Combinatorial methods in discrete distributions [[electronic resource] /] / Charalambos A. Charalambides

• Autore: Charalambides Ch. A
• Pubblicazione: Hoboken, N.J., : Wiley-Interscience, c2005
• Descrizione fisica: 1 online resource (440 p.)
• Disciplina: 511.6; 519.2/4; 519.24
• Soggetto topico: Combinatorial analysis; Distribution (Probability theory)
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 383-400) and indexes.
• Nota di contenuto: COMBINATORIAL METHODS IN DISCRETE DISTRIBUTIONS; Contents; Preface; 1 BASIC COMBINATORICS AND PROBABILITY; 1.1 Basic counting principles; 1.2 Recurrence relations; 1.3 Finite differences; 1.4 Discrete probability; 1.5 Inclusion and exclusion principle; 1.6 Distributions and moments of random variables; 1.7 Generating functions; 1.8 Reference notes; 1.9 Exercises and complements; 2 STIRLING NUMBERS; 2.1 Introduction; 2.2 Definitions and generating functions; 2.3 Explicit expressions and recurrence relations; 2.4 Generalized factorial coefficients ; 2.5 Enumeration of partitions by subsets and permutations by cycles2.6 Reference notes; 2.7 Exercises and complements; 3 GENERALIZED STIRLING AND LAH NUMBERS; 3.1 Introduction; 3.2 Associated Stirling numbers; 3.3 Associated generalized factorial coefficients; 3.4 Universal generating functions; 3.5 Generalized Stirling numbers; 3.6 Generalized Lah numbers; 3.7 Reference notes; 3.8 Exercises and complements; 4 OCCUPANCY DISTRIBUTIONS; 4.1 Introduction; 4.2 A random occupancy model; 4.3 Occupancy distributions; 4.4 Particular occupancy distributions; 4.4.1 Classical occupancy distribution ; 4.4.2 Restricted occupancy distribution4.4.3 Pseudo-contagious occupancy distribution; 4.4.4 Restricted Bose-Einstein occupancy distribution; 4.5 Statistical applications; 4.6 A general random occupancy model; 4.7 Reference notes; 4.8 Exercises and complements; 5 SEQUENTIAL OCCUPANCY DISTRIBUTIONS; 5.1 Introduction; 5.2 A sequential random occupancy model; 5.3 Sequential occupancy distributions; 5.4 Particular sequential occupancy distributions; 5.4.1 Sequential classical occupancy distributions; 5.4.2 Sequential restricted occupancy distributions ; 5.4.3 Sequential pseudo-contagious occupancy distributions5.5 Statistical applications; 5.6 A reduced sequential occupancy model; 5.7 Reference notes; 5.8 Exercises and complements; 6 CONVOLUTIONS OF TRUNCATED DISTRIBUTIONS; 6.1 Introduction; 6.2 Zero truncated discrete distributions; 6.3 Some particular convolutions; 6.3.1 Zero truncated Poisson distribution; 6.3.2 Logarithmic distribution; 6.3.3 Zero truncated binomial distribution; 6.3.4 Zero truncated negative binomial distribution; 6.4 General truncated discrete distributions; 6.5 Statistical applications ; 6.5.1 Zero truncated power series distribution6.5.2 Left truncated power series distribution; 6.6 Reference notes; 6.7 Exercises and complements; 7 COMPOUND AND MIXTURE DISTRIBUTIONS; 7.1 Introduction; 7.2 Compound discrete distributions; 7.3 Mixture discrete distributions; 7.4 Particular compounding distributions; 7.4.1 Poisson compounding distribution; 7.4.2 Binomial compounding distribution; 7.4.3 Negative binomial compounding distribution; 7.4.4 Logarithmic compounding distribution; 7.5 Compound Poisson distributions; 7.5.1 Hermite distribution; 7.5.2 Generalized Hermite distribution ; 7.5.3 Pólya-Aeppli distribution
• Sommario/riassunto: 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 distri
• Titolo autorizzato: Combinatorial methods in discrete distributions
• ISBN: 1-280-27703-3; 9786610277032; 0-470-32376-0; 0-471-73318-0; 0-471-73317-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910840956703321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley series in probability and statistics.