摘要:

Why do results obtained by different investigators characteristically disagree by more than would be expected by their estimates of uncertainty? Youden notes that everything gets changed in another laboratory, whereas the investigator can (or does) make only minor changes within his laboratory. The message of this paper—that only those bounds for uncertainty based on actual measurement will endure—is already beginning to have an impact on physical measurement. Designed experiments to estimate bounds to systematic error will replace fallible judgment based on feelings and not observation.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488878

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

Randomization, often specified as an indispensable requirement in experimental design, is required only when the order or position of the experimental unit influences the performance of the unit. Randomization, when required, may give an arrangement that is obviously undesirable and one that may doom the particular experimental program. A system of constrained randomization is proposed that eliminates the undesirable arrangements without sacrificing the customary gains achieved by randomization.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488879

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

Suppose one wants numerical estimates for the moments of the distribution of a responseXwhich is a function of the statistically independent random variablesyk,k= 1, 2, …,n, when theykare from known distributions. The functional relationship betweenXand theykis assumed to be known in the generalized sense that for given values of theykthe responseXmay be obtained somehow, e.g., by experiment., by engineering calculations, by analog. The same problem was considered in the first paper in this series (Evans, 1967) for the special case in which theykwere all from normal distributions; here the distributions for theykare general. A quadrature formula is developed for approximating the moments ofXwithin an error O(σ5) where σ2is a representative variance for theyk. It uses the values forXobtained for 2n2+ 1 selected arguments, (y1,y2, …,yn). Efficient quadrature formulas are given for the case in which multiple distributions of theykare of interest. A numerical example is included which illustrates the possible use of the quadrature method for a wide variety of problems outside of the field of statistical tolerancing.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488880

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

We consider the problem of estimating the parameters of the bivariate Poisson distribution from truncated samples. Two kinds of truncation are considered, namely, when zero values may not be observed on one or both marginals. We use the canonical form of the bivariate Poisson distribution to derive the first and second moments of the truncated distribution. Hence, the method of moments is used to obtain estimates for the parameters of the marginals λ1, λ2and the correlation coefficient ρ. The properties of the estimates are considered in some special cases. An example is given to illustrate the application of the estimation formulae.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488881

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

Experimenters often make several observations on a given experimental unit. If these observations can be associated with some continuous variable, such as t)ime or temperature, they collectively form a curve. Wishart (1938) first recommended that a general regression model be fitted to each curve and that the effects of the experimental treatments be evaluated by analyzing the coefficients in the model. Univariate (Box, 1950) and multivariate analysis of variance (Cole and Grizzle, 1966) and principal component analysis (Church, 1966) are other techniques for the analysis of response curves. A discussion of these methods is presented and a new model, which combines the univariate analysis of variance and principal component analysis, is developed. This model overcomes some of the inadequacies of the available procedures and gives results which are easy to understand and interpret. Examples are presented which compare the various methods of analysis and illustrate the usefulness of this new model.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488882

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

This paper considers the estimation of the parameters of the extreme value distribution. Best linear unbiased estimators based onk= 2(l)10 sample quantiles are used. The optimum spacings, the coelficients of the estimators, their variances and asymptotic efficiencies are given. Estimation of the parameters from censored samples is also considered.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488883

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

An approximate likelihood function has been suggested by Clutton-Brock for fitting a curve to data in the case where both the independent and dependent variables are subject to error. His iterative procedure for maximizing the likelihood is shown to be unsatisfactory in comparison with more conventional methods. It is also shown that this likelihood is a poorly chosen approximation, in that an alternative form is exact for linear functions.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488884

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

A simple estimator,p=n/(n+X+ l), for the negative binomial parameterpis derived to satisfy approximately E. J. G. Pitman's definition of “closeness.” The mean, variance, and mean-squared error ofpare investigated analytically using a technique (an extension of work by D. J. Finney) for expanding an arbitrary function of a negative-binomially disributed random variable in an infinite series. Extensive numerical computations indicate that for a wide range of useful values ofnandp,pis “closer” and has smaller mean-squared error than some other well-known estimators forp. Such an estimator should be particularly useful in applications of inverse binomial sampling, where negative binomial distributions involving small values ofnandpare encountered.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488885

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

This paper presents a statistic composed of independentF-statistics, testing the same hypothesis, combined in the manner in which Zelen (1957) combines intra and interblock information for incomplete block models with fixed treatment effects and random block effects. This work is applicable to certain two factor random effect models with interaction and unequal number of readings per cell. When the number of readings remains constant within groups of levels of one factor the data yields a number of similar but independentF-stastics, from intragroup and intergroup sources.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488886

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor

摘要:

One of the most important aspects of the analysis of data by regression methods is the examination of residuals. This implies the careful inspection of the differences,ei=yi– ŷi,i= 1,2, …,n, between the observed valuesyi, and the corresponding valuesyiwhich are predicted by the fitted model at thenobservation sites. There are many ways of looking at residuals; for basic references see Anscombe and Tukey (1963) and Anscombe (1961, 1967), or see the expository accounts by Draper and Smith (1966, Chapter 3) and Wooding (1969). Important basic techniques are the inspection of the magnitude of individual residuals to detect the presence of outliers and the plotting of the residuals against their corresponding fitted values, or against the corresponding values of the independent variables, or against the corresponding values of “new” variables, and (in all cases) observing the pattern thus formed.

ISSN:0040-1706    

DOI:10.1080/00401706.1972.10488887

出版商:Taylor & Francis Group    

年代:1972

数据来源: Taylor