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Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. Both models describe random variables arranged in order of magnitude. In addition to these well-known models, several other models of ordered random variables, known and new ones, are introduced in this book such as order statistics with non-integral sample size, sequential order statistics, k-th record values, Pfeifer' s record model, k -records from non-identical distributions and ordered random variables which arise from n truncation of distributions. These models can be effectively applied, e.g., in reliability theory. Here, an order statistic represents the life-length of some r-out-of-n-system which is an important technical structure consisting of n components. For this application, a new and more adequate model is naturally suggested. Sequential order statistics serve as a model describing certain dependencies or interactions among the system components caused by failures of components. Record values are closely connected with the occurrence times of some corresponding non-homogeneaus Poisson process and used in so~lled shock models. More flexible record models, and therefore more applicable to practical situations, are considered here. The main purpose of this book is to present a concept of generalized order statistics as a unified approach to a variety of models of ordered random variables. In the distribution theoretical sense, all of the models mentioned above are contained in the proposed model of generalized order statistics.

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This easy-to-understand introduction emphasizes the areas of probability theory and statistic that are important in environmental monitoring, data analysis, research, environmental field surveys, and environmental decision making. It communicates basic statistical theory with very little abstract mathematical notation, without omitting important details and assumptions. Topics include Bayes'Theorem, geometric distribution, computer simulation, histograms and frequency plots, maximum likelihood estimation,the tail exponential method, Bernoulli processes, Poisson processes, diffusion and dispersion of pollutants, normal distribution, confidence intervals, and stochastic dilution; gamma, chi-square, and Weibull distribution; and the two-and three-parameter lognormal distributions.

Anbieter: Orell Fuessli CH

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Frederick Mosteller has inspired numerous statisticians and other scientists by his creative approach to statistics and its applications. This volume brings together 40 of his most original and influential papers, capturing the variety and depth of his writings. The editors hope to share these with a new generation of researchers, so that they can build upon his insights and efforts. This volume of selected papers is a companion to the earlier volume A Statistical Model: Frederick Mosteller's Contributions to Statistics, Science, and Public Policy, edited by Stephen E. Fienberg, David C. Hoaglin, William H. Kruskal, and Judith M. Tanur (Springer-Verlag, 1990), and to Mosteller's forthcoming autobiography, which will also be published by Springer-Verlag. It includes a biography and a comprehensive bibliography of Mosteller's books, papers, and other writings. Stephen E. Fienberg is Maurice Falk University Professor of Statistics and Social Science, in the Departments of Statistics and Machine Learning at Carnegie Mellon University, Pittsburgh, PA. David C. Hoaglin is Principal Scientist at Abt Associates Inc., Cambridge, MA. TOC:From the contents Unbiased Estimates For Certain Binomial Sampling Problems with Applications.- on Some Useful 'Inefficient' Statistics, Frederick Mosteller.- A K-Sample Slippage Test for an Extreme Population.- The Uses and Usefulness of Binomial Probability Paper.- The Education of A Scientific Generalist.- Remarks on The Method of Paired Comparisons: I. The Least Squares Solution Assuming Equal Standard Deviations and Equal Correlations.- Remarks on The Method of Paired Comparisons: II. The Effect of an Aberrant Standard Deviation when Equal Standard Deviations And Equal Correlations are Assumed.- Remarks on The Method of Paired Comparisons: III. A Test of Significance for Paired Comparisons when Equal Standard Deviations and Equal Correlations are Assumed.- An Experimental Measurement of Utility.- A Mathematical Model for Simple Learning.- A Model for Stimulus Generalization and Discrimination.- The World Series Competition.- Principles of Sampling.- Stochastic Models for The Learning Process.- Factorial 1/2: A Simple Graphical Treatment.- A Comparison of Eight Models.- Optimal Length of Play for A Binomial Game.- Tables of The Freeman-Tukey Transformations for the Binomial and Poisson Distributions.- Understanding The Birthday Problem.- Recognizing The Maximum of A Sequence.- The Distribution of Sums of Rounded Percentages.- The Expected Coverage to the Left of the ith Order Statistic for Arbitrary Distributions.

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Anbieter: Thalia AT

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Anbieter: Thalia AT

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