{"product_id":"univariate-discrete-distributions-9780471272465","title":"Univariate Discrete Distributions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis Set Contains: \u003cbr\u003e \u003ci\u003eContinuous Multivariate Distributions, Volume 1, Models and Applications,\u003c\/i\u003e 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson\u003cbr\u003e \u003ci\u003eContinuous Univariate Distributions, Volume 1, 2nd Edition\u003c\/i\u003e by Samuel Kotz, N. Balakrishnan and Normal L. Johnson\u003cbr\u003e \u003ci\u003eContinuous Univariate Distributions, Volume 2, 2nd Edition\u003c\/i\u003e by Samuel Kotz, N. Balakrishnan and Normal L. Johnson\u003cbr\u003e \u003ci\u003eDiscrete Multivariate Distributions\u003c\/i\u003e by Samuel Kotz, N. Balakrishnan and Normal L. Johnson\u003cbr\u003e \u003ci\u003eUnivariate Discrete Distributions, 3rd Edition\u003c\/i\u003e by Samuel Kotz, N. Balakrishnan and Normal L. Johnson  \u003cp\u003e\u003cb\u003eDiscover the latest advances in discrete distributions theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe \u003ci\u003eThird Edition\u003c\/i\u003e of the critically acclaimed \u003ci\u003eUnivariate Discrete Distributions\u003c\/i\u003e provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distribut\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.”  (\u003ci\u003eXolosepo\u003c\/i\u003e, 27 October 2012)\u003c\/p\u003e \"The authors continue to do a praise-worthy job of making the material accessible in the third edition. This book should be on every library's shelf.\" (\u003ci\u003eJournal of the American Statistical Association\u003c\/i\u003e, September 2006)  \u003cp\u003e\"These authors have achieved considerable renown for their comprehensive books on statistical distributions.\" (\u003ci\u003eTechnometrics\u003c\/i\u003e, August 2006)\u003c\/p\u003e \u003cp\u003e\"Encyclopedic in nature, the book continues to be a valuable reference.\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2006d)\u003c\/p\u003e \u003cp\u003e\"This is an important book that should be part of every statistician's library.\" (\u003ci\u003eMAA Reviews\u003c\/i\u003e, January 2, 2006)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Preliminary Information 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Mathematical Preliminaries 1\u003c\/p\u003e \u003cp\u003e1.1.1 Factorial and Combinatorial Conventions 1\u003c\/p\u003e \u003cp\u003e1.1.2 Gamma and Beta Functions 5\u003c\/p\u003e \u003cp\u003e1.1.3 Finite Difference Calculus 10\u003c\/p\u003e \u003cp\u003e1.1.4 Differential Calculus 14\u003c\/p\u003e \u003cp\u003e1.1.5 Incomplete Gamma and Beta Functions and Other Gamma-Related Functions 16\u003c\/p\u003e \u003cp\u003e1.1.6 Gaussian Hypergeometric Functions 20\u003c\/p\u003e \u003cp\u003e1.1.7 Confluent Hypergeometric Functions (Kummer’s Functions) 23\u003c\/p\u003e \u003cp\u003e1.1.8 Generalized Hypergeometric Functions 26\u003c\/p\u003e \u003cp\u003e1.1.9 Bernoulli and Euler Numbers and Polynomials 29\u003c\/p\u003e \u003cp\u003e1.1.10 Integral Transforms 32\u003c\/p\u003e \u003cp\u003e1.1.11 Orthogonal Polynomials 32\u003c\/p\u003e \u003cp\u003e1.1.12 Basic Hypergeometric Series 34\u003c\/p\u003e \u003cp\u003e1.2 Probability and Statistical Preliminaries 37\u003c\/p\u003e \u003cp\u003e1.2.1 Calculus of