A Modern Course on Statistical Distributions in Scientific Work : Volume 1 -- Models and Structures Proceedings of the NATO Advanced Study Institute held at the University of Calgagry, Calgary, Alberta, Canada July 29 - August 10, 1974

These three volumes constitute the edited Proceedings of the NATO Advanced Study Institute on Statistical Distributions in Scientific Work held at the University of Calgary from July 29 to August 10, 1974. The general title of the volumes is "Statistical Distributions in Scientific Work". The individual volumes are: Volume 1 - Models and Structures; Volume 2 - Model Building and Model Selection; and Volume 3 - Characterizations and Applications. These correspond to the three advanced seminars of the Institute devoted to the respective subject areas. The planned activities of the Institute consisted of main lectures and expositions, seminar lectures and study group dis­ cussions, tutorials and individual study. The activities included meetings of editorial committees to discuss editorial matters for these proceedings which consist of contributions that have gone through the usual refereeing process. A special session was organized to consider the potential of introducing a course on statistical distributions in scientific modeling in the curriculum of statistics and quantitative studies. This session is reported in Volume 2. The overall perspective for the Institute is provided by the Institute Director, Professor G. P. Pati1, in his inaugural address which appears in Volume 1. The Linnik Memorial Inaugural Lecture given by Professor C. R. Rao for the Characterizations Seminar is included in Volume 3. Front Matter....Pages I-XX Inaugural Address — Concept and Conduct of Calgary Course and Conference: Some Thoughts....Pages 1-7 Some Recent Advances with Power Series Distributions....Pages 9-17 Multiparameter Stirling and C-Type Distributions....Pages 19-30 Models for Gaussian Hypergeometric Distributions....Pages 31-40 On the Probabilistic Structure and Properties of Discrete Lagrangian Distributions....Pages 41-57 Estimation of Parameters on Some Extensions of the Katz Family of Discrete Distributions Involving Hypergeometric Functions....Pages 59-82 A Characteristic Property of Certain Generalized Power Series Distributions....Pages 83-86 Stable Distributions: Probability, Inference, and Applications in Finance—A Survey, and a Review of Recent Results....Pages 87-102 Structural Properties and Statistics of Finite Mixtures....Pages 103-112 Distribution Theory for the Von Mises-Fisher Distribution and Its Application....Pages 113-130 Certain Statistical Distributions Involving Special Functions and their Applications....Pages 131-160 Tailweight, Statistical Inference and Families of Distributions — A Brief Survey....Pages 161-172 The Families with a “Universal” Location Estimator....Pages 173-184 Approximation Theory, Moment Problems and Distribution Functions....Pages 185-192 Kurtosis and Departure from Normality....Pages 193-201 Convergence of Sequences of Transformations of Distribution Functions and Some Moment Problems....Pages 203-211 Weak Convergence for Exponential and Monotone Likelihood Ratio Families and the Convergence of Confidence Limits....Pages 213-226 On Efficiency and Exponential Families in Stochastic Process Estimation....Pages 227-240 A Lagrangian Gamma Distribution....Pages 241-246 Multivariate Distributions at a Cross Road....Pages 247-270 Dependence Concepts and Probability Inequalities....Pages 271-279 New Families of Multivariate Distributions....Pages 281-297 Asymptotic Expansions for the Nonnull Distributions of the Multivariate Test Statistics....Pages 299-317 A Multivariate Gamma Type Distribution Whose Marginal Laws are Gamma, and which has a Property Similar to a Characteristic Property of the Normal Case....Pages 319-328 The Bivariate Burr Distribution....Pages 329-335 Multivariate Beta Distribution....Pages 337-344 Distribution of a Quadratic Form in Normal Vectors....Pages 345-354 Bivariate and Multivariate Extreme Distributions....Pages 355-361 On the Distribution of the Minimum and of the Maximum of a Random Number of I.I.D. Random Variables....Pages 363-380 Transformation of the Pearson System with Special Reference to Type IV....Pages 381-390 Distributions of Characteristic Roots of Random Matrices....Pages 391-400 On the Arithmetic Means and Variances of Products and Ratios of Random Variables....Pages 401-406 Exact and Approximate Sampling Distribution of The F-Statistic Under the Randomization Procedure....Pages 407-418 Back Matter....Pages 419-424