05491nam 22007094a 450 991101981060332120200520144314.0978661027703297812802770301280277033978047032376204703237609780471733188047173318097804717331710471733172(CKB)1000000000355415(EBL)232640(OCoLC)475938712(SSID)ssj0000125251(PQKBManifestationID)11146550(PQKBTitleCode)TC0000125251(PQKBWorkID)10026744(PQKB)11382828(MiAaPQ)EBC232640(Perlego)2754938(EXLCZ)99100000000035541520041015d2005 uy 0engur|n|---|||||txtccrCombinatorial methods in discrete distributions /Charalambos A. CharalambidesHoboken, N.J. Wiley-Intersciencec20051 online resource (440 p.)Wiley series in probability and statisticsDescription based upon print version of record.9780471680277 0471680273 Includes bibliographical references (p. 383-400) and indexes.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 coefficients2.5 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 distribution4.4.2 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 distributions5.4.3 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 applications6.5.1 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 distribution7.5.3 Pólya-Aeppli distributionA 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 distriWiley series in probability and statistics.Combinatorial analysisDistribution (Probability theory)Combinatorial analysis.Distribution (Probability theory)519.2/4Charalambides Ch. A893546MiAaPQMiAaPQMiAaPQBOOK9911019810603321Combinatorial methods in discrete distributions4422501UNINA