Probabilities 37\u003c\/p\u003e \u003cp\u003e1.2.2 Bayes’s Theorem 41\u003c\/p\u003e \u003cp\u003e1.2.3 Random Variables 43\u003c\/p\u003e \u003cp\u003e1.2.4 Survival Concepts 45\u003c\/p\u003e \u003cp\u003e1.2.5 Expected Values 47\u003c\/p\u003e \u003cp\u003e1.2.6 Inequalities 49\u003c\/p\u003e \u003cp\u003e1.2.7 Moments and Moment Generating Functions 50\u003c\/p\u003e \u003cp\u003e1.2.8 Cumulants and Cumulant Generating Functions 54\u003c\/p\u003e \u003cp\u003e1.2.9 Joint Moments and Cumulants 56\u003c\/p\u003e \u003cp\u003e1.2.10 Characteristic Functions 57\u003c\/p\u003e \u003cp\u003e1.2.11 Probability Generating Functions 58\u003c\/p\u003e \u003cp\u003e1.2.12 Order Statistics 61\u003c\/p\u003e \u003cp\u003e1.2.13 Truncation and Censoring 62\u003c\/p\u003e \u003cp\u003e1.2.14 Mixture Distributions 64\u003c\/p\u003e \u003cp\u003e1.2.15 Variance of a Function 65\u003c\/p\u003e \u003cp\u003e1.2.16 Estimation 66\u003c\/p\u003e \u003cp\u003e1.2.17 General Comments on the Computer Generation of Discrete Random Variables 71\u003c\/p\u003e \u003cp\u003e1.2.18 Computer Software 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Families of Discrete Distributions 74\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Lattice Distributions 74\u003c\/p\u003e \u003cp\u003e2.2 Power Series Distributions 75\u003c\/p\u003e \u003cp\u003e2.2.1 Generalized Power Series Distributions 75\u003c\/p\u003e \u003cp\u003e2.2.2 Modified Power Series Distributions 79\u003c\/p\u003e \u003cp\u003e2.3 Difference-Equation Systems 82\u003c\/p\u003e \u003cp\u003e2.3.1 Katz and Extended Katz Families 82\u003c\/p\u003e \u003cp\u003e2.3.2 Sundt and Jewell Family 85\u003c\/p\u003e \u003cp\u003e2.3.3 Ord’s Family 87\u003c\/p\u003e \u003cp\u003e2.4 Kemp Families 89\u003c\/p\u003e \u003cp\u003e2.4.1 Generalized Hypergeometric Probability Distributions 89\u003c\/p\u003e \u003cp\u003e2.4.2 Generalized Hypergeometric Factorial Moment Distributions 96\u003c\/p\u003e \u003cp\u003e2.5 Distributions Based on Lagrangian Expansions 99\u003c\/p\u003e \u003cp\u003e2.6 Gould and Abel Distributions 101\u003c\/p\u003e \u003cp\u003e2.7 Factorial Series Distributions 103\u003c\/p\u003e \u003cp\u003e2.8 Distributions of Order-\u003ci\u003ek\u003c\/i\u003e 105\u003c\/p\u003e \u003cp\u003e2.9 q-Series Distributions 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Binomial Distribution 108\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Definition 108\u003c\/p\u003e \u003cp\u003e3.2 Historical Remarks and Genesis 109\u003c\/p\u003e \u003cp\u003e3.3 Moments 109\u003c\/p\u003e \u003cp\u003e3.4 Properties 112\u003c\/p\u003e \u003cp\u003e3.5 Order Statistics 116\u003c\/p\u003e \u003cp\u003e3.6 Approximations, Bounds, and Transformations 116\u003c\/p\u003e \u003cp\u003e3.6.1 Approximations 116\u003c\/p\u003e \u003cp\u003e3.6.2 Bounds 122\u003c\/p\u003e \u003cp\u003e3.6.3 Transformations 123\u003c\/p\u003e \u003cp\u003e3.7 Computation, Tables, and Computer Generation 124\u003c\/p\u003e \u003cp\u003e3.7.1 Computation and Tables 124\u003c\/p\u003e \u003cp\u003e3.7.2 Computer Generation 125\u003c\/p\u003e \u003cp\u003e3.8 Estimation 126\u003c\/p\u003e \u003cp\u003e3.8.1 Model Selection 126\u003c\/p\u003e \u003cp\u003e3.8.2 Point Estimation 126\u003c\/p\u003e \u003cp\u003e3.8.3 Confidence Intervals 130\u003c\/p\u003e \u003cp\u003e3.8.4 Model Verification 133\u003c\/p\u003e \u003cp\u003e3.9 Characterizations 134\u003c\/p\u003e \u003cp\u003e3.10 Applications 135\u003c\/p\u003e \u003cp\u003e3.11 Truncated Binomial Distributions 137\u003c\/p\u003e \u003cp\u003e3.12 Other Related Distributions 140\u003c\/p\u003e \u003cp\u003e3.12.1 Limiting Forms 140\u003c\/p\u003e \u003cp\u003e3.12.2 Sums and Differences of Binomial-Type Variables 140\u003c\/p\u003e \u003cp\u003e3.12.3 Poissonian Binomial, Lexian, and Coolidge Schemes 144\u003c\/p\u003e \u003cp\u003e3.12.4 Weighted Binomial Distributions 149\u003c\/p\u003e \u003cp\u003e3.12.5 Chain Binomial Models 151\u003c\/p\u003e \u003cp\u003e3.12.6 Correlated Binomial Variables 151\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Poisson Distribution 156\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Definition 156\u003c\/p\u003e \u003cp\u003e4.2 Historical Remarks and Genesis 156\u003c\/p\u003e \u003cp\u003e4.2.1 Genesis 156\u003c\/p\u003e \u003cp\u003e4.2.2 Poissonian Approximations 160\u003c\/p\u003e \u003cp\u003e4.3 Moments 161\u003c\/p\u003e \u003cp\u003e4.4 Properties 163\u003c\/p\u003e \u003cp\u003e4.5 Approximations, Bounds, and Transformations 167\u003c\/p\u003e \u003cp\u003e4.6 Computation, Tables, and Computer Generation 170\u003c\/p\u003e \u003cp\u003e4.6.1 Computation and Tables 170\u003c\/p\u003e \u003cp\u003e4.6.2 Computer Generation 171\u003c\/p\u003e \u003cp\u003e4.7 Estimation 173\u003c\/p\u003e \u003cp\u003e4.7.1 Model Selection 173\u003c\/p\u003e \u003cp\u003e4.7.2 Point Estimation 174\u003c\/p\u003e \u003cp\u003e4.7.3 Confidence Intervals 176\u003c\/p\u003e \u003cp\u003e4.7.4 Model Verification 178\u003c\/p\u003e \u003cp\u003e4.8 Characterizations 179\u003c\/p\u003e \u003cp\u003e4.9 Applications 186\u003c\/p\u003e \u003cp\u003e4.10 Truncated and Misrecorded Poisson Distributions 188\u003c\/p\u003e \u003cp\u003e4.10.1 Left Truncation 188\u003c\/p\u003e \u003cp\u003e4.10.2 Right Truncation and Double Truncation 191\u003c\/p\u003e \u003cp\u003e4.10.3 Misrecorded Poisson Distributions 193\u003c\/p\u003e \u003cp\u003e4.11 Poisson–Stopped Sum Distributions 195\u003c\/p\u003e \u003cp\u003e4.12 Other Related Distributions 196\u003c\/p\u003e \u003cp\u003e4.12.1 Normal Distribution 196\u003c\/p\u003e \u003cp\u003e4.12.2 Gamma Distribution 196\u003c\/p\u003e \u003cp\u003e4.12.3 Sums and Differences of Poisson Variates 197\u003c\/p\u003e \u003cp\u003e4.12.4 Hyper-Poisson Distributions 199\u003c\/p\u003e \u003cp\u003e4.12.5 Grouped Poisson Distributions 202\u003c\/p\u003e \u003cp\u003e4.12.6 Heine and Euler Distributions 205\u003c\/p\u003e \u003cp\u003e4.12.7 Intervened Poisson Distributions 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Negative Binomial Distribution 208\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Definition 208\u003c\/p\u003e \u003cp\u003e5.2 Geometric Distribution 210\u003c\/p\u003e \u003cp\u003e5.3 Historical Remarks and Genesis of Negative Binomial Distribution 212\u003c\/p\u003e \u003cp\u003e5.4 Moments 215\u003c\/p\u003e \u003cp\u003e5.5 Properties 217\u003c\/p\u003e \u003cp\u003e5.6 Approximations and Transformations 218\u003c\/p\u003e \u003cp\u003e5.7 Computation and Tables 220\u003c\/p\u003e \u003cp\u003e5.8 Estimation 222\u003c\/p\u003e \u003cp\u003e5.8.1 Model