摘要:

“Nothing is more uncertain than the length of a given human life; nothing is more certain than the solvency of a life assurance company

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00612.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.tb00613.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.tb00614.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary The identity of least squares estimatorsåand maximum likelihood estimatorsâis studied in non‐linear models of the typez=g(a), wherezare observable quantities with a probability density functionpr(z). This identity was proved for independent random variableszand for distributionspr(z), of which the arithmetic sample mean is an optimal est

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00615.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary Many books about probability and statistics only mention the weak and the strong law of large numbers for samples from distributions with finite expectation. However, these laws also hold for distributions with infinite expectation and then the sample average has to go to infinity with increasing sample size.Being curious about the way in which this would happen, we simulated increasing samples (up ton= 40000) from three distributions with infinite expectation. The results were somewhat surprising at first sight, but understandable after some thought. Most statisticians, when asked, seem to expect a gradual increase of the average with the size of the sample. So did we. In general, however, this proves to be wrong and for different parent distributions different types of conduct appear from this experiment.The samples from the “absolute Cauchy”‐distribution are most interesting from a practical point of view: the average takes a high jump from time to time and decreases in between. In practice it might well happen, that the observations causing the jumps would be discarded as outlying obser

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00616.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary Controlling is intervening in a situation on the basis of measurements. The three elements occurring in this definition may each contain an uncertainty that sets a limit to the control efficiency:Themeasurementsmay be in error owing to both inaccuracies and sluggishness of the measurements. Proper and rapid data‐processing is essential therefore.Theinterventionsmay lose part of their effect through over‐determinancy or dynamically unfavourable (sluggish) responses. In either case statistical calculations disclose the average control errors that are liable to be made, and also the way in which these can be minimized.Thesituationmay be unclear, i.e. the static and dynamic process characteristics are insufficiently known. In such cases regression and correlation techniques may aid in finding a solution.Following a general review, we shall discuss in more detail those aspects that are bound up with the dynamics of the phenomena. Arguments from information theory reveal that the dynamic efficiency of control actions depends on correlation functions of time series (disturbances) and response curves of the systems (processes). The effects of disturbance correlation time, disturbance variance, sampling time, sample treatment, measuring errors, measuring time, rapidity of the intervention, etc., on the efficiency are elucidated by means of some formulae, graphs and exa

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00617.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Summary The known results of optimal allocation in two‐stage simple random sampling with stratification from finite population are generalized for J‐stages. The optimalization is treated by minimizing the cost function for given variance as well as by minimizing the variance for given cost. It turns out that for both cases the optimal values differ only for the first‐stage units and are the same for all the subsequent. The general formula for minimum variance of the unbiased estimator of the population mean per element i

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00618.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.tb00619.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY

摘要:

Book reviewed in this article:Convex transformations of random variables, W. R. VAN ZWETHypothesis Testing Problems with the Alternative Restricted by a Number of Inequalities, W. SCHAAFSMAStochastic Processes, E. PARZEN, Holden‐DayApplied Queueing Theory, A. M. LEE, MacMillanRecent Advances in Mathematical Programming, edited by R. L. GRAVES and PH. WOLFEExercises in probability and statistics, N. A. RAHMANDie Monte‐Carlo‐Methode und ihre Verwirklichung mit elektronische Oigitalrechner, N. P. BusLENKO and J. A. SCHREIDER, B. G. TeubnerMonte Carlo Methods, J. M. HAMMERSLEY and D. C. HANDSCOMBThe art of simulation, K. D. TOCHEREntscheidungskriterien bei Risiko, H. SCHNEEWEISSNumerical models of economic development, A.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1960.tb00620.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.tb00621.x

出版商:Blackwell Publishing Ltd    

年代:1968

数据来源: WILEY