摘要:

This paper is concerned with the estimation of the parameters of a mixed-exponential response law, given some sample observations. Two alternative laws are considered, each having two parameters. The first law expresses the proportionF(t) of the population who have responded within timetin the form

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480640

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

This paper presents an extension of the mathematical model used to justify accident proneness. It assumes that the distribution of accidents incurred by an individual in non-overlapping intervals is a correlated bivariate Poisson (C.B.P.). On compounding this correlated bivariate Poisson through a Gamma distribution an extended bivariate negative binomial or, more precisely, a compound correlated bivariate Poisson (C.C.B.P.) distribution is obtained. Recurrence relations and expressions for the required probabilities are illustrated for two sets of data. The C.C.B.P. proved to fit as well as the bivariate negative binomial when the estimate of B12was close to zero, and much better than the latter distribution when the estimate of B12 was not close to zero.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480641

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

Expectational data on manufacturers' inventory investment and sales are analysed. These data are provided byFortuneMagazine's survey of corporations. It is found that firms tend to underanticipate investment changes and that entrepreneurs tend to be conservative in anticipations when economic conditions are depressed and less conservative when conditions are favorable. A theory of investment behavior is then derived and two realization functions are tested, one assuming perfect competition and cost minimization and the second assuming profit maximization and an oligopolistic market. The second performs best. Certain ex ante and ex post estimating forms are tested; the ex post form yielding excellent statistical results with real inventory stock as dependent variable involves the explanatory variables of real unfilled orders, real sales and a distributed lag variable. A major conclusion is that theFortuneex ante data appear to be only marginally useful in explaining inventory investment; and until observation errors are substantially reduced (inter alia), the marginal work units involved in using this data may not be warranted. A positive conclusion is that the real unfilled order variable appears to be highly useful.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480642

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

This paper discusses a multiple-regression chain-index technique for the construction of an index of quality change, and illustrates its feasibility by reference to a price index for automobiles. The interaction of our quality index with the usual Laspeyre type price index is studied. It is demonstrated that the quality index suggested bears the same relationship to a constant-satisfaction index as does an ordinary price index, and that this index is an appropriate deflator for the CPI.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480643

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

The expected length of a confidence interval is shown to equal the integral over false values of the probability each false value is included. Thus two desiderata for choosing among confidence procedures lead to the same measure of desirability. Furthermore, by common definitions of “optimum,” a procedure is optimum as regards including false values if and only if it is optimum as regards expected length. However, the procedure with minimum expected length ordinarily depends on the true value of the parameter. The possibility is explored of minimizing the average expected length, averaging according to some weighting on the possible parameter values. (This is not the same as assuming a prior distribution and using Bayes' Theorem.) The ideas are applied to the mean and variance of a normal distribution and the probability of success in binomial trials.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480644

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

Religious, demographic, and economic data gathered on three Survey Research Center studies have been analyzed by major religious groups. The analysis indicates only slight differences in sex composition, marital status, and age structure among Protestants, Roman Catholics, and Jews except for a middle-aged concentration among Episcopalians and Presbyterians. People who report they are without a religion are heavily male and have a larger percentage single than does the nation as a whole. The number of children in Jewish, Episcopalian and Presbyterian families is similar, but smaller than the number in the other religious groups. On education, occupation, and income, the religious groups can be separated into three descending ranks: (1) a top-rank, having large percentages of college graduates and white collar workers, and enjoying high incomes, composed of Episcopalians, Jews, and Presbyterians; (2) a middle rank, containing smaller percentages of college graduates and white collar workers, and earning less income, consisting of Methodists, Lutherans, Roman Catholics, and the “no religion” group; (3) the bottom ranked Baptists with few college graduates or white collar workers and low family incomes.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480645

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

The Final Report contains only two assertative conclusions: A(1) that commercial cloud seeding in mountainous areas produced 10–15 per cent increase in precipitation, and A(3) that no seeding project meant to increase precipitation was found in which the indicated effect of cloud seeding was negative. With reference to A(1) evidence is introduced showing that the apparent 10–15 per cent increase in precipitation is likely to be due to a combination of factors other than cloud seeding. Conclusion A(3) was found inconsistent with some of the Advisory Committee's own findings and with some other published results. Section 8 indicates that a Bayes decision rule whether to seed or not, published in Volume II of the Final Report as minimizing the risks, may well maximize these risks. Section 9 indicates a misrepresentation and a significant omission in Volume II of the Final Report.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480646

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

A discussion is given of point estimates and interval estimates of the population standard deviation σ, based on the sample range and quasi-ranges. In the case of a rectangular population, the efficient point estimate and the most effective interval estimates are those based on the sample range, so it is not necessary to consider estimates based on sample quasi-ranges. The coefficients of the sample rangewin the exact confidence bounds for the population standard deviation σ are found by taking the reciprocals of percentage points of the (standardized) rangeW = w/σ. A six-decimal-place table of percentage points for the range corresponding to selected cumulative probabilities and sample sizes is presented. A second table shows coefficients of the sample range in exact lower confidence bounds.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480647

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

Some congruential pseudo-random number generators are shown to be subject to sub-periods or harmonics whose effect is to constrain the variability of the numbers generated. An experiment with such a generator produced a long sequence whose variance was significantly less than the theoretical value.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480648

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

The asymptotic unbiasedness and normality of alternative statistical estimators θ, θ,1··· of a given parameter θ* are generally proved without reference to any explicit knowledge of the exact finite sample distribution functions,Fn(x),Gn(x) ···. (Herendenotes sample size.) Within the class of asymptotically unbiased and normally distributed estimators of a given parameter it is sometimes possible to demonstrate that one estimator possesses a smaller asymptotic variance than another, or that one estimator possesses the smallest asymptotic variance within a particular subclass. Asymptotic theory obviously does not predict anything about finite sample distribution functionsFn(x), Gn(x) ···. In particular we cannot deduce from asymptotic theorems that the estimator with the smallest asymptotic variance will continue to exhibit the smallestdispersionin finite samples. Consequently it remains an essential task in positive estimation theory to derive the exact finite sample distribution functions of the alternative estimators that appear to be promising on the basis of asymptotic considerations.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480649

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor