Lagrangian expansions can be used to obtain numerous very useful probability models, which have been applied to real life situations including, but not limited to branching processes, queuing processes, stochastic processes, environmental toxicology, diffusion of information, ecology, strikes in industries, sales of new products, and amount of production for optimum profits. This book is a comprehensive, systematic treatment of the two classes of Lagrangian probability distributions along with some of their sub-families and their properties; important applications are also given.Graduate students and researchers interested in Lagrangian probability distributions, who have sound knowledge of standard statistical techniques, will find this book valuable. It may be used as a reference text or in courses and seminars on distribution theory and Lagrangian distributions. Applied scientists and researchers in environmental statistics, reliability, sales management, epidemiology, operations research, and the optimization of profits in manufacturing and marketing will benefit immensely from the various applications in the book.

This book describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance.

A solid, rigorous, yet comprehensible analysis of process capability indices, this work bridges the gap between theoretical statisticians and quality control practitioners, showing how an understanding of these indices can lead to process improvement.

A solid, rigorous, yet comprehensible analysis of process capability indices, this work bridges the gap between theoretical statisticians and quality control practitioners, showing how an understanding of these indices can lead to process improvement.

This is author-approved bcc: This is the third volume of a collection of seminal papers in the statistical science written during the past 110 years. These papers have each had an outstanding influence on the development of statistical theory and practice over the last century. Each paper is preceded by an introduction written by an authority in the field providing background information and assessing its influence. Volume III concertrates on articles from the 1980's while including some earlier articles not included in Volumes I and II. Samuel Kotz is Professor of Statistics in the College of Business and Management at the University of Maryland. Norman L. Johnson is Professor Emeritus of Statistics at the University of North Carolina. Also available: Breakthroughs in Statistics Volume I: Foundations and Basic Theory Samuel Kotz and Norman L. Johnson, Editors 1993. 631 pp. Softcover. 0-387-94037-5 Breakthroughs in Statistics Volume II: Methodology and Distribution Samuel Kotz and Norman L. Johnson, Editors 1993. 600 pp. Softcover. 0-387-94039-1

Arthur Lyon Bowley, the founding father of modern statistics, was an important and colorful figure and a leader in cementing the foundations of statistical methodology, including survey methodology, and of the applications of statistics to economical and social issues during the late 19th and early 20th centuries. In many respects, he was ahead of his time. The giants in this field around that time were largely concentrated in the British Isles and Scandinavian countries; among these contributors, Arthur Bowley was one of the most active in revolutionizing statistical methodology and its economic applications. However, Bowley has been vastly undervalued by subsequent commentators ???????????????????????? while hundreds of articles and books have been written on Karl Pearson, those on Arthur Bowley amount to a dozen or less. This book seeks to remedy this and fill in an important omission in the monographical literature on the history of statistics. In particular, the recent resurgence of interest in poverty research has led to a renewed interest in Bowley's legacy.

by S. Geisser.- Fisher, R.A. (1922) On the Mathematical Foundations of Theoretical Statistics.- by T.W. Anderson.- Hotelling, H. (1931) The Generalization of Student's Ratio.- by E.L. Lehmann.- Neyman, J. and Pearson, E.S. (1933) On the Problem of the Most Efficient Tests of Statistical Hypotheses.- by D.A.S. Fraser.- by D.A.S. Fraser.- by R.E. Barlow.- de Finetti, B. (1937) Foresight: It's Logical Laws, Its Subjective Sources.- by M.R. Leadbetter.- Cramer, H. (1942) On Harmonic Analysis in Certain Functional Spaces.- by R.L. Smith.- Gnedenko, B.V. (1943) On the Limiting Distribution of the Maximum Term in a Random Series.- by P.K. Pathak.- Rao, C.R. (1945) Information and the Accuracy Attainable in the Estimation of Statistical Parameters.- by B.K. Ghosh.- Wald, A. (1945) Sequential Tests of Statistical Hypotheses.- by P.K. Sen.- Hoeffding, W. (1948) A Class of Statistics with Asymptotically Normal Distribution.- by L. Weiss.- Wald, A. (1949) Statistical Decision Functions.- by D.V. Lindley.- by D.V. Lindley.- by I.J. Good.- Robbins, H.E. (1955) An Empirical Bayes Approach to Statistics.- by H.P. Wynn.- Kiefer, J.C. (1959) Optimum Experimental Designs.- by B. Efron.- by B. Efron.- by J.F. BjTHrnstad.- Birnbaum, A. (1962) On the Foundations of Statistical Inference.- by W.U. DuMouchel.- Edwards, W., Lindman, H., and Savage, L.J. (1963) Bayesian Statistical Inference for Psychological Research.- by N. Reid.- Fraser, D.A.S. (1966) Structural Probability and a Generalization.- by J. de Leeuw.- Akaike, H. (1973) Information Theory and an Extension of the Maximum Likelihood Principle.

Statistical distributions are fundamental to Statistical Science and are a prime indispensable tool for its applications. This monograph is the first to examine an important but somewhat neglected field - univariate continuous distribution on a bounded domain, excluding the beta distribution. It provides an elementary but thorough discussion of "novel" contributions developed in recent years, such as the two-sided power, generalized trapezoidal and generalized Topp and Leone distributions, among others. It discusses a general framework for constructing two-sided distributions and some of its properties. It contains a comprehensive chapter on the triangular distribution as well as a chapter on earlier extensions not emphasized in existing literature. Special attention is given to estimation, in particular, non-standard maximum likelihood procedures. The applications are drawn mainly from the econometric and engineering domains.

