„Highly recommended.“ (CHOICE, January 2006)
„... a valuable and up-to-date account on Sterling numbersand occupancy distributions.“ (Mathematical Reviews,2006c)
Combinatorial Methods in Discrete Distributions
von Charalabos A. CharalambidesA unique approach illustrating discrete distribution theory throughcombinatorial methods
This book provides a unique approach by presenting combinatorialmethods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeperunderstanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach toconditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequentialoccupancy distributions, convolutions of truncated discretedistributions, and compound and mixture distributions.
Combinatorial Methods in Discrete Distributions begins with abrief presentation of set theory followed by basic countingprinciples. Fundamental principles of combinatorics, finitedifferences, and discrete probability are included to give readersthe necessary foundation to the topics presented in the text.
A thorough examination of the field is provided andfeatures:
* 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 complextheory and discovering how theory can be applied to solve practicalproblems. An appendix with hints and answers to the exercises helpsreaders work through the more complex sections. Reference notes areprovided at the end of each chapter, and an extensive bibliographyoffers readers a resource for additional information on specializedtopics.
This book provides a unique approach by presenting combinatorialmethods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeperunderstanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach toconditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequentialoccupancy distributions, convolutions of truncated discretedistributions, and compound and mixture distributions.
Combinatorial Methods in Discrete Distributions begins with abrief presentation of set theory followed by basic countingprinciples. Fundamental principles of combinatorics, finitedifferences, and discrete probability are included to give readersthe necessary foundation to the topics presented in the text.
A thorough examination of the field is provided andfeatures:
* 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 complextheory and discovering how theory can be applied to solve practicalproblems. An appendix with hints and answers to the exercises helpsreaders work through the more complex sections. Reference notes areprovided at the end of each chapter, and an extensive bibliographyoffers readers a resource for additional information on specializedtopics.
