摘要:

Npoints are independently drawn from the uniform distribution on (0, 1). Denote byE(n|N; p), the event: There exists a subinterval of (0, 1) of lengthpthat contains at leastnout of theNpoints. We find the probability,P(n|N; p), ofE(n|N; p) forn>N/2 in terms of simple tabulated quantities.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480810

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Two exact tests are presented for testing the hypothesis that the residuals from a least squares regression are homoscedastic. The results can be used to test the hypothesis that a linear [ratio] model explains the relationship between variables as opposed to the alternative that the ratio [linear] specification is correct. The first test is parametric and uses theF-statistic. The second test is nonparametric and uses the number of peaks in the ordered sequence of unsigned residuals. In conclusion, the results of some experimental calculations of the powers of the tests are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480811

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

In this paper the robustness of some of the existing tests for the exponential distribution when some outliers are present is reviewed. It is noted that the tests proposed by Epstein and Sobel [4] can be used without any major modification in the presence of outliers and a more suitable flexible test criterion is proposed for the exponential lower limit which is superior to Carlson's statistic [2] in all situations. The distribution of this statistic is derived and tables are constructed to facilitate the use of this statistic. Also some tests for outliers in the exponential case are proposed.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480812

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

An estimation procedure, called the “partial totals” method, is presented, illustrated and evaluated for the modely=exp(-pt)+ewhen the values oftare equally spaced. Tables of estimates using this estimation procedure are given for the case where the smallest value oftis zero. The evaluation consists of an analytical investigation of the large sample properties of the partial totals estimator and a report on a comparative study of its small sample properties relative to three other estimators based on Monte Carlo results where it is assumed either thatyis a binomial proportion or thatyis a proportion with variance proportional to a binomial variance.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480813

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Various methods based on Studenttvariates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariatetdistribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480814

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Two simple inequalities involving two parameters, expected terminal losses (expected losses due to wrong decisions), expected sampling losses, and optimal (Bayes) and non-optimal sample sizes are shown to hold for several fixed sample size decision problems. The two parameters depend on the type of loss structure assumed. One inequality relates to the division of total expected losses for a sample of optimal size between expected terminal losses and expected sampling losses. The other inequality gives upper bounds on the ratio of total expected losses at non-optimal sample sizes to those at the optimal sample size. The latter inequality shows that total expected losses are often quite insensitive to the use of non-optimal sample sizes; in conjunction with optimal sample size formulas, it can be used to show that total expected losses are also insensitive to the use of a “wrong” prior distribution or the wrong cost parameters.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480815

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

A Bayes solution is supplied for an estimation problem involving a sample from a multivariate normal population having an arbitrary unknown covariance matrix, but a vector mean whose components are all equal. Assuming that a particular unnormed prior density is a convenient expression for displaying prior ignorance, it is then demonstrated that a posterior interval for this common mean can be based on Student'stdistribution. If prior information can be conveniently represented by a natural conjugate prior density, the posterior interval will also depend on Student'st.An extension is made to the case of estimating the constant difference between two parallel profiles.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480816

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

In this paper we review the derivation of the predictive density function for the normal multiple regression model, state and prove a general theorem on optimal point prediction, and show how the predictive density can be employed in the analysis of an illustrative investment problem. Then we derive the predictive density function for the multivariate normal regression model and indicate how it can be used in the analysis of several problems.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480817

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

A selected group of 1950 SMA's are examined to determine the extent to which they comprise self-sufficient trading areas with respect to local service activities. By comparing the self-sufficiency of each SMA to the self-sufficiency of its urbanized area and of an areal unit made up of the SMA plus contiguous counties, the quality of each SMA is evaluated. Each SMA is classified as being either overbounded, underbounded or truebounded. The type of boundary discrepancy exhibited by an SMA is strongly related to its degree of proximity to other SMA's and is unrelated to its population size.

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480818

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor

摘要:

Horvitz and Thompson [3] have suggested for the estimation of population characteristic certain classes of linear estimators depending on weights associated with the sample observations, when a sample of sizenis drawn without replacement using arbitrary probabilities of selection for each draw. However, it should be observed here, that there might not exist even a single linear unbiased estimator for the class which is termed an empty class. A situation arises where the minimum variance linear unbiased estimator for the non-empty class depends on the population values. In such a case, the criterion of the ‘necessary best estimator’ is proposed, in order to choose a serviceable estimator purely from the practical point of view. This is illustrated by one of the classes of linear estimators (T5).

ISSN:0162-1459    

DOI:10.1080/01621459.1965.10480819

出版商:Taylor & Francis Group    

年代:1965

数据来源: Taylor