This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions — one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field.

This book provides a survey of recent methodology, both theoretical and applied, regarding the statistical analysis and detection of defective (non-conforming) items in various types of inspection for attributes, when the inspection itself is subject to error. This error can be of two kinds: false positive (classifying non-defective as defective) and false negative (classifying defective as non-defective).

. . ) (under the assumption that the spectral density exists). For this reason, a vast amount of periodical and monographic literature is devoted to the nonparametric statistical problem of estimating the function tJ( T) and especially that of leA) (see, for example, the books [4,21,22,26,56,77,137,139,140,]). However, the empirical value t;; of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . . . , X , usually depends in n a complicated manner on the cyclic frequency). . This fact often presents difficulties in applying the obtained estimate t;; of the function I to the solution of specific problems rela ted to the process X . Theref ore, in practice, the t obtained values of the estimator t;; (or an estimator of the covariance function tJ~( T" are almost always "smoothed," i. e. , are approximated by values of a certain sufficiently simple function 1 = 1

This book is devoted to an investigation of control problems which can be described by ordinary differential equations and be expressed in terms of game theoretical notions. In these terms, a strategy is a control based on the feedback principle which will assure a definite equality for the controlled process which is subject to uncertain factors such as a move or a controlling action of the opponent. "Game" "Theoretical Control Problems" contains definitions and formalizations of differential games, existence for equilibrium and extensive discussions of optimal strategies. Formal definitions and statements are accompanied by suitable motivations and discussions of computational algorithms. The book is addessed to mathematicians, engineers, economists and other users of control theoretical and game theoretical notions.

This book describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance.

This is author-approved bcc: This is the third volume of a collection of seminal papers in the statistical sciences written during the past 110 years. These papers have each had an outstanding influence on the development of statistical theory and practice over the last century. Each paper is preceded by an introduction written by an authority in the field providing background information and assessing its influence. Volume III concerntrates on articles from the 1980's while including some earlier articles not included in Volume I and II. Samuel Kotz is Professor of Statistics in the College of Business and Management at the University of Maryland. Norman L. Johnson is Professor Emeritus of Statistics at the University of North Carolina. Also available: Breakthroughs in Statistics Volume I: Foundations and Basic Theory Samuel Kotz and Norman L. Johnson, Editors 1993. 631 pp. Softcover. ISBN 0-387-94037-5 Breakthroughs in Statistics Volume II: Methodology and Distribution Samuel Kotz and Norman L. Johnson, Editors 1993. 600 pp. Softcover. ISBN 0-387-94039-1

McCrimmon, having gotten Grierson's attention, continued: "A breakthrough, you say? If it's in economics, at least it can't be dangerous. Nothing like gene engineering, laser beams, sex hormones or international relations. That's where we don't want any breakthroughs. " (Galbraith, 1. K. (1990) A Tenured Profes- sor, Houghton Miffiin; Boston. ) To judge [astronomy] in this way [a narrow utilitarian point of view] demon- strates not only how poor we are, but also how small, narrow, and indolent our minds are; it shows a disposition always to calculate the payolIbefore the work, a cold heart and a lack of feeling for everything that is great and honors man. One can unfortunately not deny that such a mode of thinking is not uncommon in our age, and I am convinced that this is closely connected with the catastro- phes which have befallen many countries in recent times; do not mistake me, I do not talk of the general lack of concern for science, but of the source from which all this has come, of the tendency to everywhere look out for one's advan- tage and to relate everything to one's physical well-being, of the indilIerence towards great ideas, ofthe aversion to any elIort which derives from pure enthu- siasm: I believe that such attitudes, if they prevail, can be decisive in catas- trophes of the kind we have experienced. [Gauss, K. F. : Astronomische An- trittsvorlesung (cited from Buhler, W. K. (1981) Gauss: A Biographical Study, Springer: New York)].

McCrimmon, having gotten Grierson's attention, continued: "A breakthrough, you say? If it's in economics, at least it can't be dangerous. Nothing like gene engineering, laser beams, sex hormones or international relations. That's where we don't want any breakthroughs. " (Galbraith, 1. K. (1990) A Tenured Profes- sor, Houghton Mifflin; Boston. ) To judge [astronomy] in this way [a narrow utilitarian point of view] demon- strates not only how poor we are, but also how small, narrow, and indolent our minds are; it shows a disposition always to calculate the payolTbefore the work, a cold heart and a lack of feeling for everything that is great and honors man. One can unfortunately not deny that such a mode of thinking is not uncommon in our age, and I am convinced that this is closely connected with the catastro- phes which have befallen many countries in recent times; do not mistake me, I do not talk of the general lack of concern for science, but of the source from which all this has come, of the tendency to everywhere look out for one's advan- tage and to relate everything to one's physical well-being, of the indilTerence towards great ideas, ofthe aversion to any elTort which derives from pure enthu- siasm: I believe that such attitudes, if they prevail, can be decisive in catas- trophes of the kind we have experienced. [Gauss, K. F. : Astronomische An- trittsvorlesung (cited from Buhler, W. K. (1981) Gauss: A Biographical Study, Springer: New York)].

Almost all published results on multivariate t-distributions (spanning the last 50 years) are collected in this comprehensive reference. The book begins with theoretical probabilistic results and then presents statistical aspects. Generalizations and applications are dealt with in the final chapters, including material on estimation and regression models of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.