Showing papers in "International Statistical Review in 1979"
TL;DR: In this paper, the authors analyze the recent development of the theory of the asymptotic distribution of extremes in the light of the questions (i) and (ii). Several dependence concepts will be introduced, each of which leads to a solution of (i).
Abstract: Abstract. Let X j denote the life length of the j th component of a machine. In reliability theory, one is interested in the life length Z n of the machine where n signifies its number of components. Evidently, Z n = min (X j : 1 ≤ j ≤ n). Another important problem, which is extensively discussed in the literature, is the service time W n of a machine with n components. If Y j is the time period required for servicing the j th component, then W n = max (Y j : 1 ≤ j ≤ n). In the early investigations, it was usually assumed that the X's or Y's are stochastically independent and identically distributed random variables. If n is large, then asymptotic theory is used for describing Z n or W n . Classical theory thus gives that the (asymptotic) distribution of these extremes (Z n or W n ) is of Weibull type. While the independence assumptions are practically never satisfied, data usually fits well the assumed Weibull distribution. This contradictory situation leads to the following mathematical problems: (i) What type of dependence property of the X's (or the Y's) will result in a Weibull distribution as the asymptotic law of Z n (or W n )? (ii) given the dependence structure of the X's (or Y's), what type of new asymptotic laws can be obtained for Z n (or W n )? The aim of the present paper is to analyze the recent development of the (mathematical) theory of the asymptotic distribution of extremes in the light of the questions (i) and (ii). Several dependence concepts will be introduced, each of which leads to a solution of (i). In regard to (ii), the following result holds: the class of limit laws of extremes for exchangeable variables is identical to the class of limit laws of extremes for arbitrary random variables. One can therefore limit attention to exchangeable variables. The basic references to this paper are the author's recent papers in Duke Math. J. 40 (1973), 581–586, J. Appl. Probability 10 (1973, 122–129 and 11 (1974), 219–222 and Zeitschrift fur Wahrscheinlichkeitstheorie 32 (1975), 197–207. For multivariate extensions see H. A. David and the author, J. Appl. Probability 11 (1974), 762–770 and the author's paper in J. Amer. Statist. Assoc. 70 (1975), 674–680. Finally, we shall point out the difficulty of distinguishing between several distributions based on data. Hence, only a combination of theoretical results and experimentations can be used as conclusive evidence on the laws governing the behavior of extremes.
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TL;DR: In this article, the meanings of representative sample and representative sampling as used in the extrastatistical scientific literature are described and illustrated, and six categories seem adequate to describe these uses.
Abstract: This paper describes and illustrates the meanings of 'representative sample' and 'representative sampling' as used in the extrastatistical scientific literature. Six categories seem adequate to describe these uses. The first five appeared also in the review of non-scientific uses in 'Representative Sampling, I' (Kruskal and Mosteller, 1979). We define and illustrate these in Sections 1-5 of the paper.
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TL;DR: In this article, the orthogonal polynomial regression approach for curve fitting when the independent variable occurs at unequal intervals and is observed with unequal frequency is discussed. And the computations required for determining orthogonality are described with a simple example.
Abstract: Summary We discuss in basic terms the orthogonal polynomial regression approach for curve fitting when the independent variable occurs at unequal intervals and is observed with unequal frequency. The computations required for determining orthogonal polynomials are described with a simple example.
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TL;DR: In this article, the relative advantages of samples, censuses, and registers are compared along eight criteria: cost, detail, timeliness, relevance, etc., and current and future paths are indicated for combining the strengths of the three sources, in order to obtain accurate estimates which are both timely and detailed for local areas and small domains.
Abstract: Summary Two related topics receive brief but comprehensive reviews, for guiding decisions about three sources for collecting data. First, the relative advantages of samples, censuses, and registers are compared along eight criteria: cost, detail, timeliness, relevance, etc. Second, 15 methods are indicated for using samples in connection with censuses; they are sorted into five kinds of purposes: as substitutes for, or as aids to, censuses; sampling from census tapes; censuses as auxiliary data for sampling. Finally, current and future paths are indicated for combining the strengths of the three sources, in order to obtain accurate estimates which are both timely and detailed for local areas and small domains. The Editor draws attention to the timeliness of this contribution in connection with the design and execution of the censuses to be taken in 1980/81 and the many kinds of sample involved.
TL;DR: In this article, the author specifies the differences between his own conception and terminology, their misinterpretations by Hamaker, and the concepts of Hamaker for himself, as all that is seen and criticized by a subjectivist.
Abstract: With reference chiefly to the paper by Hugo C. Hamaker in this Review (45 (1977) 223-231), having essentially the same title as the present one but for the change from 'Objective' to 'Subjective', the author specifies the differences between his own conception and terminology, their misinterpretations by Hamaker, and the concepts of Hamaker for himself, as all that is seen and criticized by a subjectivist.
TL;DR: The International Statistical Institute (ISI) was established in 1885 as an international society for the development and application of statistical methods as mentioned in this paper and has become increasingly diversified in its membership, particularly with the formation of sections.
