Norman L. Johnson – författare

Discover the latest advances in discrete distributions theory

The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method.

A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions.

Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including:

Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications.

With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.

Geometry of Derivation with Applications is the fifth work in a longstanding series of books on combinatorial geometry (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes, and Combinatorics of Spreads and Parallelisms). Like its predecessors, this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment.

The book builds upon over twenty years of work concerning combinatorial geometry, charted across four previous books and is suitable as a reference text for graduate students and researchers. It contains a variety of new ideas and generalizations of established work in finite affine geometry and is replete with examples and applications.

Geometry of Derivation with Applications is the fifth work in a longstanding series of books on combinatorial geometry (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes, and Combinatorics of Spreads and Parallelisms). Like its predecessors, this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment.

The book builds upon over twenty years of work concerning combinatorial geometry, charted across four previous books and is suitable as a reference text for graduate students and researchers. It contains a variety of new ideas and generalizations of established work in finite affine geometry and is replete with examples and applications.

Geometry of Derivation, Volume III: Classification of Skewfield Flocks is the third book in a series of books on the topic. This book continues establishing the techniques, examples, and future directions of the specifics of flock theory over skewfields. Like its predecessors, it will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases.

Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment.

Since the work is valid for finite fields, infinite fields, non-commutative skewfields, there are left and right flocks over generalized hyperbolic quadrics, and generalized quadratic cones, there is a number of possibilities. The contribution of this volume is the main classification.

The book continues the presentation in Geometry of Derivations with Applications, Volume I, Johnson (2023), and Geometry of Derivation, Volume II: Theory of Skewfield Flocks (2026) is also available. This is the seventh work in a longstanding series of books on combinatorial geometry by the author, including Subplane Covered Nets, Johnson (2000); Foundations of Translation Planes, Biliotti, Jha, and Johnson (2001); Handbook of Finite Translation Planes, Johnson, Jha, and Biliotti (2007); and Combinatorics of Spreads and Parallelisms, Johnson (2010), all published by CRC Press.

This book is concerned mainly with the theory of flocks over skewfields. It begins with discussing what conditions would be required to find a possible way to extend flocks of hyperbolic quadrics and flocks of quadratic cones. This theory completely changes the idea of derivation of an affine plane that contains a derivable net.

This volume will give the necessary theory for the reader to understand how to construct examples and become researchers in the field. It shows how to construct four types of determinants, the (i,j)-determinants, which if never zero for the non-zero matrices of the spread will indicate that the first condition for existence of a spread then holds. If applicable, the left unwrapping principle, if this also is valid, will show that a left flock spread is constructed.

The book continues the presentation in Geometry of Derivation with Applications, Volume I, and a third volume, Geometry of Derivation, Volume III: Classification of Skewfield Flocks (2026) is also available, both from CRC Press. This is the sixth work in a longstanding series of books on combinatorial geometry by the author, including Subplane Covered Nets, Johnson (2000); Foundations of Translation Planes, Biliotti, Jha, and Johnson (2001); Handbook of Finite Translation Planes, Johnson, Jha, and Biliotti (2007); and Combinatorics of Spreads and Parallelisms, Johnson (2010), all published by CRC Press.

Like its predecessors, this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment.

Geometry of Derivation, Volume III: Classification of Skewfield Flocks is the third book in a series of books on the topic. This book continues establishing the techniques, examples, and future directions of the specifics of flock theory over skewfields. Like its predecessors, it will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases.

Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment.

Since the work is valid for finite fields, infinite fields, non-commutative skewfields, there are left and right flocks over generalized hyperbolic quadrics, and generalized quadratic cones, there is a number of possibilities. The contribution of this volume is the main classification.

The book continues the presentation in Geometry of Derivations with Applications, Volume I, Johnson (2023), and Geometry of Derivation, Volume II: Theory of Skewfield Flocks (2026) is also available. This is the seventh work in a longstanding series of books on combinatorial geometry by the author, including Subplane Covered Nets, Johnson (2000); Foundations of Translation Planes, Biliotti, Jha, and Johnson (2001); Handbook of Finite Translation Planes, Johnson, Jha, and Biliotti (2007); and Combinatorics of Spreads and Parallelisms, Johnson (2010), all published by CRC Press.

This book is concerned mainly with the theory of flocks over skewfields. It begins with discussing what conditions would be required to find a possible way to extend flocks of hyperbolic quadrics and flocks of quadratic cones. This theory completely changes the idea of derivation of an affine plane that contains a derivable net.

This volume will give the necessary theory for the reader to understand how to construct examples and become researchers in the field. It shows how to construct four types of determinants, the (i,j)-determinants, which if never zero for the non-zero matrices of the spread will indicate that the first condition for existence of a spread then holds. If applicable, the left unwrapping principle, if this also is valid, will show that a left flock spread is constructed.

The book continues the presentation in Geometry of Derivation with Applications, Volume I, and a third volume, Geometry of Derivation, Volume III: Classification of Skewfield Flocks (2026) is also available, both from CRC Press. This is the sixth work in a longstanding series of books on combinatorial geometry by the author, including Subplane Covered Nets, Johnson (2000); Foundations of Translation Planes, Biliotti, Jha, and Johnson (2001); Handbook of Finite Translation Planes, Johnson, Jha, and Biliotti (2007); and Combinatorics of Spreads and Parallelisms, Johnson (2010), all published by CRC Press.

Like its predecessors, this book will primarily deal with connections to the theory of derivable nets and translation planes in both the finite and infinite cases. Translation planes over non-commutative skewfields have not traditionally had a significant representation in incidence geometry, and derivable nets over skewfields have only been marginally understood. Both are deeply examined in this volume, while ideas of non-commutative algebra are also described in detail, with all the necessary background given a geometric treatment.