Combinatorial Methods in Discrete Distributions / Wiley Series in Probability and Statistics (PDF)

A unique approach illustrating discrete distribution theory through
combinatorial methods

This book provides a unique approach by presenting combinatorial
methods in tandem with discrete distribution theory. This method,
particular to discreteness, allows readers to gain a deeper
understanding of theory by using applications to solve problems.
The author makes extensive use of the reduction approach to
conditional distributions of independent random occupancy numbers,
and provides excellent studies of occupancy and sequential
occupancy distributions, convolutions of truncated discrete
distributions, and compound and mixture distributions.

Combinatorial Methods in Discrete Distributions begins with a
brief presentation of set theory followed by basic counting
principles. Fundamental principles of combinatorics, finite
differences, and discrete probability are included to give readers
the necessary foundation to the topics presented in the text.

A thorough examination of the field is provided and
features:

* Stirling numbers and generalized factorial coefficients

* Occupancy and sequential occupancy distributions

* n-fold convolutions of truncated distributions

* Compound and mixture distributions

Thoroughly worked examples aid readers in understanding complex
theory and discovering how theory can be applied to solve practical
problems. An appendix with hints and answers to the exercises helps
readers work through the more complex sections. Reference notes are
provided at the end of each chapter, and an extensive bibliography
offers readers a resource for additional information on specialized
topics.