Ebook: 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

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, ~. 974. 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. As discussed in the Institute inaugural address, not mL.

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Content:
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 Phragm?n — Lindel?f 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
L1-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 ?- 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

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Content:
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 Phragm?n — Lindel?f 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
L1-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 ?- 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
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