Summary

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:

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.

Choice Review

A course in discrete mathematics typically includes some simple probability theory to illustrate the applications of counting techniques; probability courses, for their part, typically make short work of discrete distributions before concentrating on continuous distributions via analytical, not combinatorial, tools. This rarity, an advanced book on discrete probability, by Charalambides (Univ. of Athens, Greece), offers undergraduates an interesting follow-up to either sort of course. Half the book collates copious, valuable, detailed, and hard-to-find information on Stirling numbers and their kin. The remainder develops detailed applications to occupancy (balls in urns) problems, waiting-time problems, zero-truncated discrete distributions, and compound distributions. Hundreds of exercises not only challenge the reader, but considerably amplify the range of topics and applications; a 50-page appendix presents hints and answers. A chapter on basics makes the book essentially self-contained, and detailed chapter notes sketch the subject's history and offer possibilities for further reading. ^BSumming Up: Highly recommended. Upper-division undergraduates through professionals. D. V. Feldman University of New Hampshire