摘要:

This paper considers the use of rank sums from a combined ranking ofkindependent samples in order to decide which populations differ. Such a procedure is suggested as a convenient alternative to making separate rankings for each pair of samples, and the two methods are compared. Asymptotic use of the normal tables is given and the treatment of ties is discussed. A numerical example is given.

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490181

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

Experimental plans are presented for split plot experiments in which the whole plot treatments and the split plot treatments each consist of combinations of two-level factors. The technique of split plot confounding, whereby interactions among split plot factors are confounded with various whole plot contrasts, is utilized to construct some full and fractional replicate plans.

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490182

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

Letx1,x2, …xn, … be a sequence of independent random variables with a common density functionP(x= 1) =p,P(x= 0) = 1 –p, 0 <p< 1. This paper considers the non-randomized sequential procedures δ's for estimatingpand the following three problems on choice of δ. (i) Choose δ to minimizeEv(Zδ–P)2subject toEpNδ≤mwherem≥ 1 andZδis an unbiased estimate ofp; (ii) Choose δ to minimizeEpNδsubject toEp(Zδ–p)2≤ α where α is a real positive number; (iii) choose δ to minimizeCEpNδ+Ep(Zδ–p)2whereCis the cost of an observation. In each case the minimization is to be done uniformly inpif possible; otherwise the supremum overpof the risk in question is to be minimized. A procedure is constructed for problem (i) whenmis not an integer. A fixed sample size procedure is shown to be admissible and minimax for problem (ii). A procedure is constructed which is asymptotically uniformly better than the fixed sample size for problem (ii). Furthermore, for problem (iii) some optimum procedures are constructed.

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490183

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490184

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

A shot noiseX(t) is a superposition of impulses occurring at timestj, where theTjfollow a Poisson point process. For the case of a rectangular impulse function (height a, length b) the cumulant generating function of the sample meanM(T), (2), is obtained, also the mean and variance of the sample varianceV(T), (3). This, together with the covariance ofVandM, is used to calculate the standard error of the coefficient of dispersionV/M. An approximate distribution is conjectured forI(T) =V(T)/aM(T) and based on it, percentage points of this statistic are given. They could be used to test the hypothesis that a given noise is shot noise. An application to a textile problem is described.

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490185

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

In a general non-destructive testing situation involving variables data, several “instruments” are used to measure the same characteristic. “Instruments” may refer to different measuring devices, or possibly to different operators using the same device.

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490186

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

For a one-parameter negative exponential population, reasonably good interval estimates of the parameter σ may be obtained from one suitably chosen order statistic. The coefficients of themth order statisticxmin exact confidence bounds for σ are found by taking the negative reciprocals of the natural logarithms of percentage points of the Beta distribution. The interval between exact lower and upper confidence bounds, each associated with confidence 1 –P, is, of course, an exact central confidence interval (confidence 1 – 2P). Results have been computed for several values ofm, clustered about the value which yields the most efficient point estimator, for sample sizen= 1(1)20(2)40 andP= .0001, .0005, .001, .005, .01, .025, .05, .1(.1).5. The definition of efficiency commonly used for point estimators is extended to confidence bounds and confidence intervals. The following tables are included, together with a description of the method of computation and a brief discussion of possible uses: (1) a table of upper confidence bounds and central confidence intervals for σ, based on one order statistic, together with their efficiencies, for that value ofmwhich maximizes the efficiency of the upper confidence bound, for each combination ofnand 1 –Pand (2) a similar table for that value ofmwhich maximizes the efficiency of the central confidence interval, when the two values ofmdiffer. A numerical example is also given.

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490187

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490188

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490189

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1964.10490190

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor