摘要:

The use of spline functions in the analysis of empirical two-dimensional data (yi,xi) is described. The definition of spline functions as piecewise polynomials with continuity conditions give them unique properties as empirical function. They can represent any variation ofywithxarbitrarily well over wide intervals ofx. Furthermore, due to the local properties of the spline functions, they are excellent tools for differentiation and integration of empirical data. Hence, spline functions are excellent empirical functions which can be used with advantage instead of other empirical functions, such as poly-nomials or exponentials.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489142

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

A squared rank test is introduced as a tool for evaluating precipitation data from a commonly employed weather modification experimental design termed a cross-over design. The existence of tied observations is taken into account in obtaining a lkormslized form of the test. An asymptotic comparison is made of distributions for which this squared rank test, the Wilcoxon test and the median test are asymptotically optimum against location alternatives. Also a specific numerical example is given.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489143

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

It is known that in the random effect model, exactF-tests are not obtainable from the analysis of variance table for testing the main effects in a three-way layout. Similarly exactF-tests are not obtainable for the main effects and certain interactions in higher-way layouts. In this paper level-α: tests obtainable from the analysis of variance table are given for testing these effects. Tables are provided to illustrate the size function and the power function of the tests.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489144

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

In this paper a Monte Carlo study of four test statistics used to test the null hypothesis that two or more multivariate normal populations have equal covariance matrices is presented. The statistics −2 In λ, −2 InW, −2ρ2In λ and −2ρ2lnW, where λ is the likelihood ratio criterion andWis Bartlett's modification of λ, are investigated. The reslllts indicate that for small samples the actual significance levels of the first, two statistics are somewhat greater than the nominal significance levels set, whereas for the latter two statistics the actual significance levels are close to the nominal levels. For these test statistics, −2ρP1In h and −2ρ2In W, the power is seen to be essentially identical; fnrther it increases as the sample size increases, as the inequality of the covariance matrices increases, and as the number of variates increases. Also, their power is seen to be a concave function of the number of populations.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489145

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

It is often desirable to execute the observations in an experimental design in such an order that the number of factor level changes is kept small. This paper describes a study which utilized a computer program written to examine run orders requiring a minimum number of factor level changes and select those in which the correlations between the main effects and a linear time trend are small. Some results are given for the 24and 25designs.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489146

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

In a life testing situation the failure of an individual, either a living organism or an inanimate object, may be classified into one ofk(< 1) mutually exclusive classes, usually causes of failure. One often has dependent causes of failure in actual physical situations, i.e., the theoretical lifetime of an individual failing from one cause may be correlated with the theoretical lifetime of the same individual failing from a different cause. This paper i) discusses some properties of a bivariate Weibull distribution and ii) is concerned with estimating, by the method of maximum likelihood, the unknown parameters of life distributions belonging to two particular parametric families, viz., bivariate normal and bivariate Weibull, when the causes of failure are dependent. An example involving the failure of small electrical appliances is analyzed and compared with an analysis which assumes the causes of failure to be independent.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489147

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

A simple unbiased estimator is proposed for the location parameter of the extreme-value distribution. This estimator is shown to have high eficiency, especially when heavy censoring is used. A simple estimator of reliability, when failure times follow the Weibull distribution, is also obtained, and it is shown to have high asymptotic efficiency when heavy censoring is employed.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489148

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

We construct prediction intervals for an exponential order statistic of a sample from a population with unknown scale parameter based on subsets of the order statistics. This encompasses the situations where some of the data are missing or where optimal selection of the order statistics is desired. Predictions are made in the cases of right censored samples and two independent samples. We also construct prediction intervals for the mean of a future sample based on subsets of a first sample. Accurate and easily computed approximate prediction intervals using the F distribution are given.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489149

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

Distributions with heavier-than-exponential tails are studied for describing empirical phenomena. It is argued that the concept of increasing “conditional mean exceedance” provides a reasonable way of describing the heavy-tail phenomenon, and a family of Pareto distributions is shown to represent distributions for which this parameter is linearly increasing. A test is developed and modified so as to be suitable for testing heavy-tailedness, and some graphical procedures are also suggested.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489150

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor

摘要:

The problem of obtaining the derivative of a set of data arises naturally in many fields. The usual methods for obtaining derivatives are based on abstract formulations of the problem, which do not take errors of observation explicitly into account. For this reason, their performarice when applied to observational data is unpredictable. By introducing random errors into the model, one may derive methods whose performance may be stated in statistical terms. The theory of time series analysis provides useful tools for discussing such a model. A parametric family of models is introduced, and estimation of the parameters is discussed.

ISSN:0040-1706    

DOI:10.1080/00401706.1974.10489151

出版商:Taylor & Francis Group    

年代:1974

数据来源: Taylor