while the flame is burning, in order to limit the probability of false alarm. In this article a method is given for determining upper and lower bounds for the distribution function of the output voltage at any moment, answering the question of the alarm level to be chosen. Results are given for a special ci

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00629.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary ABRAHAM DE MOIVRE (1667 Vitry ‐ 1754 London) was one of the foremost pioneers in the domain of the theory of probability. His principal contributions are laid down in his “Doctrine of Chances” (three editions, 1718, 1738, 1756). This classic work, almost forgotten, is now republished, as a splendid photographic reprint of the third (last) edition, by Chelsea Publishing Company of New York (1967).In this article we specially mention his original contributions respecting the problem of the duration of play, the theory and application of recurrent series, the theory of runs, and especially his extension of the value of BERNOULLI'S theorem by the aid of STIRLING'S theorem.In the last mentioned research DE MOIVRE obtained the equation for the curve of error, thus antedating LAPLACE by about 50 and GAUSS by 76 years. This important fact is discovered by KARL PEARSON

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00630.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

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 expressionOf 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 compu

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00631.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary Quarterly figures may be required when only a sequence of annual totals is available. This article presents two reasonable methods for “interpolating” quarterly figures by means of appropriate minimizing procedures.The first method relates to minimizing the sum of squared second differences of the quarterly figures, the other one is a linear programming procedure which refers to the absolute second differences. Both methods are illustrated by a numerical example, the first one giving somewhat better re

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00632.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary A table and a nomogram are given to find the growth rate of a regression line drawn on so‐called semi‐logarithmic graph paper. The growth rate is determined by: a) the slope of the regression line, b) the length ratio between the logarithmic and the metric unit, in other words, the number of years on the time axis (if a year is the time unit) corresponding in length to one cycle on the logarithmic axis (say, 1 to 10, or 100 to 1000). With an example, the use of the table and nomogram is expl

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00633.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary “Simple estimation of the parameters of the logistic curve.”By means of an appropriate transformation of the dependent variableYtinto a simple function ofYt, 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 pres

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00634.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00636.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Book reviewed in this article:Slippage tests, R. DOORNBOSMarkov Processes and Potential Theory, Proceedings of an Advanced Symposium Conducted by the Mathematics Research Center, United States ArmyVarianzanalyse, HEINZ AHRENSJoint Statistical Papers of J. Neyman and E. S. PearsonA Selection of Early Statistical Papers of J. NeymanStatistical Methods in Engineering Experiments, E. M. BARTEEÖkonometrische Prognosen, G. MENGESPapers on National Income and Allied Topics, Vol. III, edited by N. S. R. SASTRY, V. M. DANDEKAR, S. G. TIWARI and UMA DATTADie Messung des technischen Fortschritts im Rahmen des gesamtwirtschaftlichen Wachstums‐prozesses, FLORIAN H. FLECKSurrey Sampling, LESLIE KISHHandbook of mathematical psychology, Vols. I, II and III, R. DUNCAN LUCE, ROBERT R. BUSH and EUGENE GALANTERReadings in mathematical psychology, Vols. I and II, R. DUNCAN LUCE, ROBERT R. BUSH and EUGENE GALANTER (Ed

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00637.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00638.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY