A Modern Course on Statistical Distributions in Scientific Work

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.

Contenu

1. Inaugural Address.- 1.1 Concept and Conduct of Calgary Course and Conference: Some Thoughts.- 2. Power Series and Related Families.- 2.1 Some Recent Advances with Power Series Distributions.- 2.2 Multiparameter Stirling and C-Type Distributions.- 2.3 Models for Gaussian Hypergeometric Distributions.- 2.4 On the Probabilistic Structure and Properties of Discrete Lagrangian Distributions.- 2.5 Estimation of Parameters on Some Extensions of the Katz Family of Discrete Distributions Involving Hypergeometric Functions.- 2.6 A Characteristic Property of Certain Generalized Power Series Distributions.- 3. Recent Trends in Univariate Models.- 3.1 Stable Distributions: Probability, Inference, and Applications in Finance-A Survey, and a Review of Recent Results.- 3.2 Structural Properties and Statistics of Finite Mixtures.- 3.3 Distribution Theory for the von Mises-Fisher Distribution and Its Application.- 3.4 Certain Statistical Distributions Involving Special Functions and Their Applications.- 3.5 Tailweight, Statistical Inference and Families of Distributions - A Brief Survey.- 3.6 The Families With a "Universal" Location Estimator.- 4. Moments-Related Problems.- 4.1 Approximation Theory, Moment Problems and Distribution Functions.- 4.2 Kurtosis and Departure From Normality.- 4.3 Convergence of Sequences of Transformations of Distribution Functions and Some Moment Problems.- 5. Limit Distributions and Processes.- 5.1 Weak Convergence for Exponential and Monotone Likelihood Ratio Families and the Convergence of Confidence Limits.- 5.2 On Efficiency and Exponential Families in Stochastic Process Estimation.- 5.3 A Lagrangian Gamma Distribution.- 6. Multivariate Concepts and Models.- 6.1 Multivariate Distributions at a Cross Road.- 6.2 Dependence Concepts and Probability Inequalities.- 6.3 New Families of Multivariate Distributions.- 6.4 Asymptotic Expansions for the Nonnull Distributions of the Multivariate Test Statistics.- 7. Certain Multivariate Distributions.- 7.1 A Multivariate Gamma Type Distribution Whose Marginal Laws Are Gamma, and Which Has a Property Similar to a Characteristic Property of the Normal Case.- 7.2 The Bivariate Burr Distribution.- 7.3 Multivariate Beta Distribution.- 7.4 Distribution of a Quadratic Form in Normal Vectors (Multivariate Non-Central Case).- 7.5 Bivariate and Multivariate Extreme Distributions.- 8. Sampling Distributions and Transformations.- 8.1 On the Distribution of the Minimum and of the Maximum of a Random Number of I.I.D. Random Variables.- 8.2 Transformation of the Pearson System With Special Reference to Type IV.- 8.3 Distributions of Characteristic Roots of Random Matrices.- 8.4 On the Arithmetic Means and Variances of Products and Ratios of Random Variables.- 8.5 Exact and Approximate Sampling Distribution of the F-Statistic Under the Randomization Procedure.