Abstract: The IS1 was established in 1885 as an international society for the development and application of statistical methods. The Institute, originally composed largely of official statisticians, has since grown to a size of more than 1000 members from over 80 countries; it has become increasingly diversified in its membership, particularly with the formation of sections. There are now four of these: the Bernoulli Society for Mathematical Statistics and Probability (formerly the International Association for Statistics in the Physical Sciences), the International Association of Survey Statisticians, the International Association for Regional and Urban Statistics, and the International Association for Statistical Computation. In addition, approximately ten international and 20 national statistical societies are affiliated with the ISI; this establishes the Institute as the foremost international statistical body, with responsibilities in the scholarly, communications, program management, political and educational areas of statistics. Examples of ISI's numerous functions include: 1. The promotion of research and professional practice through learned articles in its Review, and papers presented at its various Conferences and Symposia. 2. The creation in 1959, and the regular maintenance of the Statistical Theory and Method
TL;DR: In this article, the authors used statistical techniques common to industrial quality control and reliability engineering to analyse the mean time to failure of 100-banknotes printed on paper with flax and without flax.
Abstract: Summary For over two years the issue and subsequent withdrawal of approximately 1,2 million Dutch f 100-banknotes has been recorded with the aid of the Bank's banknote sorting system. The banknotes were printed on two varieties of paper differing in quality, i.e. with and without flax. The results are analysed using statistical techniques common to industrial quality control and reliability engineering. Technically and economically, it appears advantageous to switch from conventional paper with flax to paper without flax. The consumption off 100banknotes will consequently be reduced by approximately 23 per cent, provided the fit/unfit criterion used until now will be maintained. The mean time to failure offl100-banknotes printed on paper with flax is assessed at 150 weeks and on paper without flax at 196 weeks. Furthermore, the rate at which banknotes are returned to the Bank appears to be independent of age or deterioration, contrary to common notion.* The cumulative fraction of banknotes withdrawn may be approximated by a two-parameter gamma distribution, the scale parameter being a measure of the circulation rate and the shape parameter a measure of the paper quality.
TL;DR: The Second International Congress of Ecology was held in Jerusalem, Israel, during September 1978 as mentioned in this paper, and a Satellite Program in Statistical Ecology was planned in this connection by the International Statistical Ecology Program.
Abstract: The Second International Congress of Ecology was held in Jerusalem, Israel, during September 1978. A Satellite Program in Statistical Ecology was planned in this connection by the International Statistical Ecology Program. The emphasis was on research, review, and exposition concerned with creative interface between quantitative ecology and relevant quantitative methods. The emphasis was on both theory and application, coupled with synthesis of both ecological and methodological aspects of the problem. The program consisted of instructional coursework, seminar series, thematic research conferences, and collaborative research workshops in the modern setting. The 1977 and 1978 Satellite Program in Statistical Ecology consisted of NATO Advanced Study Institutes at College Station, Berkeley, and Parma; NATO Advanced Research Institute at Parma; ISEP Research Conferences, Seminars, and Workshops at College Station, Berkeley, Parma, and Jerusalem; and Research Conference at the Second International Ecological Congress at Jerusalem. The Satellite Program in Statistical Ecology has been supported by Army Research Office, USA; Commission of the European Communities, Belgium; Environmental Protection Agency, USA; Fish and Wildlife Service, USA; Italian Society of Ecology, Italy; National Marine Fisheries Service, USA; National Research Council, Italy; NATO Advanced Study Institutes Program; NATO Ecosciences Program; The University of Parma; The Pennsylvania State University; The Texas AM The University of California at Berkeley; and the participants and their home institutions and organizations. Carefully refereed and edited research-review-expositions and research papers have been specially prepared for the program by concerned experts and expositors. These valuable materials have been processed for publication in a series of volumes to appear in 1979.
TL;DR: In the field of multivariate analysis, Tintner et al. as discussed by the authors introduced the notion of principal components, which are ordered roots of determinantal equations, in multiple factor analysis.
Abstract: Hotelling (1933), one of the pioneers in the field of multivariate analysis, was also among the first to use methods based on order statistics in that field. He introduced the method of principal components, which are ordered roots of determinantal equations, in multiple factor analysis. During the next 15 years, related work was performed by Thomson (1934), Girshick (1936), Hotelling (1936a), Aitken (1937), Bartlett (1938), Lawley (1940) and Tintner (1945). Hotelling (1936b) studied relations between two sets of variates, obtained distributions of canonical correlations, which are also roots of determinantal equations, and of functions of canonical correlations, arranged in order of magnitude. Other early contributors to the theory of canonical analysis were Girshick (1939), Bartlett (1947a, b, 1948) and Tintner (1946). Fisher (1938), in a fundamental paper on linear discriminant analysis, dealt with s-I orthogonal comparisons of s components, arranged in order of the magnitude of their contributions. No fewer than four authors (Fisher, 1939; Girshick, 1939; Hsu, 1939; Roy, 1939) independently published fundamental results on the distribution of the ordered roots of determinantal equations, and during the next ten years further results were obtained by Roy, Hsu, Wilks, Anderson, Bartlett, Geary, Nanda and Rao. Tintner (1946) summarized some applications of four methods of multivariate analysis (discriminant analysis, principal components, canonical correlation, and weighted regression), all based on order statistics, to economic data. The author of this paper discusses these are other early applications to multivariate analysis, including the use of order statistics in obtaining tolerance regions (first proposed by Wald, 1943), and gives a list of references selected from the first volume (pre-1950) of his chronological annotated bibliography on order statistics.