摘要:

The words “indeterministic study” are used to designate research aiming to determinehow frequentlya quantityXcharacterizing the phenomena considered assumes its various particular values. If the purpose of research is to establish the exact value ofXas a function of other variables, then this research is “deterministic.” In the history of indeterminism in science four (overlapping) periods are discernible.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483363

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

The hypothesis that market growth leads to reduced sellers' concentration is presented and briefly elaborated. Then, after an evaluation of the data, they are used to make a direct and an indirect test of the hypothesis. In the direct test, a negative relationship is found between concentration change and market growth, both for aggregate changes and for those of individual markets. In the indirect test concentration change is found to be related to the increasing importance of multi-product plants in a fashion that implies that the increased diversification of companies, rather than that of their plants alone, has brought lower levels of product concentration. Both tests lend positive though not conclusive support to the hypothesis.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483364

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

In the estimation of econometric simultaneous equations models, hypothesized necessary conditions for the identifiability of a single equation usually specify the exclusion of a number of variables from the structural equation in question. If the pre-determined variables are completely exogenous, if the disturbances in the equations are jointly normally distributed, and if a moderately high degree of precision can be obtained in reduced-form estimation, then the exact finite sample distribution of the generalized classical linearidentifiability test statisticcan be closely approximated by Snedecor'sFwith appropriate degrees of freedom.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483365

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

The efficiency (measured in terms of ratio of average sample size to fixed sample size) of the Wald sequential probability ratio test relative to the best competing fixed sample procedure for testingH0:θ = θ0versusH1:θ = θ1(θ0< θ1) whenXis distributedN(X|θ, σ2) with known σ1is studied for fixed (θ, θ0, θ1) as the specified probabilities of error, α (the probability of rejectingH0when θ = θ0) and β (the probability of acceptingH0when θ = θ1), approach zero. The limit is shown to depend on the relative rates at which α and β approach zero in a prescribed manner. In particular, whenaα= β(a> 0) this limiting relative efficiency is equal to (θ1– θ0)/(4|θ1+θ0− 2θ|). The practical implications of this result are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483366

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

A methodological survey of statistics on internal migration used in the new enlarged edition ofHistorical Statistics of the United States. No one body of materials gives a complete picture but much can be pieced out from the essentially complementary series that exist: the state-of-birth data of the decennial censuses, 1850–; the special migration reports of the 1940 and 1950 censuses; the annual migration estimates of the Current Population Survey, 1947–; and the Department of Agriculture's annual estimates of migration to and from farms, 1920–. An additional important series can be derived from census age-sex-color-nativity distributions by survival methods. All such estimates are inexact but important migration streams are clearly delineated and the margin of error is probably less than that of most economic series to which they are related.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483367

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

A bivariate distribution is not determined by the knowledge of the margins. Two bivariate distributions with exponential margins are analyzed and another is briefly mentioned.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483368

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

A simple exact formula for the variance of the product of two random variables, say,xandy, is given as a function of the means and central product-moments ofxandy. The usual approximate variance formula forxyis compared with this exact formula; e.g., we note, in the special case wherexandyare independent, that the “variance” computed by the approximate formula is less than the exact variance, and that the accuracy of the approximation depends on the sum of the reciprocals of the squared coefficients of variation ofxandy. The case wherexandyneed not be independent is also studied, and exact variance formulas are presented for several different “product estimates.” (The usefulness of exact formulas becomes apparent when the variances of these estimates are compared.) Whenxandyare independent, simple unbiased estimates of these exact variances are suggested; in the more general case, consistent estimates are presented.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483369

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

LetT1andT2be two odd location statistics, such as the sample mean and the sample median. LetS1andS2be two even location-free statistics, such as the sample variance and the sample range. When sampling from a symmetric distribution, it is proved that the conditional expectation of either odd location statistic, given the even location-free statistics, is equal to θ, the midpoint of the distribution. This implies that if the random weightsW1andW2are functions of even location-free statistics so thatW1+W2= 1, thenW1T1+W2T2is an unbiased estimator of θ.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483370

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

A new way of approximating the hypergeometric distribution with a binomial is described which is obtained by equating the mean and variance of the binomial to those of the hypergeometric distribution. The paper gives several examples which show the approximation to be much more accurate than the usual binomial.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483371

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor

摘要:

A problem which often arises in connection with the determination of probabilities of various miss distances of bombs and missiles is the following: Letxandybe two normally and independently distributed orthogonal components of the miss distance, each with mean zero and with standard deviations σxand σy, respectively, where for convenience one labels the components so that σx≥σy. Now for various values ofc= σy/σx, it is required to determine (1) the probabilityPthat the point of impact lies inside a circle with center at the target and radiusKσx, and (2) the value ofKsuch that the probability isPthat the point of impact lies inside such a circle. Solutions of (1), forc= 0.0(0.1) 1.0 andK= 0.1 (0.1) 5.8, and (2), for the same values ofcandP= 0.5, 0.75, 0.9, 0.95, 0.975, 0.99, 0.995, 0.9975, and 0.999, are given along with some hypothetical examples of the application of the tables.

ISSN:0162-1459    

DOI:10.1080/01621459.1960.10483372

出版商:Taylor & Francis Group    

年代:1960

数据来源: Taylor