Combinatorial Methods In Probability And Statistics
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Author | : Charalambos A. Charalambides |
Publisher | : John Wiley & Sons |
Total Pages | : 440 |
Release | : 2005-06-24 |
Genre | : Mathematics |
ISBN | : 0471733172 |
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.
Author | : N. Balakrishnan |
Publisher | : Springer Science & Business Media |
Total Pages | : 576 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461241405 |
Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.
Author | : R. C. Bose |
Publisher | : |
Total Pages | : 264 |
Release | : 1984-03-19 |
Genre | : Mathematics |
ISBN | : |
A ``hands-on'' constructive and computational approach to combinatorial topics with real-life modern applications. Provides a simple treatment of the subject. Introduces topics such as counting, designs and graphs. The notation is standard and kept to a minimum. Chapters end with historical remarks and suggestions for further reading.
Author | : N. Balakrishnan |
Publisher | : Boston : Birkhäuser |
Total Pages | : 562 |
Release | : 1997-01-01 |
Genre | : Combinatorial probabilities |
ISBN | : 9783764339081 |
Author | : S. G. Mohanty |
Publisher | : |
Total Pages | : 42 |
Release | : 1971* |
Genre | : |
ISBN | : |
Author | : Luc Devroye |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461301254 |
Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.
Author | : Lajos Takács |
Publisher | : |
Total Pages | : 288 |
Release | : 1977 |
Genre | : Mathematics |
ISBN | : |
Author | : Philippe Flajolet |
Publisher | : Cambridge University Press |
Total Pages | : 825 |
Release | : 2009-01-15 |
Genre | : Mathematics |
ISBN | : 1139477161 |
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author | : Graham Brightwell |
Publisher | : Cambridge University Press |
Total Pages | : 27 |
Release | : 2007-03-08 |
Genre | : Mathematics |
ISBN | : 0521872073 |
This volume celebrating the 60th birthday of Béla Bollobás presents the state of the art in combinatorics.
Author | : Raj Chandra Bose |
Publisher | : |
Total Pages | : 632 |
Release | : 1969 |
Genre | : Combinatorial analysis |
ISBN | : |