摘要:

Polynomial smoothing to estimate the derivative of a large sequence of sampled data requires the proper choice of the degree polynomial and the smoothing interval. Linear and cubic polynomial smoothing are compared. It is found that a linear polynomial will produce nearly the same first derivative as a cubic polynomial if the linear smoothing interval is properly chosen. A formula for the proper choice of the smoothing interval is derived. The technique is applied to a problem in meteorology and consistent results obtained.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488820

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Estimation in nonlinear regression usually requires a considerable amount of computational work. If it is possible to linearize the original formulas, the linear regression is sometimes applied to transformed linear relations. The method of quasilinearized regression (first order approximation of nonlinear regression), comparable to linear regression, with respect to computational effort, is described in this paper. This method gives substantially better results than linear regression of linearized formula.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488821

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

A test is given for a general hypothetical regression of a random variableYon an independent variablexagainst an unknown general alternative regression, when replication is not possible. We make the usual assumptions of normality, independence of and constancy of variance of theYvalues.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488822

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

This paper presents a method for determining the shapes of two overlapping functionsf1(x) andf2(x) from an observed set of additive mixtures, [αif1(x) + βif2(x);i= 1, …,n), of the two functions. This type of problem arises in the fields of spectrophotometry, chromatography, kinetic model building, and many others. The methods described by this paper are based on the use of principal component techniques, and produce two bands of functions, each of which contains one of the unknown, underlying functions. Under certain mild restrictions on thefj(x), each band reduces to a single curve, and thefi(x) are completely determined by the analysis.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488823

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Bayesian methods are utilized to analyse the one-way random effect modelyij= μ +ai+eijin whicheijare assumed normal,N(0, σ2e), andaiare assumed to have a mixture of two normals, .95N(−.05ø(k– 1)σ, σ2) + .05N(.95ø(k– l)σ,k2ø2). It is shown by a moderately sized sample that inferences regarding σ2e= var (eij) are insensitive but those of σ2e= var (ai) are very sensitive to changes of the two non-normality parameters (k, ø). The data are also used to illustrate what inferences can be made about (k, ø). Further, for σ = 0 it is found in general that extreme observations have less importance in comparison to others in the posterior expectation of σ2e2. Finally, the ways of assessing the contributions fromaiandeiito the variation ofyijare considered.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488824

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Owen (1964) has developed tolerance limits based on the sample mean, x, and the sample standard deviation,s, which control percentages in each tail of the normal distribution. In this paper tolerance limits based on x and the rangeRor the mean rangeRg,rare developed. Tables of factors for the tolerance limits are given.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488825

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Sum and sum-of-product algorithms, some designed to minimize significance error, are compared and recommendations for usage are offered. A simplified method of rounding is presented and the benefit of using it demonstrated. Results are presented for the IBM 360 as well as the IBM 7040 computers with obvious application to some other machines.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488826

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488827

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

A conservative rule of thumb is derived for a quick calculation of the sample size needed to compare two groups. The rule is worked out for qualitative variables with a failure or success outcome. The rule is defined in terms of the difference desired to be detected between two dicotomous groups.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488828

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The distribution of the number of successes in a sample given the outcome of previous sample is obtained by Bsyesian methods. It is shown that the solution the prediction problem is completely independent of population size.

ISSN:0040-1706    

DOI:10.1080/00401706.1971.10488829

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor