A Modern Course on Statistical Distributions in Scientific Work: Volume 3 - Characterizations and Applications Proceedings of the NATO Advanced Study Institute held at the University of Calgary, Calgary, Alberta, Canada July 29 – August 10, 1974

Front Matter....Pages I-XVIII
Some Problems in the Characterization of the Multivariate Normal Distribution....Pages 1-13
Properties of Non-Negative Definite Solutions of Certain Ordinary Differential Equations....Pages 15-45
General Solution of a Functional Equation Connected with a Characterization of Statistical Distributions....Pages 47-55
An Extension of the Phragmén — Lindelöf Theory Which is Relevant for Characterization Theory....Pages 57-69
Characterizations of Probability Distributions by Properties of Order Statistics I....Pages 71-88
Characterizations of Probability Distributions by Properties of Order Statistics II....Pages 89-101
Characterization of Distributions Based on the ‘Scores’ Arising in the Theory of Rank Tests....Pages 103-112
Characterization of Distributions by the Form of Predictors of Order Statistics....Pages 113-115
Characterization of the Exponential Distribution Using Lower Moments of Order Statistics....Pages 117-129
A Characterization of the Exponential Distribution....Pages 131-135
L 1 -Completeness of a Class of Beta Densities....Pages 137-141
Expected Value of the Spacings between Order Statistics....Pages 143-147
Characterizations of Distributions by Statistical Properties on Groups....Pages 149-161
Transcendental Functions of a Vector Variable and a Characterization of a Multivariate Poisson Distribution....Pages 163-171
On the Conditions of Asymptotic ɛ- Admissibility of the Polynomial Pitman Estimators of a Location Parameter and Certain Properties of Information Measures of Closeness....Pages 173-184
Characterizations of the Gamma Distribution and Related Laws....Pages 185-198
Characterization of Normal Law by Constancy of Regression....Pages 199-209
A Characterization of the Normal Distribution....Pages 211-219
On Characterization of Probability Distributions by Conditional Expectations....Pages 221-230
On a Characterization of Probability Distributions on Locally Compact Abelian Groups-II....Pages 231-235
Some Characterizations of the Exchangeable Processes and Distribution-Free Tests....Pages 237-248
Characterization by Functional Equations of Branching Process Limit Laws....Pages 249-254
Problems of Damaged Random Variables and Related Characterizations....Pages 255-270
On Some Characterizations of the Binomial and Poisson Distributions Based on a Damage Model....Pages 271-277
Some New Characterizations of Discrete Lagrangian Distributions....Pages 279-290
A Characterization of a Dependent Bivariate Poisson Distribution....Pages 291-297
Maximum Entropy Characterizations of Some Distributions....Pages 299-304
On Fisher’s Amount of Information for Location Family....Pages 305-312
Characterizations Based on Second-Order Entropy....Pages 313-319
Some Recent Applications of Functional Equations and Inequalities to Characterizations of Probability Distributions, Combinatorics, Information Theory and Mathematical Economics....Pages 321-337
Some Characterizations Involving Additivity and Infinite Divisibility and Their Applications to Poisson Mixtures and Poisson Sums....Pages 339-351
On Characterizing the Hypergeometric and Multivariate Hypergeometric Distributions....Pages 353-357
Characterizations of Certain Discrete Distributions....Pages 359-364
Characterizations of Directional Distributions....Pages 365-385
Maximum Likelihood Characterization of the Von Mises Distribution....Pages 387-398
On Characterizing Univariate and Multivariate Exponential Distributions with Applications....Pages 399-421
Characterizations of Linear Exponential Families....Pages 423-431
Back Matter....Pages 433-436