Selection 222\u003c\/p\u003e \u003cp\u003e5.8.2 P Unknown 222\u003c\/p\u003e \u003cp\u003e5.8.3 Both Parameters Unknown 223\u003c\/p\u003e \u003cp\u003e5.8.4 Data Sets with a Common Parameter 226\u003c\/p\u003e \u003cp\u003e5.8.5 Recent Developments 227\u003c\/p\u003e \u003cp\u003e5.9 Characterizations 228\u003c\/p\u003e \u003cp\u003e5.9.1 Geometric Distribution 228\u003c\/p\u003e \u003cp\u003e5.9.2 Negative Binomial Distribution 231\u003c\/p\u003e \u003cp\u003e5.10 Applications 232\u003c\/p\u003e \u003cp\u003e5.11 Truncated Negative Binomial Distributions 233\u003c\/p\u003e \u003cp\u003e5.12 Related Distributions 236\u003c\/p\u003e \u003cp\u003e5.12.1 Limiting Forms 236\u003c\/p\u003e \u003cp\u003e5.12.2 Extended Negative Binomial Model 237\u003c\/p\u003e \u003cp\u003e5.12.3 Lagrangian Generalized Negative Binomial Distribution 239\u003c\/p\u003e \u003cp\u003e5.12.4 Weighted Negative Binomial Distributions 240\u003c\/p\u003e \u003cp\u003e5.12.5 Convolutions Involving Negative Binomial Variates 241\u003c\/p\u003e \u003cp\u003e5.12.6 Pascal–Poisson Distribution 243\u003c\/p\u003e \u003cp\u003e5.12.7 Minimum (Riff–Shuffle) and Maximum Negative Binomial Distributions 244\u003c\/p\u003e \u003cp\u003e5.12.8 Condensed Negative Binomial Distributions 246\u003c\/p\u003e \u003cp\u003e5.12.9 Other Related Distributions 247\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Hypergeometric Distributions 251\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Definition 251\u003c\/p\u003e \u003cp\u003e6.2 Historical Remarks and Genesis 252\u003c\/p\u003e \u003cp\u003e6.2.1 Classical Hypergeometric Distribution 252\u003c\/p\u003e \u003cp\u003e6.2.2 Beta–Binomial Distribution, Negative (Inverse) Hypergeometric Distribution: Hypergeometric Waiting-Time Distribution 253\u003c\/p\u003e \u003cp\u003e6.2.3 Beta–Negative Binomial Distribution: Beta–Pascal Distribution, Generalized Waring Distribution 256\u003c\/p\u003e \u003cp\u003e6.2.4 Pólya Distributions 258\u003c\/p\u003e \u003cp\u003e6.2.5 Hypergeometric Distributions in General 259\u003c\/p\u003e \u003cp\u003e6.3 Moments 262\u003c\/p\u003e \u003cp\u003e6.4 Properties 265\u003c\/p\u003e \u003cp\u003e6.5 Approximations and Bounds 268\u003c\/p\u003e \u003cp\u003e6.6 Tables Computation and Computer Generation 271\u003c\/p\u003e \u003cp\u003e6.7 Estimation 272\u003c\/p\u003e \u003cp\u003e6.7.1 Classical Hypergeometric Distribution 273\u003c\/p\u003e \u003cp\u003e6.7.2 Negative (Inverse) Hypergeometric Distribution: Beta–Binomial Distribution 274\u003c\/p\u003e \u003cp\u003e6.7.3 Beta–Pascal Distribution 276\u003c\/p\u003e \u003cp\u003e6.8 Characterizations 277\u003c\/p\u003e \u003cp\u003e6.9 Applications 279\u003c\/p\u003e \u003cp\u003e6.9.1 Classical Hypergeometric Distribution 279\u003c\/p\u003e \u003cp\u003e6.9.2 Negative (Inverse) Hypergeometric Distribution: Beta–Binomial Distribution 281\u003c\/p\u003e \u003cp\u003e6.9.3 Beta–Negative Binomial Distribution: Beta–Pascal Distribution, Generalized Waring Distribution 283\u003c\/p\u003e \u003cp\u003e6.10 Special Cases 283\u003c\/p\u003e \u003cp\u003e6.10.1 Discrete Rectangular Distribution 283\u003c\/p\u003e \u003cp\u003e6.10.2 Distribution of Leads in Coin Tossing 286\u003c\/p\u003e \u003cp\u003e6.10.3 Yule Distribution 287\u003c\/p\u003e \u003cp\u003e6.10.4 Waring Distribution 289\u003c\/p\u003e \u003cp\u003e6.10.5 Narayana Distribution 291\u003c\/p\u003e \u003cp\u003e6.11 Related Distributions 293\u003c\/p\u003e \u003cp\u003e6.11.1 Extended Hypergeometric Distributions 293\u003c\/p\u003e \u003cp\u003e6.11.2 Generalized Hypergeometric Probability Distributions 296\u003c\/p\u003e \u003cp\u003e6.11.3 Generalized Hypergeometric Factorial Moment Distributions 298\u003c\/p\u003e \u003cp\u003e6.11.4 Other Related Distributions 299\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Logarithmic and Lagrangian Distributions 302\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Logarithmic Distribution 302\u003c\/p\u003e \u003cp\u003e7.1.1 Definition 302\u003c\/p\u003e \u003cp\u003e7.1.2 Historical Remarks and Genesis 303\u003c\/p\u003e \u003cp\u003e7.1.3 Moments 305\u003c\/p\u003e \u003cp\u003e7.1.4 Properties 307\u003c\/p\u003e \u003cp\u003e7.1.5 Approximations and Bounds 309\u003c\/p\u003e \u003cp\u003e7.1.6 Computation, Tables, and Computer Generation 310\u003c\/p\u003e \u003cp\u003e7.1.7 Estimation 311\u003c\/p\u003e \u003cp\u003e7.1.8 Characterizations 315\u003c\/p\u003e \u003cp\u003e7.1.9 Applications 316\u003c\/p\u003e \u003cp\u003e7.1.10 Truncated and Modified Logarithmic Distributions 317\u003c\/p\u003e \u003cp\u003e7.1.11 Generalizations of the Logarithmic Distribution 319\u003c\/p\u003e \u003cp\u003e7.1.12 Other Related Distributions 321\u003c\/p\u003e \u003cp\u003e7.2 Lagrangian Distributions 325\u003c\/p\u003e \u003cp\u003e7.2.1 Otter’s Multiplicative Process 326\u003c\/p\u003e \u003cp\u003e7.2.2 Borel Distribution 328\u003c\/p\u003e \u003cp\u003e7.2.3 Consul Distribution 329\u003c\/p\u003e \u003cp\u003e7.2.4 Geeta Distribution 330\u003c\/p\u003e \u003cp\u003e7.2.5 General Lagrangian Distributions of the First Kind 331\u003c\/p\u003e \u003cp\u003e7.2.6 Lagrangian Poisson Distribution 336\u003c\/p\u003e \u003cp\u003e7.2.7 Lagrangian Negative Binomial Distribution 340\u003c\/p\u003e \u003cp\u003e7.2.8 Lagrangian Logarithmic Distribution 341\u003c\/p\u003e \u003cp\u003e7.2.9 Lagrangian Distributions of the Second Kind 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Mixture Distributions 343\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Basic Ideas 343\u003c\/p\u003e \u003cp\u003e8.1.1 Introduction 343\u003c\/p\u003e \u003cp\u003e8.1.2 Finite Mixtures 344\u003c\/p\u003e \u003cp\u003e8.1.3 Varying Parameters 345\u003c\/p\u003e \u003cp\u003e8.1.4 Bayesian Interpretation 347\u003c\/p\u003e \u003cp\u003e8.2 Finite Mixtures of Discrete Distributions 347\u003c\/p\u003e \u003cp\u003e8.2.1 Parameters of Finite Mixtures 347\u003c\/p\u003e \u003cp\u003e8.2.2 Parameter Estimation 349\u003c\/p\u003e \u003cp\u003e8.2.3 Zero-Modified and Hurdle Distributions 351\u003c\/p\u003e \u003cp\u003e8.2.4 Examples of Zero-Modified Distributions 353\u003c\/p\u003e \u003cp\u003e8.2.5 Finite Poisson Mixtures 357\u003c\/p\u003e \u003cp\u003e8.2.6 Finite Binomial Mixtures 358\u003c\/p\u003e \u003cp\u003e8.2.7 Other Finite Mixtures of Discrete Distributions 359\u003c\/p\u003e \u003cp\u003e8.3 Continuous and Countable Mixtures of Discrete Distributions 360\u003c\/p\u003e \u003cp\u003e8.3.1 Properties of General Mixed Distributions 360\u003c\/p\u003e \u003cp\u003e8.3.2 Properties of Mixed Poisson Distributions 362\u003c\/p\u003e \u003cp\u003e8.3.3 Examples of Poisson Mixtures 365\u003c\/p\u003e \u003cp\u003e8.3.4 Mixtures of Binomial Distributions 373\u003c\/p\u003e \u003cp\u003e8.3.5 Examples of Binomial Mixtures 374\u003c\/p\u003e \u003cp\u003e8.3.6 Other Continuous and Countable Mixtures of Discrete Distributions 376\u003c\/p\u003e \u003cp\u003e8.4 Gamma and Beta Mixing Distributions 378\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Stopped-Sum Distributions 381\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Generalized and Generalizing Distributions 381\u003c\/p\u003e \u003cp\u003e9.2 Damage Processes 386\u003c\/p\u003e \u003cp\u003e9.3 Poisson–Stopped Sum (Multiple Poisson) Distributions 388\u003c\/p\u003e \u003cp\u003e9.4 Hermite Distribution 394\u003c\/p\u003e \u003cp\u003e9.5 Poisson–Binomial Distribution 400\u003c\/p\u003e \u003cp\u003e9.6 Neyman Type A Distribution 403\u003c\/p\u003e \u003cp\u003e9.6.1 Definition 403\u003c\/p\u003e \u003cp\u003e9.6.2 Moment Properties 405\u003c\/p\u003e \u003cp\u003e9.6.3 Tables and Approximations 406\u003c\/p\u003e \u003cp\u003e9.6.4 Estimation 407\u003c\/p\u003e \u003cp\u003e9.6.5 Applications 409\u003c\/p\u003e \u003cp\u003e9.7 Pólya–Aeppli Distribution 410\u003c\/p\u003e \u003cp\u003e9.8 Generalized Pólya–Aeppli (Poisson–Negative Binomial) Distribution 414\u003c\/p\u003e \u003cp\u003e9.9 Generalizations of Neyman Type A Distribution 416\u003c\/p\u003e \u003cp\u003e9.10 Thomas Distribution 421\u003c\/p\u003e \u003cp\u003e9.11 Borel–Tanner Distribution: Lagrangian Poisson Distribution 423\u003c\/p\u003e \u003cp\u003e9.12 Other Poisson–Stopped Sum (multiple Poisson) Distributions 425\u003c\/p\u003e \u003cp\u003e9.13 Other Families of Stopped-Sum Distributions 426\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Matching, Occupancy, Runs, and \u003ci\u003eq\u003c\/i\u003e-Series Distributions 430\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 430\u003c\/p\u003e \u003cp\u003e10.2 Probabilities of Combined Events 431\u003c\/p\u003e \u003cp\u003e10.3 Matching Distributions 434\u003c\/p\u003e \u003cp\u003e10.4 Occupancy Distributions 439\u003c\/p\u003e \u003cp\u003e10.4.1 Classical Occupancy and Coupon Collecting 439\u003c\/p\u003e \u003cp\u003e10.4.2 Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac Statistics 444\u003c\/p\u003e \u003cp\u003e10.4.3 Specified Occupancy and Grassia–Binomial Distributions 446\u003c\/p\u003e \u003cp\u003e10.5 Record Value Distributions 448\u003c\/p\u003e \u003cp\u003e10.6 Runs Distributions 450\u003c\/p\u003e \u003cp\u003e10.6.1 Runs of Like Elements 450\u003c\/p\u003e \u003cp\u003e10.6.2 Runs Up and Down 453\u003c\/p\u003e \u003cp\u003e10.7 Distributions of Order k 454\u003c\/p\u003e \u003cp\u003e10.7.1 Early Work on Success Runs Distributions 454\u003c\/p\u003e \u003cp\u003e10.7.2 Geometric Distribution of Order \u003ci\u003ek\u003c\/i\u003e 456\u003c\/p\u003e \u003cp\u003e10.7.3 Negative Binomial Distributions of Order \u003ci\u003ek\u003c\/i\u003e 458\u003c\/p\u003e \u003cp\u003e10.7.4 Poisson and Logarithmic Distributions of Order \u003ci\u003ek\u003c\/i\u003e 459\u003c\/p\u003e \u003cp\u003e10.7.5 Binomial Distributions of Order \u003ci\u003ek\u003c\/i\u003e 461\u003c\/p\u003e \u003cp\u003e10.7.6 Further Distributions of Order \u003ci\u003ek\u003c\/i\u003e 463\u003c\/p\u003e \u003cp\u003e10.8 \u003ci\u003eq\u003c\/i\u003e-Series Distributions 464\u003c\/p\u003e \u003cp\u003e10.8.1 Terminating Distributions 465\u003c\/p\u003e \u003cp\u003e10.8.2 q-Series Distributions with Infinite Support 470\u003c\/p\u003e \u003cp\u003e10.8.3 Bilateral \u003ci\u003eq\u003c\/i\u003e-Series Distributions 474\u003c\/p\u003e \u003cp\u003e10.8.4 \u003ci\u003eq\u003c\/i\u003e-Series Related Distributions 476\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Parametric Regression Models and Miscellanea 478\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Parametric Regression Models 478\u003c\/p\u003e \u003cp\u003e11.1.1 Introduction 478\u003c\/p\u003e \u003cp\u003e11.1.2 Tweedie–Poisson Family 480\u003c\/p\u003e \u003cp\u003e11.1.3 Negative Binomial Regression Models 482\u003c\/p\u003e \u003cp\u003e11.1.4 Poisson Lognormal Model 483\u003c\/p\u003e \u003cp\u003e11.1.5 Poisson–Inverse Gaussian (Sichel) Model 484\u003c\/p\u003e \u003cp\u003e11.1.6 Poisson Polynomial Distribution 487\u003c\/p\u003e \u003cp\u003e11.1.7 Weighted Poisson Distributions 488\u003c\/p\u003e \u003cp\u003e11.1.8 Double-Poisson and Double-Binomial Distributions 489\u003c\/p\u003e \u003cp\u003e11.1.9 Simplex–Binomial Mixture Model 490\u003c\/p\u003e \u003cp\u003e11.2 Miscellaneous Discrete Distributions 491\u003c\/p\u003e \u003cp\u003e11.2.1 Dandekar’s Modified Binomial and Poisson Models 491\u003c\/p\u003e \u003cp\u003e11.2.2 Digamma and Trigamma Distributions 492\u003c\/p\u003e \u003cp\u003e11.2.3 Discrete Adès Distribution 494\u003c\/p\u003e \u003cp\u003e11.2.4 Discrete Bessel Distribution 495\u003c\/p\u003e \u003cp\u003e11.2.5 Discrete Mittag–Leffler Distribution 496\u003c\/p\u003e \u003cp\u003e11.2.6 Discrete Student’s t Distribution 498\u003c\/p\u003e \u003cp\u003e11.2.7 Feller–Arley and Gegenbauer Distributions 499\u003c\/p\u003e \u003cp\u003e11.2.8 Gram–Charlier Type B Distributions 501\u003c\/p\u003e \u003cp\u003e11.2.9 “Interrupted” Distributions 502\u003c\/p\u003e \u003cp\u003e11.2.10 Lost-Games Distributions 503\u003c\/p\u003e \u003cp\u003e11.2.11 Luria–Delbrück Distribution 505\u003c\/p\u003e \u003cp\u003e11.2.12 Naor’s Distribution 507\u003c\/p\u003e \u003cp\u003e11.2.13 Partial-Sums Distributions 508\u003c\/p\u003e \u003cp\u003e11.2.14 Queueing Theory Distributions 512\u003c\/p\u003e \u003cp\u003e11.2.15 Reliability and Survival Distributions 514\u003c\/p\u003e \u003cp\u003e11.2.16 Skellam–Haldane Gene Frequency Distribution 519\u003c\/p\u003e \u003cp\u003e11.2.17 Steyn’s Two-Parameter Power Series Distributions 521\u003c\/p\u003e \u003cp\u003e11.2.18 Univariate Multinomial-Type Distributions 522\u003c\/p\u003e \u003cp\u003e11.2.19 Urn Models with Stochastic Replacements 524\u003c\/p\u003e \u003cp\u003e11.2.20 Zipf-Related Distributions 526\u003c\/p\u003e \u003cp\u003e11.2.21 Haight’s Zeta Distributions 533\u003c\/p\u003e \u003cp\u003eBibliography 535\u003c\/p\u003e \u003cp\u003eAbbreviations 631\u003c\/p\u003e \u003cp\u003eIndex 633\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":51037069672791,"sku":"9780471272465","price":206.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471272465.jpg?v=1750934252","url":"https:\/\/bookcurl.com\/products\/univariate-discrete-distributions-9780471272465","provider":"Book Curl","version":"1.0","type":"link"}